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len to 52d. flemish, per crown: What may be gained per cent. by drawing on Paris and remitting to Amsterdam.

Ans. 31. 14s. O d. gained per cent.

COMPOUND ARBITRATION. In compound arbitration the rate or price of exchange be. tween three, four, or more places, is given, in order to find how much a remittance passing through them all will amount to at the last place : or to find the arbitrated price, or par of arbitration, between the first place and the last.

Rules 1st. Distinguish the given rates or prices into an. tecedents and consequents : place the antecedents in one column, and the consequents in another on the right, fronting one another by way of equation.

2d. The first antecedent, and the last consequent to which an antecedent is required, must always be of the same kind.

3rd. The second antecedent must be of the same kind with the first consequent, and the third antecedent of the same kind th the second consequent, &c.

4tr. If to any of the numbers a fraction be annexed, both the antecedent and its consequent must be multiplied into the denominator.

5th. To facilitate the operation, terms that happen to be equal or the same in both columns, may be dropped or rejected, and the othe: terms may be abridged.

6th. Multiply the antecedents continually for a divisor, and the consequents continually for a dividend, and the quotient will be the answer, or antecedent required.

EXAMPLES. 6. Suppose a merchant in any part of the United States would remit $2000 to London the direct exchange being $445 for 1001. sterling. It is required whether will be more profitable the direct remittance, or by remitting first to Holland at 40 cents per gilder banco: thence to France, at, 584. flem. per croʻyn, thence to Venice, at 100 crowns, for ( 3 ducats, and thence to London at 50d. ster. per ducat. Antecedents. Consequents.

Abridged. 40 cents

1 guilder or 40d. Flem. 1 1
58d. Flem
1 crown,

29 = 1
100 crowns
63 ducats,

1
1 ducat
50d. sterling.

1 How many 2.ster. $2000

1625

21

Then 29 divisor ; and 21x625=13125 dividend : Hence,

29)13125( 452. 115.-8d: 25 qr8.2000 by circular ex. change.

But 8445 : 1001. ster. :: 2000 : 4491. &s. 9d. 04. grs. = S2000 by direct exchange.

7. Holland owes the United States 4000 guilders : whether is it more advantageous to draw at 38 cents per guilder, or to have the money remitted first to Paris, at 54d. flem. per crown; thence to Genoa at 5 liv, tour. per piastre; thence to London at 50d. sterling per piastre, and then drawn for from the United States at par?

Ans. $126.097 gain by remitting. 8. If London rcmit 1000l. ster. to Spain by way of Holland at 35s. Flem. per & ster. thence to France at 58d. Flem. per crown; thence to Venice, at 100 crowns per 60 ducats : and thence to Spain, 360 maravadies per ducat: how many piastres of 272 maravadies, will the 1000l. ster. amount to in Spain. Antecedente. Consequents.

Abridged. 1 & Sterling,

358. or 420d. Flem. 1=210 58d. Flemish, 1 Crown France,

1 100 Crowns France, 60 ducats Venice. de 30

1 ducat Venice, = 360 maravedies Spain. 1 45 272 maravadies,

1 piastre.

17: 1 How many piastres, =1000 . Sterling. 210 X30X 45 X 10

-5750piastres. Ans. . 29 x 17 9. A banker in Amsterdam remits to London 4001. Flem. ish ; first to France at 56d. Flem. per crown, from France to Venice, at 100 crowns per 60 ducats ; from Venice to Ham. burgh at 100d. Flem. per ducat ; from Hamburgh to Lisbon, at 50d. Flem. per crusade of 400 rees; and, lastly from Lis. bon to London, at 64d. ster. per milree : How much ster. money will the remittance amount to ? and how much will be gained, supposing the direct exchange from Holland to London at 36.10 Flemish per £. sterling?

Ans.

21. 48. 81d. gained. 10.. A merchant at London has credit for 680 piastres at Leghorn, for whicn he can draw directly at 50d. ster. per pi. astre but chusing to try the circular way, they are by his order remitted, first to Venice, at 94 piastres per 100 ducats banco; thence to Cadiz, at 320 maravedies per ducat ; thence to Lisbon at 630 rees per piastre of 272 Maravedies ; thence to Amsterdam, at 50d. Flem. per crusade of 400 rees ; thence to Paris, at 56d. Flemish per crown ; thence to London, at 3134. sterling per crown, What is the arbitrated price be

- 10

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tween London and Leghorn per piastre ; and how much is the circular remittance better than the direct draft, without reckoning changes.

Ans.

141. 11s. 8d. gained. Note-Not only may different sorts of money be equated in the manner above described, but also weights and measures.

EXAMPLES. 11. If 102 lb. of Hamburgh be equal to 100 lb. at Amsterdam, and 100 lb. of Amsterdam to 98 lb. at Frankfort, and 98 lb. at Frankfort to 105 lb. at Leipsic, and 105 lb. of Leipsic to 145 Ib. at Leghorn, and 145 lb. at Leghorn to 106 lb. at Cadiz, and 100 lb. at Cadiz to 1031 lb. at London : how many lb. at London are equal to 3060 lb. at Hamburgh.

Ans. 3286 lb. at Lando:1 12. If 11 ells, or aunes of Hamburgh, make 1 ell in Hola land, and o7 in Holland make 4 in France, and 7. in France make 5 yards in England ; how many yards in England are equal to 588 ells, or aunes of Hamburgh ? and what their price, at the rate of 4l. sterling for 5 yards English.

