ANALYSIS.-In this example an element of the second effect is required, viz: the length of the wall, and the question may be read thus: If 32 men, in 4 days, working 12 hours a day, can build a wall 36 feet long, 8 feet high, and 4 feet thick, 48 men in 36 days, working 9 hours a day, can build a wall how many (or x) feet long, 6 feet high, and 3 feet thick?

Or, 32 × 4 × 12 : 48 × 36 × 9 : : 36x8x4 : xx6x3. 239. Hence, we have the following

RULE.-I. Arrange the terms in the statement so that the causes shall compose one couplet, and the effects the other, putting x in the place of the required element:

II. Then if x fall in one of the extremes, make the product of the means a dividend, and the product of the extremes a divisor; but if x fall in one of the means, make the product of the extremes a dividend, and the product of the means a divisor.

EXAMPLES.

1. If I pay $24 for the transportation of 96 barrels of flour 200 miles, what must I pay for the transportation of 480 barrels 75 miles?

2. If 12 ounces of wool be sufficient to make 1 yards of cloth 6 quarters wide, what number of pounds will be required to make 450 yards of flannel 4 quarters wide?

3. What will be the wages of 9 men for 11 days, if the wages of 6 men for 14 days be $84 ?

4. How long would 406 bushels of oats last 7 horses, if 154 bushels serve 14 horses 44 days?

5. If a man travel 217 miles in 7 days, travelling 6 hours day, how far would he travel in 9 days if he travelled 11 hours a day?

239. What is the rule for finding the unknown part?

6. If 27 men can mow 20 acres of grass in 5 days, working 33 hours a day, how many acres can 10 men mow in 41⁄2 days, by working 8 hours a day?

7. How long will it take 5 men to earn $11250, if 25 men can earn $6250 in 2 years?

8. If 15 weavers, by working 10 hours a day for 10 days, can make 250 yards of cloth, how many must work 9 hours a day for 15 days to make 607 yards?

9. A regiment of 100 men drank 20 dollars' worth of wine at 30 cents a bottle how many men, drinking at the same rate, will require 12 dollars' worth at 25 cents a bottle?

10. If a footman travel 341 miles in 7 days, travelling 12 hours each day, in how many days, travelling 10 hours a day, will he travel 155 miles?

11. If 25 persons consume 300 bushels of corn in 1 year, how much will 139 persons consume in 8 months, at the same rate?

12. How much hay will 32 horses eat in 120 days, if 96 horses eat 3 tons in 7 weeks?

13. If $2.45 will pay for painting a surface 21 feet long and 13 feet wide, what length of surface that is 10% feet wide, can be painted for $31.72?

14. How many pounds of thread will it require to make 60 yards of 3 quarters wide, if 7 pounds make 14 yards 6 quarters wide?

15. If 500 copies of a book, containing 210 pages, require 12 reams of paper, how much paper will be required to print 1200 copies of a book of 280 pages?

16. If a cistern 17 feet long, 10 feet wide, and 13 feet deep, hold 546 barrels of water, how many barrels will a cistern 12 feet long, 10 feet wide, and 7 feet deep, contain?

17. A contractor agreed to build 24 miles of railroad in 8 At the months, and for this purpose employed 150 men. end of 5 months but 10 miles of the road were built: how many more men must be employed to finish the road in the time agreed upon?

18. If 336 men, in 5 days of 10 hours each, can dig a trench of 5 degrees of hardness, 70 yards long 3 wide and 2 deep: what length of trench of 6 degrees of hardness, 5 yards wide and 3 yards deep, may be dug by 240 men in 9 days of 12 hours each?

PARTNERSHIP.

240. PARTNERSHIP is the joining together of two or more persons in trade, with an agreement to share the profits or losses.

PARTNERS are those who are united together in carrying on business.

CAPITAL, is the amount of money or property employed: DIVIDEND is the gain or profit:

Loss is the opposite of profit:

241. The Capital or Stock is the cause of the entire profit: Each man's capital is the cause of his profit:

The entire profit or loss is the effect of the whole capital : Each man's profit or loss is the effect of his capital: hence,

Whole Stock: Each man's Stock

:: Whole profit or loss: Each man's profit or loss.

EXAMPLES.

1. A and B buy certain goods amounting to 160 dollars, of which A pays 90 dollars and B, 70; they gain 32 dollars by the purchase: what is each one's share?

240. What is a partnership? What are partners? What is capital or stock? What is dividend? What is loss?

241. What is the cause of the profit? What is the cause of each man's profit? What is the effect of the whole capital? What is the effect of each man's capital? What proportion exists between causes and their effects? What is the rule?

Hence, the following

RULE. As the whole stock is to each man's share, so is the whole gain or loss to each man's share of the guin or loss.

EXAMPLES.

1. A and B have a joint stock of $2100, of which A owns $1800 and B $300; they gain in a year $1000: what is each one's share of the profits?

2. A, B and C fit out a ship for Liverpool. A contributes $3200, B $5000, and C $4500; the profits of the voyage amount to $1905: what is the portion of each?

3. Mr. Wilson agrees to put in 5 dollars as often as Mr. Jones puts in 7; after raising their capital in this way, they trade for 1 year and find their profits to be $3600: what is the share of each?

4. A, B and C make up a capital of $20,000; B and C each contribute twice as much as A; but A is to receive onethird of the profits for extra services; at the end of the year they have gained $4000: what is each to receive?

5. A, B and C agree to build a railroad and contribute $18000 of capital, of which B pays 2 dollars, and C, 3 dollars as often as A pays 1 dollar; they lose $2400 by the operation: what is the loss of each?

COMPOUND PARTNERSHIP.

242. When the causes of profit or loss are compound.

When the partners employ their capital for different periods of time, each cause of profit or loss is compound, being made up of the two elements of capital and time. The product of these elements, in each particular case, will be the cause of each man's gain or loss; and their sum will be the cause of the entire gain or loss: hence, to find each share,

Multiply each man' stock by the time he continued it in trade; then say, as the sum of the products is to each product, so is the whole gain or loss to each man's share of the gain or loss.

242. When is the cause of profit or loss compound? What are the elements of the compound caus? What is the rule in this case?

EXAMPLES.

1. A and B entered into partnership. A put in $840 for 4 months, and B, $650 for 6 months; they gained $363: what

is each one's share?

2. A puts in trade $550 for 7 months and B puts in $1625 for 8 months; they make a profit of $337: what is the share of each?

3. A and B hires a pasture, for which they agreed to pay $92.50. A pastures 12 horses for 9 weeks and B 11 horses for 7 weeks what portion must each pay?

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4. Four traders form a company. A puts in $400 for 5 months; B $600 for 7 months; C $960 for 8 months; D $1200 for 9 months. In the course of trade they lost $750; how much falls to the share of each?

5. A, B and C contribute to a capital of $15000 in the following manner: every time A puts in 3 dollars B puts in $5 and C, $7. A's capital remains in trade 1 year; B's 13 years; and C's 23 years; at the end of the time there is a profit of $15000: what is the share of each?

6. A commenced business January 1st, with a capital of $3400. April 1st, he took B into partnership, with a capital of $2600; at the expiration of the year they had gained $750 what is each one's share of the gain?

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7. James Fuller, John Brown and William Dexter formed a partnership, under the firm of Fuller, Brown & Co., with a capital of $20000; of which Fuller furnished $6000, Brown $5000, and Dexter $9000. At the expiration of 4 months, Fuller furnished $2000 more; at the expiration of 6 months, Brown furnished $2500 more; and at the end of a year Dexter withdrew $2000. At the expiration of one year and a half, they found their profits amounted to $5400: what was each partner's share?