5. If a man travel 240 mls. 5. If a man travel 240 mls. in 12 days, when the days are in 12 days, when the days are 12 hours long, how far can he 12 hours long, how far can he travel in 27 days, when the travel in 27 days, when the days are 16 hours long? days are 16 hours long?

Operation.

Operation.

How far?|27 days 9 Days 12 16 hours 4 4hours 12 240 miles 20

720 miles, Ans.

In Compound Proportion, the terms in the supposition and demand may be distinguished by cause and effect, or producing and produced terms. That which causes any thing, or produces an effect, as men, time, length, breadth, depth, &c., may be denominated a producing term. Thus, in the foregoing question, among the terms of supposition, one man, 12 days, 12 hours long, are the joint cause, or producing terms, and miles the effect, or produced term. Among the terms of demand, 27 days, 16 hours long, are the joint cause, or the producing terms, and the rods required are the effect, or the produced term. In all questions in Proportion the answer required will be either cause or effect, (a producing or produced term.) Hence the RULE.

When the term required is a produced term,

Draw a perpendicular line, and place the terms of demand, QUESTIONS. 1. What is meant by producing and produced terms. 2. Rule, when the term required is a produced term?

or those numbers which follow "HOW," &c., on the right of the line, and those which follow "IF," on the left, as in the Rule of Three Direct, closing the statement, in all cases, with that number which is of the same kind with the answer sought, and proceed to cancel, as before instructed. NOTE. All questions under the foregoing head will be found to be in Direct Proportion.

6. If 4 students spend £19 in 3 months, how many £ will 8 students spend in 9 months?

Producing terms of the supposition.

How many
Students
(Months 3

}

Answer, £114.

Operation.
8 students. Producing terms
49 months. of the demand.
Produced term of the
supposition.

19€.

[114£, Answer.

7. If 7 men can reap 84 acres in 12 days, 12 hours long, how many acres can 20 men reap in 5 days, 14 hours long? Answer, 116 acres. 8. If 8 reapers receive 3 £. 4 s. for 4 days' work, how much ought 20 reapers to receive for 15 days' work?

Answer, 30£. 9. If 3 men receive 8.9£ for 19.5 days' labor, how much ought 20 men to receive for 100.25 days' labor?

Answer, 305 £. 0 s. 8 d. 1 qr. 10. If 20 cwt. may be carried 80 miles for $35, how much will it cost to transport 40 cwt. 100 miles?

Answer, $87.

11. If the freight of 9 hhds. of sugar, each weighing 12 cwt., 20 leagues, cost 16. what must be paid for the freight of 50 tierces, each weighing 24 cwt., 100 leagues?

NOTE. Hundred weight and distance are the producing terms, and the money received, the produced term.

12. If 21 yards of cloth, 13 yard wide, cost 33£, how much will 36 yards, 1 yard wide, cost?

Answer, 543£. 13. If 24 bushels of wheat be consumed by 8 persons in 5 months, how many persons will consume 36 bushels in 15 months?

Operation.

How many persons? 36 bushels 4.

3 bushels 24 5 months.

3 men 158 persons.

4 persons, Answer.

It is evident, if 24 bushels are consumed by 8 persons in 5 months, that 1 person would consume 1 of 24=3, and in 1 month g of a bushel, and in 15 months X15= 45-9 bushels. Then 36-9-4 persons, the answer. It will be observed, that the answer required is a producing term; and, also, that the product of the 36 bushels, the produced term in the demand, and 8 persons, 5 months, the producing terms in the supposition, are divided by the product of 24 bushels and 15 persons, the produced and producing terms in the supposition. Hence the RULE :

When the term required is a producing term,

Draw a perpendicular line, and place the produced term of the demand and the producing terms of the supposition on the right, and the remaining terms on the left of the line, and proceed as before.

NOTE. The above will be found to correspond with Inverse Proportion, and may be applied to both Simple and Compound.

14. If 6 men build a wall, 20 feet long, 6 feet high, and 4 feet thick, in 16 days, working 12 hours in a day, in how many days will 24 men build a wall 200 feet long, 8 feet high, and 6 feet thick, working 10 hours in a day?

Answer, 96 days.

Produced term of demand.

6

6

supposition.

Producing terms of supposition.

96 days, Answer.

15. If 3 men, in 24 days, 9 hours long, can dig 328 rods of trench, 6 feet wide and 4 feet deep, how many men will it take to dig a trench 984 rods long, 9 feet wide and 8 feet deep, in 27 days, when the days are 12 hours long? Answer, 18 men.

