7. Sold a repeating watch for 175 dollars, and by so doing lost 17 per cent. whereas I ought in dealing to have cleared 20 per cent. how much was it sold for under the just value? Ans. 231. 8s. od.

FELLOWSHIP.

FELLOWSHIP is a general rule, by which merchants, &c. trading in company, with a joint stock, determine each person's particular share of the. gain or loss in proportion to his share in the joint stock.

By this rule a bankrupt's estate may be divided among his creditors; as also legacies adjusted, when there is a deficiency of assets or effects.

for

SINGLE FELLOWSHIP.

Single Fellowship is when different stocks are employed certain equal time.

any

RULE.*

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

METHOD OF PROOF.

Add all the shares together, and the sum will be equal to the gain or loss, when the question is right.

EXAMPLES.

*That the gain or loss, in this rule, is in proportion to their stocks is evident: for, as the times the stocks are in trade are equal, if I put in of the whole stock, I ought to have of the whole gain; if my part of the whole stock be, my share of the whole gain or loss ought to be also. And, generally, if I put in of the stock, I ought to have part of the whole gain or loss; that is, the same ratio, that the whole stock has to the whole gain or loss, must each person's particular stock have to his particular gain or loss.

EXAMPLES.

1. Two persons trade together; A put into stock 130l. and B 2201. and they gained 5ool. what is each person's

1851. 14s. 31d. A's share. 3141. 5s. 8d. B's share.

ΤΟ

gool. os. od. the Proof.

2. A and B have gained by trading 1821. A put into stock 300l. and B 400l. what is each person's share of the profit ? Ans. A 781. and B 104l.

3. Divide 120l. between three shares shall be to each other as 1, 2

persons, so that their and 3, respectively. Ans. 201. 40l. and 60l.

4. Three persons make a joint stock; A put in 1841. 10s. B 961. 15s. and C 761. 5s. they trade and gain 220l. 12s. what is each person's share of the gain?

688

I 2

Ans. A 1131. 16s. 13, B 591. 145.75 C471. 18.75 5. Three merchants A, B and C, freight a ship with 340 tuns of wine; A loaded 110 tuns, B 97, and C the rest. In a storm the seamen were obliged to throw 85 tuns overboard; how much must each sustain of the loss?

A 27, B 24, and C 334

6. A ship worth 860l. being entirely lost, of which belonged to A, to B, and the rest to C; what loss will each sustain, supposing 500l. of her to be insured?

Ans. A 451. B 90l. and C 2251.

7. A bankrupt is indebted to A 2751. 148. to B 3041. 78. to C 1521. and to D 104l. 6s. His estate is worth only 6751. 155. how must it be divided ?.

Ans. A 2221. 15s. 2d. B 245l. 18s. 1d.

C 1221. 165. 2 d. and D 841. 5s. 5d.

8. A and B, venturing equal sums of money, clear by joint trade 1541. By agreement A was to have 8 per cent. because he spent his time in the execution of the project, and B was to have only 5 per cent. ; what was A allowed for his trouble? Ans. 351. 10s. 93d.

DOUBLE FELLOWSHIP.

Double Fellowship is when different or equal stocks are employed for different times.

S

RULE.

RULE.*

Multiply each man's stock into the time of its continuance, then say,

As the total sum of all the products is to the whole gain or loss,

So is each man's particular product to his particular share of the gain or loss.

EXAMPLES.

1. A and B hold a piece of ground in common, for which they are to pay 361. A put in 23 oxen for 27 days, and B 21 oxen for 35 days; what part of the rent ought each man to pay ?

:: 621:

621

36

* Mr. MALCOLM, Mr. WARD, and several other authors, have given an analytical investigation of this rule but the most general

:

and

2. Three graziers hired a piece of land for 6ol. 1os. A

put in 5 sheep for 4

and C put in 9 for 6 of the rent?

months, B put in 8 for 5 months, months: how much must each pay Ans. A 111. 5s. B 20l. and C 291. 5s..

3. Two merchants enter into partnership for 18 months; A put into stock at first 200l. and at the end of 8 months he put in 100l. more; B put in at first 550l. and at the end of 4 months took out 140l. Now at the expiration of the

time

and elegant method, perhaps, is that, which Dr. HUTTON has given in his Arithmetic, viz.

When the times are equal, the shares of the gain or loss are evidently as the stocks, as in Single Fellowship; and when the stocks are equal the shares are as the times; wherefore, when neither are equal, the shares must be as their products.