er, place the least of the other terms for the first, but if less place the greater for the first term, and the remaining one for the second.

Multiply the second and third terms together, and divide the product by the first; the quotient will be the answer required.

EXAMPLES.

1. If 30 horses plow 12 acres, how many will 40 horses plow in the same time?

2. If 30 horses plow 12 acres in 10 days, in how many days will 40 horses plow the same quantity?

3. If 800 soldiers in a garrison have provisions sufficient for 2 months; how many must depart that the provisions may last them for 5 months? Ans. 480.

4. Bought a hogshead of Madeira wine for 119 dollars, nine gallons of which leaked out; what was the remainder sold at per gallon, to gain 12 dollars on the whole? ̧·

Ans. 2 dolls. 42+ cts. 5. If 225 pounds be carried 512 miles for 20 dollars, how many pounds may be carried 64 miles for the same money? Ans. 1800lb. 6. If 87 dolls. 50 cents be assessed on 1750 dolls. what is the tax of 10 dolls. at the same rate? Ans. 50 cts.

Promiscuous Questions in Direct and Inverse Proportion.

1. Suppose a man travels to market with his wagon loaded, at the rate of 21⁄2 miles an hour, and returns with it empty at the rate of 34 miles an hour; how long will he be in performing a journey, going and returning, to a place 123 miles distant? Ans. 8413 hours.

2. A lent B 1000 dollars for 189 days, without interest how long should B lend A 650 dollars to requite the favor? Ans. 29019 days.

3. Bought 14 casks of butter, each weighing 1cwt. 1qr. 4lb. at 12 dollars 60 cents per cwt.; what did they come to, and how much per lb.?

Ans. 226 dolls. 80 cts. whole cost; 11 cts 24 m. per lb.

4. Sold 4 chests of tea, each weighing 1cwt. Oqr. 14lb. the first for 80 cents per lb. the second for 90 cents, the third for 1 doll. 5 cents, and the fourth for 1 doll. 25 cents; how many pounds of tea were there, what was the average price, and what did the whole come to?

Ans. 504lb.-average 1 doll.-come to 504 dolls. 5. When flour is sold at 2 dolls. 24 cents per cwt. what will be the first cost of one dozen of rolls, each weighing 5oz. allowing the bread to be in proportion to the flour, as five is to four? Ans. 6 cents.

6. If a merchant bought 270 barrels of cider for 780 dollars, and paid for freight 37 dolls. 70 cents, and for other charges and duties 30 dolls. 60 cents; at what must he sell it per barrel to gain 143 dolls. Ans. 3 dolls. 674 cts. 7. If half a ton of hay was equally divided among 80 horses, how much must be given to 7 ? Ans. 3qr. 14lb.

8. Suppose the circumference of one of the larger wheels of a wagon to be 12 feet, and that of one of the smaller wheels 9 feet 3 inches; in how many miles will the smaller wheel make 1000 revolutions more than the larger?

Ans. 7 m. 5 fur. 34 yds. 1 ft. 77 in.

9. If a man perform a journey in 18 days, when the days are 15 hours long, how many days will it require to perform the same journey when the days are only 12 hours long? Ans. 224 days.

10. A merchant bought a piece of broadcloth measuring 42 yds. for 191. dolls. 25 cents; 15 yards of this being damaged, he sells it at two-thirds of its cost; the residue he is willing to sell so as to gain 1 doll. per yard on the whole piece; at what rate must he sell the remainder?

Ans. 6 dolls. 86,4 cents per yd. 11. If 60 yards of carpeting will cover a floor that is 30 feet long and 18 broad, what is the width of the carpeting? Ans. 3 feet.

12. If a piece of land be 40 rods in length, how wide must it be to contain 4 acres?

Ans. 16 rods.

13. Suppose a large wheel, in mill work, to contain 70 cogs, and a smaller wheel, working in it, to contain 52 cogs; in how many revolutions of the greater wheel, will the lesser one gain 100 revolutions? Ans. 2888.

14. The number of pulsations in a healthy person is, say 70 in a minute, and the velocity of sound through the air is found to be 1142 feet in a second: now I counted 20 pulsations between the time of observing a flash of lightning from a thunder cloud, and hearing the explosion of the thunder; what was the distance of the cloud?

