128. How many men, by working 12 hours a day, will accomplish as much work in 24 days, as 16 men can accomplish in 36 days, by working 10 hours a day?

129. If 2500 slates, each 8 inches long and 5 inches wide, will cover a roof, how many will be required that are 6 inches long and 4 inches wide?

130. If 3 compositors set 15 pages of type in 138 hours, how many will be required to set 693 pages of the same work in 6 hours?

131. If 12 oxen eat 73 tons of hay in 22 weeks, how many oxen will eat 133 tons in 43,3⁄4 weeks?

132. If 18 men, in 9 months, consume flour worth $78.75, when wheat is $1.12 per bushel, how many months will $145 supply 35 men with flour, when wheat is $1.00 per bushel?

133. If a cellar 22.5ft. long, 17.3ft. wide, and 10.25ft. deep, be dug in 2.5 days by 6 men, working 12.3 hours a day, in how many days of 8.2 hours, would 9 men dig a cellar 56.25ft. long, 25.95ft. wide, and 16.4ft. deep?

134. If 36 men, in 1271⁄2 days of 131⁄2 hours, dig a trench 333yd. long, 10 ft. deep, and 153 ft. wide, how many men, in 7 days of 12 hours, will dig a similar trench 8281yd. long, 7 ft. deep, and 10ft. wide?

135. If 19 men, in 713 days of 103 hours, dig a trench 41 yd. long, 57 ft. deep, and 74 ft. wide, how long a trench that is 83 ft. deep and 4 ft. wide, will 11 men dig in 291 days of 47 hours?

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136. How many days of 81⁄2 hours will 42 men require, to build a wall 983 ft. long, 71⁄2 ft. high, and 2 ft. thick, if 63 men can build a wall 45 ft. long, 6 ft. high, and 3 ft. thick, in 68 days of 11 hours?

137. If 100 pounds at Rochelle equal 1067b. at Leipsic, 1187b. at Leipsic equal 1631b. at Leghorn, 1377b. at Leghorn equal 100lb. at Seville, 101lb. at Seville equal 15817b. at Venice, 140lb. at Venice equal 831b, at Franckfort, and 894lb. at Franckfort equal 100lb. Avoirdupois, how many lb. Avoirdupois equal 350lb. at Rochelle?

138. If 750 tiles, each 10in. long and Sin. wide, will pave an area 12 ft. wide, how many tiles that are 16in.

long and 9in. wide, will pave an area of twice the length and 15 ft. wide?

139. If $3281 support a family of 16 persons 94 months, each person consuming 44lb. per day, how much would support a family of 28 persons 7 months, each consuming 51lb. per day?

CHAPTER XII.

FELLOWSHIP.

By the rule of Fellowship, we determine the gain or loss of partners in trade or joint adventures, the worth of debts in bankruptcy, &c.

The whole gain or loss should evidently be distributed among the stockholders, in proportion to each man's share: hence we have the following

RULE.

Divide the whole gain or loss by the whole stock, for the gain or loss of one dollar, and multiply the quotient reduced to its lowest terms, by each man's share.

1. A., B. and C. entered into partnership. A. contributed $500, B. $300, and C. $600. At the end of a year they had gained $350. What was the share of each?

2. The debts of a bankrupt amount to $1275, and his whole property is worth but $950. What proportion of the whole can he pay, and what is the value of a debt of $361.25?

3. A vessel during a storm sustained a damage of $1950. How much of the loss should be sustained by A., whose share of the cargo was $1000, the whole value of the vessel and cargo being $21500?

4. William Johnson, Samuel Buffum, and Moses Clark, entered into partnership. Johnson contributed $4750, Buffum $5250, and Clark $6000. At the end of three years they had lost $2500. What was the loss of each?

5. A., B. and C. traded in company; A. put in $3000, B. $2000, and C. the remainder. They gained $1500, of

which C. took $500.

What did C. contribute, and what

was A.'s share of the gain?

6. The property of a bankrupt is worth but $5163.90, and he owes A. $1765.75, B. $840.00, C. $2329.50, and D. $1380.10. How much will each creditor receive?

7. A. contributed $380 to an adventure, B. $420, C. $500, and D. $700. What was each man's share of the gain, which was $900?

The use of $500 for 3 months, is worth as much as the use of $1500 for 1 month. Therefore, when the stock of the several partners is employed for unequal times, multiply each stock by the time it is employed, and work with the products as with the original stocks in the general rule.

