1. Suppose a merchant has effects at Amsterdam to the amount of $3530, which he can remit by way of Lisbon at 840 rees per dollar, and thence to Boston, at 8s. 1d. per milree (or 1000 rees :) Or, by way of Nantz, at 53 livres per dollar, and thence to Boston at 6s. 3d. per crown; It is required to arbitrate these exchanges, that is, to choose that which is most advantageous?

1 dollar at Amsterdam
1000 rees at Lisbon

840×97×3530
1000×1

840 rees at Lisbon.

= 97d. at Boston.

3530 dollars at Amsterdam.

£1198 8s. 8d. by way of Lisbon.

1 dollar at Amsterdam

6 livres at Nantz

*5 × 80 × 3530
1X6

= £1059 by way of Nantz.

Here it may be observed that the difference is £139 8s. 8,4d. in favour of remitting by way of Lisbon rather than by Nantz, which depends on the course of exchange, at that time; but the course may vary so, that, in a short time by way of Nantz may be better; hence appears the necessity and advantage of an extensive correspondence, to acquire a thorough knowledge in the courses of exchange, to make this kind of remittance.

2. A merchant in England can draw directly for 1000 piastres in Leghorn at 50d. sterling per piastre; but he chooses to remit the sum to Cadiz at 19 piastres for 7000 maravedies; thence to Amsterdam at 189d. Flemish for 680 maravedies; and thence to Liverpool at 9d. Flemish for 5d. sterling: what is gained by this circular remittance, and what is the value of a piastre to him?

Ans. Gain £23 14s. sterling nearly. Value of a piastre 56d. 3.55qr. sterling. 3. A merchant in New York orders £500 sterling, due him at London at 54d, sterling per dollar, to be sent by the following cir cuit; to Hamburgh at 15 marks banco per pound sterling; thence to Copenhagen at 100 marks banco for 33 rix dollars; thence to Bourdeaux at one rix dollar for 6 francs; thence to Lisbon at 125 francs for 18 milrees; and thence to New York at $11 per milree: did he gain or lose by this circular remittance, and what was the arbitrated value of a dollar by this remittance?

Ans. He gained.

Value of a dollar was 69d. sterling nearly.

FELLOWSHIP.

THE Rules of Fellowship are those by which the accompts of several merchants or other persons, trading in partnership, are so adjusted, that each may have his share of the gain, or sustain his

share of the loss, in proportion to his share of the joint stock, together with the time of its continuance in trade.

SINGLE FELLOWSHIP

Is, when the stocks are employed for any certain equal time.

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.

PROOF. Add all the particular shares of the gain or loss together, and, if it be right, the sum will be equal to the whole gain or loss.

EXAMPLES.

1. Divide the number 360 into four parts, which shall be to each other, as 3, 4, 5 and 6.

2. A, B, C, and D companied; A put in £145; B, £219; C, £378, and D, £417, with which they gained £569: What was the share of each?

£ s. d.

3. A, B, C, and D are concerned in a joint stock of $1000; of which A's part is $150; B's $250; C's $275, and D's $325. Upon the adjustment of their accompts, they have lost $337 50c. What is the loss of each ? Ans. A's loss $50 624c. B's $84 374c. C's $92 814c. and D's $109 68 c.

4. A and B companied; A put in £45, and took of the gain; What did B put in? 5-3=2. Then, As 3: 45:: 2 : 30 Ans.

5. A, B and C freighted a ship with 68900 feet of boards: A put in 16520 feet; B 28750; and C the rest; but in a storm, the captain threw overboard 26450 feet: How much must each sustain of the loss? Ans. A, 63413 feet. B, 110363 and C, 9071 do.

6. A gentleman died, leaving three sons and a daughter, to whom he bequeathed his estate in the following manner : To the eldest son, he gave 312 moidores, to the second, 312 guineas, to the third,

That their gain or loss, in this rule, is in proportion to their stocks is evident: For, as the times, in which the stocks are in trade, are equal, if I put in of the whole stock, I ought to have of the gain: If my part of the stock be , my share of the gain or loss ought to be also. And generally the same ratio that the whole stock has to the whole gain or loss, must earh person's part'eular stock have to his re pective gain or loss.

312 pistoles, and to the daughter, 312 dollars; but when his debts were paid, there were but 312 half joes left: What must cach have in proportion to the legacies which had been bequeathed them? Ans. 1st son £293 0s. 3d.-2d. son £227 17s. 103d.-3d. son £179 1s. 21d. and the daughter £48 16s. 81d.

7. A ship, worth $3000, being lost at sea, of which belonged to A, to B, and the rest to C: What loss will each sustain, supposing $450 to have been insured upon her?

Ans. A's loss $312 50c.

B's

C's

937 50
625

8. A and B venturing equal sums of money, cleared by joint trade $140: By agreement, as A executed the business, be was to have 8 per cent. and B was to have 5 per cent. : allowed for his trouble?

$$ $ $ $

$ $ $

What was A

$

As 8-5 140: 8: 862 And, as 8+5: 140 :: 5 : 531.
Ans. $32 30c. 7m.