16. If a man can travel 240 miles in 16 days, when the days are 14 hours long, how many days will it take him to travel 720 miles, when the days are 12 hours long? Answer, 56 days.

QUESTION. 3. Rule, when the term required is a producing term?

17. If 98 lbs. of bread be sufficient to serve 7 men 14 days, how many days will 63 lbs. serve 21 men? Answer, 3 days.

18. If 40 men in 15 days, 12 hours long, build a wall 200 feet long, 12 feet high and 5 feet thick, how many hours long must the day be, that 20 men, in 12 days, may build a wall 100 feet long, 10 feet high and 6 feet thick? Answer, 15 hours.

19. If 20 men in 12 days, 15 hours long, can build a wall 100 feet long, 10 feet high and 6 feet thick, in how many days, of 12 hours long, can 40 men build a wall 200 feet long, 12 feet high and 5 feet thick?

Answer, 15 days. 20. If 16 compositors set 150 pages of types, each page consisting of 48 lines, and each line of 50 letters, in 8 days, 10 hours long, how many compositors will be required to set 500 pages of 72 lines in 6 days, 8 hours long?

each, and 45 letters in a line, Answer, 120 compositors.

SUPPLEMENT

TO THE

RULES OF PROPORTION.

EXAMPLES.

1. If I can hire 30 horses pastured 7 weeks for 6€, how many weeks may 5 horses be pastured for 4£ 5 s. 84 d.? Answer, 30 weeks.

2. If 8 men build 48 rods of fence in 1 day, how many rods will 24 men build in the same time?

Answer, 144 rods. 3. If 24 men build 144 rods of fence in 1 day, how many rods will 8 men build in the same time? Answer, 48 rods. 4. How many men will it require to build 144 rods of fence in 1 day, if 8 men build 48 rods in the same time? Answer, 24 men. 5. If 20 men build a mill in 160 days, in how many days could 25 men build the same mill?

Answer, 128 days. 6. If 25 men build a mill in 128 days, how many men will build the same mill in 160 days? Answer, 20 men.

7. How many cords of wood may be bought for 40£, if 2 cords cost $6? Answer 53 cords.

8. How many bushels of wheat may be bought for 40£, if 1 bushel of wheat be worth 2 bushels of rye, and 4 bushels of rye be worth 5 bushels of corn, and 8 bushels of corn be worth 16 bushels of oats, and 1 bushel of oats be worth 2 shillings? Answer, 80 bushels.

9. If 18 cords of oak wood be worth 263 cords of hemlock, and a cord of hemlock 142 shillings, how much will 4 cords of oak cost in cents, and how many guineas? Answer, 33 guineas. ( 1600 cents.

10. How many stoves may be bought for 672 shillings, if 8 fire-frames are worth 33 stoves, and 16 fire-frames are worth 32 guineas? Answer, 5 stoves. 11. How much will $450 gain in a year, if 100 in the same time gain $8?

Answer, $36. 12. A merchant owning of a vessel, sold ğ of his share for $934. What was the value of the ship?

Answer, $3736. 13. How many guineas will 8 yards of cloth cost, if of a yard cost § of a dollar? Answer, 12 guinea. 14. If of a pound of sugar cost of a shilling, what will of a pound cost? Answer, 4 d. 31957 qr. 15. If 2 lbs. of tobacco cost 4 s. 6 d., 180 lbs. cost in dollars?

23

how much will Answer, $54. 16. If when wheat is 4 s. 6 d. per bushel, the penny loaf weigh 12 oz., what ought it to weigh when wheat is $.50 per bushel?

Answer, 18 oz. 17. How many yards of cloth, & yd. wide, are equal in measure to 30 yds. 11 yard in width? Answer, 60 yds. 18. If 40 bushels of grain will pay a debt when the price is 60 cents per bushel, how many bushels will it take when the price is $1.20 ? Answer, 20 bushels. 19. How far may 30 cwt. be transported for $8, if 21 cwt. be carried 180 miles for the same money ? Answer, 15 miles. '20. How many yards, of yd. wide, will it take to line 850 suits of clothes, each suit to contain 3 yards of cloth, 1 yd. in width? Answer, 6941 yds. 2 qrs. 23 nails. 21. If 30 horses consume 600 bushels of oats in 8 months, how much will each horse consume per day?

Answer, 2 quarts.