8. In a certain firm A. contributes $5000 for 4 months, B. $6000 for 3 months, C. $2000 for 6 months, D. $4000 for 5 months, and E. $5000 for 2 months. How should the gain, which was $1680, be divided among the partners?

9. A. and B. form a limited partnership for 2 years and 6 months. A. at first contributed $2000, and in 13 months $1000 more. B. contributed at first $2500, and at the end of the first year $600 more, but at the end of 19 months he withdrew $2000. At the end of 14 months, C. was admitted to the firm, and contributed $3700. How should the gain, which was $3000, be divided?

10. A. and B. traded in company. A. contributed at first $800, and B. $1000. At the end of 3 months A. advances $1200 more. What sum must B. add to the firm at the end of 6 months, to entitle him to one-half of the year's profits?

11. The amount of the legacies bequeathed in a will was $35000, but the whole amount of the testator's property was found to be only $31500. What was the value of the wife's legacy, which was $10000, and of the eldest son's, which was $15000?

12. A., B. and C. form a joint stock of $1098, by which they gain $234. A.'s money is in trade 4 months, B.'s 5 months, and C.'s 13 months, and their shares of the gain

are as the numbers 2, 3 and 4, respectively. What was euch man's stock and gain?

13. A privateer captured a prize valued at $15000, which the crew agree to divide in proportion to their pay, and the time each has been on board; the officers and midshipmen have been on board 4 months, and the sailors 3 months; the pay of the officers is $20 a month, of the midshipmen $15, and of the sailors $12, and there are 3 officers, 6 midshipmen, and 40 sailors. How much does each receive?

14. Three men hire a pasture for $40. A. put in 4 horses for 3 months and 6 for 2 months, B. put in 5 for 4 months and 10 for 1 month, and C. put in 7 for 4 months and 3 for 2 months. How much ought each to pay?

15. A man failing in trade owed $75000, to meet which he had property valued at $14500. How much can he pay A., who is a creditor for $10000, B., who is a creditor for $3750, and C., who is a creditor for $12362.50 ?

16. A. commenced business with a capital of $2500. Five months afterwards he received B. as a partner, who added $4000 to the stock. Six months after B. was admitted, C. joined the firm with a capital of $6000. Two years from the commencement, they had gained $8000. What was each man's share of the gain?

17. It is required to divide $36000 among 4. persons, in such manner that the second may have twice as much as the first, the third as much as the first and second, and the fourth three times as much as the third?

18. A legacy of $40000 was left to four heirs, in the proportion of to the first, to the second, to the third, and to the fourth. What was the share of each?

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19. A levy of 1200 horses is to be distributed among three regiments in the proportion of 1, and, respectively. How many will each regiment receive?

20. Five men hire a pasture for $294. A. put in 10 cows for 3 months; B. put in 5 cows for 2 months; C. put in 8 cows for 1 months; D. put în 16 months; and E. put in 20 cows for 4 months. ought each to pay?

cows for 21

How much

21. A bankrupt owes $150000, to pay which he has the following property real estate worth $17500, merchandise worth $3750, personal property worth $20000, and sums due from various individuals amounting to $100000. If he collects all his dues, how much can he pay on every dollar of his debts?

22. A., B. and C. purchase a house for $10000, A. contributing $4000, B. $3600, and C. $2400. The house rents for $800, and the taxes and repairs amount to $50 a year. What income does each of the owners derive from the estate, and what per cent. of his investment?

23. Divide 7500 into 5 parts, in the proportions of, ,,, and .

24. In the distribution of a bankrupt's property, $763. 50 was divided among four of his creditors. A.'s bill was $250, B's. $300, C.'s $325, and D.'s $362.50. How much did each receive?

25. Four men were joint owners of a farm, their shares being in the proportion of 6, 2, 5, and 3, respectively. It is required to divide the annual rent, which is $1500, equitably among them.

CHAPTER XIII.

ALLIGATION.

When the values of a variety of ingredients are given, and it is desired to make a mixture of any fixed value, the quantity of each ingredient to be employed is determined by ALLIGATION.

When there is no limitation in the quantity of either ingredient, we may make the desired mixture by the following

RULE.

Having written the values of the ingredients in a perpendicular column, connect by a line each value that is less than the required average with one or more that is greater, and each value that is greater with one or more that is less.

Write the difference between each value and the average, op