Ans. 200 yards, and 1601. sterling,

FELLOWSHIP. Fellowship, called also Partnership, is when two or more persons put together a generał «stock in trade, or are concerned in ships, &c.

By this rule are adjusted the gains, losses or charges of partners in company the effects of bankrupts ; legacies in case of a deficiency of effects ; shares of prizes, &c. &c.

Fellowship is either without or with time, called single or compound

SINGLE FELLOWSHIP. : RULE-Add the several stocks into one sum.

Then as the general stock : is to the general gain or loss :: so is each. man's particular stock: to his particular share of the gain or loss.

EXAMPLES. 1. Two men, A. and B. are partners in trade : A. put in 2501. and B. 7501. by trading they gain 1551. 12s. 6d. Required each man's share of the gain? 1. general stock. general gain. Š 250 : 38 18 14 A's gain. 250+750 : 155 12 6 : : 7750 : 116 14 4. B's gain.

£155 12 6 Proof.
2. Divide 240 into three parts as shall be in propor-
tion to each other as the three numbers 1, 2 and 3 ?

Ans. 40, 80, 120.
K

S. d.

gain?

175

1434

3. Three persons have gained $1320; now when A. takes S6, B. takes $4, and C. $2. I demand how much each gets ?

Ans. A. $660, B. $440, C. $220. 4. A. B. and C. make a joint stock : A. puts in 4601. B. 5101. and C. 4801.; they gain 3401. What is each partners

1. 8. d. qrs.

A.= 1075 17 2 3-85
Ans. gain of B.= 119 11 8 2i1g

C.= 112 11 0 119,95 5. Four merchants, A. B. C. and D. built a sloop which cost $1730 ; and the freight for her first voyage amounted to $370, of which A's share was 874, B's $111, C's $148, and D's $37. What was each partners stock ?

Ans. A's stock was $346, B’s S519, C's $692, D's $173. 6. Three persons A. B. & C. freighted a ship with 340 tuns of wine ; of which A. loaded 110 tuns, B. 97, and C. the rest : in a storm the seamen were obliged to throw overboard 85 tuns. How much must each sustain of the loss?

Ans. A's loss was 27 } tuns, B's 241, C°331. 7. A general imposing a contribution of $70000 on four towns, to be id in proportion to the number of inhabitants contained in each ; the 1st. containing 2500, the 2d. 3500, the 3d. 4000, and the 4th. 5000 persons. What part must each town pay? Ans. The 1st. to pay $116663, the 2d. $1633 }, the 3d.

$186663, the 4th. $23333 8. A detachment, consisting of 5 companies, being sent into a garrison, in which the duty required 76 men a day : What number of men must be furnished by each company in proportion to their strength; the 1st. consisting of 54 men, the ad. of 51 men, the 3d. of 48 men, the 4th of 39, and the 5th. of 36 men ? Ans. The 1st. must furnish 18, the 2d. 17, the 3d. 16, the

4th 13, and the 5th. 12 men. 9. A. B. C. and D. in partnership had a joint stock of $6000, and gained a certain sum ; of which A. B. and C. took up $600 ; B. C. and D. $900; A. C. and D. $800 ; and A. B. and D. $700. What was the stock and gain of each partner?

A's stock $ 600, and his gain $100.
B's $1200,

$200.
Answer,
$1800,

$300. D's $2400,

$400. 10. Suppose A. B. and C. join in an adventure to Upper Canada, for which they jointly purchase goods to the value of 30001. and to complete the assortment, the partners from their own stores put in such articles as they had proper, viz :

C's

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A. to the value of 1001. B. 2001. and C. 3001. ; the neat proceeds of their returns in furs and peltries, amounted to 69301. What share of this belongs to each partner?

Ans. T. A. 21171. 10s. to B. 23101. to C. 25021. 10s.

{

A’s gain. 34 B's gain.

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COMPOUND FELLOWSHIP. Compound Fellowship as has been said, is concerned in cases in which the stocks of partners are employed for different times.

RULE–Multiply each person's stock by the time it has continued in trade, and proceed with the products, as with the particular stocks in Single Fellowship.

EXAMPLES. 1. A. and B. are partners; A. put in 601. for 3 months, and B. 501. for 4 months ; at the end of which they find a gain of 301. Required each man's share thereof?

60X3=180 50x4=200

l.

8. d. qrs.

180 : 14 4 2 2310 380 : 30 :

380 2. Three merchants, A. B. and C. enter into partnership, thus; A. puts into the stock 2401. for 4 months, B. 1201. for 6 months, and.C. 2001. for 8 months ; with this joint stock they traffic and gain 2601. it is required to find each person's gain ?

2.

111 1216 A's
57 ] 5 2 80 B's gain.
126 16

7 0-32
3. Three butchers A. B. and C. hire a pasture for $24: A.
puts in 40 sheep for 4 months, B. 30 sheep for 2 months, and
C. 36 sheep for 5 months : what share of the rent must each
pay? Ans. A's share $9 60c. B's share $3 60c. C's share $10 80c.

4. A ships company take a prize, value 4000l. sterling, which they agree to divide amongst them, according to their pay and time they have been on board : now the officers and midshipmen have been on board 4 months, and the sailors 3 ; the officers have 50s. a month, the midshipmen 40s. and the sailors 27s. moreover there are 4 officers, 8 midshipmen, and 120 sailors : I demand to know what each person's share is of the said prize?

1.

65 15 9 110888 each officer's
Answer 52 12 7 2 3840 each midship. share,

27 12 7 2 3,84 each sailor's

s. d. grs.

76

Ans.

C's

3 28

s. d. qrs.

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