9. A bankrupt is indebted to A £120, to B £230, to C £340. and to D £450, and his whole estate amounts only to £560: How must it be divided among the creditors?

Ans. A, £53 18s. 114d. B, £112 19s.73d. C, £167 Os. 4d. and D. £221 1s. Old.

10. A, B, and C put their money into a joint stock; A put in $40; B and C together $170: They gained $126, of which B took $42; What did A and C gain, and B and C put in respectively?

Ans. $24 A's gain, $70 B's stock, $100 C's stock. $60 C's gain. 11. A, B, and C companied; A put in £40; B 60, and C a sum unknown: They gained £72; of which C took £32 for his share; What did A and B gain, and C put in?

Ans. £16 A's gain, £24 B's gain, and £80 C's stock. 12. A, B, and C put in $720, and gained $540, of which, so oftten as A took up $3, B took 5, and C 7: What did each put in and gain?

Instead of the above rule, you may find a common multiplier to multiply the proportions by, or multiplicand to be multiplied by the given proportions, thus, 15)720(48 multiplicand to find the stock. And 15)540(36 multiplicand to find the gains.

$

48x3=144 A's stock.

-48×5=240 B's ditto. And

48X7 336 C's ditto.

$

36x3=108 A's gain.

36x5=180 B's ditto.

38X7 252 C's ditto, as before. 13. A, B, C, and D companied; and gained a sum of money of which A, B and C took £120, B. C and D, £180, C, D and A, £160, and D, A and B, £140: What distinct gain had each ?

The sum of these 4 numbers is £600, and as each man's money is named 3 times, therefore, viz. £200 is the whole gain.-Therefore £200-£ 120 A's B's and C's gain=£30 D's gain ; And £200-£ 180 B's, C's and D's gain £20 A's gain.- 200— £160 C's, D's, and A's gain=£40 B's gain. And £200-£140 D's, A's and B's gain=£ 60 C's gain.

14. Two merchants companied; A put in £40, and B 288 docats. They gained £135, of which A took £60. What was the value of a ducat?

As £60, A's gain: £40, his stock :: £135 the whole gain—£ 60, A's gain; £50, B's stock.

Duc. £ Duc. s. d.

And, as 288 50 :: 1 : 3 53 Ans.

15. Four men spent, at a reckoning, 20 shillings, of which they agreed that A should pay 3, B, 2, C, 1, and D, 1. What must each pay in that proportion?

16. A, B, and C companied; A put in £40-25; B £80.5; and C £161: they gained £120.

£

£

What is each man's share?

£ £ £

40 25-30.5+161: 120 :: 40·25; 17-142475=A's

£

17. A, B, C, and D gain $200 in trade, of which as often as A has $6, B must have $10, C $14, and D $20: What is the share of each? Ans. A's share $24, B's $40, C's $56, and D's $80.

18. An insolvent estate of $633 60c. is indebted to A, $312 75c. to B, $297, to C, $50 25c. to D, $0 25c. to E, $200, to F, $142 50c. and to G, $21 25c.; what proportion will each creditor receive?

$

C.

19. A ship was driven on shore in a gale, and in lightening and getting her afloat again and in reloading, an expense of $768 was incurred; the ship was valued at $10000, freight at $3200, molasses owned by A, at $5200, sugar owned by B, at $4700, and rum owned by C, at $2500: how much is this loss on every $100, and how much must each party pay of it?

$

$ $

$ $

10000+3200+5200+4700+2500=25600. As 25600: 768::100:3

$ $ $ $

Ans. on each $100.

Then, As 100: 3 :: 1000: 300 to be paid by the ship,

20. A vessel, valued at $13000 was laden with hardware for E valued at $3000, with cordage for F, at $5000, with dry goods for G, at $3200, with goods for H, at $7900, and for I, at $4400; the captain was obliged to prevent sinking in a storm to throw overboard three fifths of the hardware, and two fifths of the cordage, with goods of H valued at $2700; allowing the freight to be $3500, what will be the average of the loss on 100 dolls, and what must be paid to E, F, and H, for their property thrown overboard?

Ans. $16 25cts. on $100, and E, F, and H must receive together $5443 75cts.

See Policies

Note. If the property of E, F, and H, had been insured, the remainder of their loss must be paid by the insurers. of Insurance.

DOUBLE FELLOWSHIP,*

Or, Fellowship with Time, is occasioned by the shares of partners being continued unequal times.

RULE.

Multiply each man's stock, or share by the time it was continued in trade. Then,

As the whole sum of 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, B, and C hold a pasture in common, for which they pay £40 per annum. A put in 9 oxen for 5 weeks; B, 12 oxen for 7 weeks, and C 3 oxen for 16 weeks. What must each pay of the rent ?

9x5=45. 12x7=84, and 8×16=128, then 128+84+45=257. As 257: 40 :: 45 As 257: 40 :: 84 As 257: 40 :: 128

*When 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 thei products.