Ans. 3 m. 5 fur. 145 yds. 24 ft.

15. A merchant bought 5 pieces of cloth, of different qualities, but of equal lengths, at the rate of 5, 4, 3, 2, and 1 doll. per yd. for the different pieces; the whole came to 532 dolls. 50 cents; how many yards did each piece contain? Ans. 35 yds.

16. What principal will gain as much in 1 month, as 127 dollars would gain in 12 months? Ans. 1524 dolls.

17. If a pair of steelyards be 36 inches in length to the centre of motion, the pea 5 lb. and the draught end inch in length, what weight will they draw? Ans. 360 lb. 18. Supposing the above steelyards would only draw 90 b., what is the length of the draught end?

Ans. 2 inches. 19. If 1 yard of cloth cost 2 dolls. 71 cts. 14 mills, what will 67 yards come to at the same rate?

Ans. 183 dolls. 4 c. 6 m. 20. If a man's income be 16s. 5d. 1qr. per day, what

is it per annum?

Ans. 3001.

21. How many pieces of wall paper that is 3 qrs. wide and 11 yards long, will it require to paper the walls of a room that is 25 feet long, 15 wide, and 10 reduction of for doors and windows?

high, allowing a Ans. 10

22. The length of a wall being tried by a measuring line, appears to be 1287 feet 4 inches; but on examination the line is found to be 50 feet 10 inches in length, instead of 50 feet its supposed length; required the true length of the wall? Ans. 1309 feet 1017 inch.

23. If a dealer in liquors use, instead of a gallon, a measure which is deficient by half a pint, what will be the true measure of 100 of these false gallons? Ans. 93 galls.

SECTION 3.

THE DOUBLE RULE OF THREE.

THE DOUBLE RULE OF THREE, or as it is often called, Compound Proportion, is used for solving such questions as have five terms given to find a sixth. In all questions belonging to this rule, the three first terms must be a supposi tion, the two last a demand.

RULE FOR STATING.

1. Set the two terms of the supposition, one under the other.

2. Place the term of the same kind with the answer sought in the second place.

3. Set the terms of the demand, in the third place, ob serving to place the correspondent terms of the supposition and demand in the same line. Consider the upper and lower extremes, with the middle terms, separately, as in the single rule of three; if both lines are direct, then the question will be in direct proportion; but if either lines are inverse, then will the question be in inverse proportion.

When the question is in direct proportion, multiply the product of the two last terms by the middle term for a dividend, and multiply the two first terms for a divisor; the quotient will be the answer in the same name with the middle term.

But if the proportion be inverse, transpose the inverse terms and proceed in the same manner as in direct proportion.

DIRECT PROPORTION.

EXAMPLE.

1. It 6 men in 8 days earn 100 dollars, how much will 12 men earn in 24 days?

2. If 10 bushels of oats suffice 18 horses for 20 days, how many bushels will serve 60 horses 36 days?

3. If 56 pounds of bread will suffice 7 nuch bread wili serve 21 men 3 days?

Ans. 60 bushels. men 14 days, how Ans. 36 pounds.

4. If 8 students spend 384 dollars in 6 months, how much will maintain 12 students 10 months? Ans. 960 dollars. 5. If 20 hundred weight is carried 50 miles for 25 dollars, how much must be given for the carriage of 40 hundred weight 100 miles? Ans. 100 dollars.

6. If 14 dollars interest is gained by 700 dollars in 6 months, what will be the interest of 400 dollars for 5 years? Ans. 80 dollars. 7. If 4 men can do 12 rods cf ditching in 6 days, how many rods may be done by 8 men in 24 days?

INVERSE PROPORTION.

EXAMPLE.

Ans. 96 rods.

1. If 4 dollars pay 8 men for 3 days, how many days must 20 men work for 40 dollars?

Here the lower line is inverse, which transposed will stand

2. If 4 men are paid 24 dollars for 3 days work, how many days may 16 men be employed for 384 dollars?

Ans. 12 days.

3. If 4 men are paid 24 dollars for 3 days work, how many men may be employed 16 days for 96 dollars?

Ans. 3 men.