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change is called simple arbitration, and when through two or more intervening exchanges is called compound arbitration.

501. Since the actual course or rate of exchange between any two places is almost always, from various circumstances, different from the arbitrated course, the object of arbitration is to enable an individual in one place to ascertain whether he can most advantageously draw and remit directly between his own place and another, or circuitously through other places.

502. Exchange of merchandise, and the different weights and measures of different countries, may be arbitrated in the same manner as bills of exchange and currencies.

503. The value, in the standards of the United States, of the principal weights and measures of the most important commercial places, is shown in the following

Igal. Stock

TABLE.

Value
ENGLAND.

Fuder
Value.
= 6 ahms,

229.5gal. Avoirdupois pound,

1lb.
Last of grain,

89.64bu. Old wine gallon,

134.4bu.

1. last, Imperial gallon,

27.58in. 1.20gal.

Brabant ell, Old ale gallon,

1.22gal. DENMARK AND NORWAY. Old Winchester bushel,

lbu.
Pound,

1.10lb. Imp. corn bu. (= 8 inp.gal.), 1.03bu. Centner = 100 pounds, 110.28lb. Quarter of grain (=8 imp.bu.), 8.25bu. Viertel of wine,

2.04gal. Imperial yard,

36in.
Anker of wine,

10gal.
FRANCE.
Ahm = 4 ankers,

40gal. Kilogramme, 2.20lb. Fuder of wine,

237.16gal. Quintal 100kil., 220.54lb. Toende or barrel of grain,

3.95bu. Millier 1000kil., 2205.48lb. Last = 12 toende

47.50bu. Litre, 2.11pt. Danish ell,

24.66in. Velt,

2gal.

SWEDEN. Decalitre = 10 litre,

.931b. Hectolitre 100 litre, 26.42gal. Pound of iron,

.75lb. Hectolitre 100 litre,

2.84bu.
Anker of wine,

10 35gal. Metre,

39.36in.
Eimer of wine,

20.75gal. HOLLAND AND BELGIUM. Ahm = 2 eimers,

41.50gal. Pond, 1.08lb. Pipe = 3 ahins,

124.25gal. Fr. kilograrome,

2.2016. Tun or barrel of grain, 4.16bu. Last, marine,

2000 p.
44101b. Ell,

23.36in, Vat= 100kai = 1 hectol. Fr., 26.42gal.

BREMEN. Ahm of wine,

1.091b. Mudde=100 kop=1 hectolitre, 2.84bu.

Centner,

1161b. Last of grain, 85.25bu. Viertel of wine,

1.93gal. Amsterdam ell,

27in.
Anker = 5 viertels,

9.65gal.
HAMBURG.
Oxhoft 6 ankers,

58gal. Pound, 1.061b. Scheffel of grain,

2bu. 100 pounds, 106.8lb. Last = 40 scheffels,

80.70bu. Ahm of wine, 38.25gal. Ell,

22.75in.

2.64gal. Pound,

41gal. Pound,

82.131b. Rottolo,

TRIESTE.

Value. Value. Pound,

1.23lb. Cantaro or arroba of wine, 4.25gal. 100 pounds, 123.6016. | Moyo of wine

16 arrobas, 68gai. Eimer of wine,

15ga). Botta = 38ar, of wine = 38far. Staro of grain,

234bu.
of oil,

127.5gal. Ell for silks, 25.20in. Fanega of grain,

1.57bu. Ell for woollens,

26.60in. Cabiz = 12 fanegas, 18.91bu. Vara or yard,

33.37in. CONSTANTINOPLE.

CUBA. Quintal.

124.45lb. Alma for liquids,

101.75lb. 1.37gal.

Quintal,
Arroba of wine,

4.1gal. Kisloz of grain, .94bu.

3bu. Pik, commercial,

Fanega of grain,
27in.
Vara,

33.34in. CALCUTTA.

NAPLES. Maund, 74.66lb.

1.96lb. Bazaar maund, Guz,

36in.

Cautaro grosso=100 rottolo, 196.50lb.
Cantaro piccolo,

1061b.
RUSSIA.
Salma of oil,

42.75gal. Pound, .90lb. Carro of wine

264gal. Pood 40 pounds, 361b. Carro of grain,

52.20bu. 100 pounds, 90.26lb. Canna,

83in. Wedro of wine,

3.25gal.

SICILY. Sorokovy = 40 wedros, 130gal.

Cantaro grosso,

192.50lb. Chetwert of grain,

5.95bu.
Cantaro sottile,

175lb. Arsheen,

28in.
100 Sicilian pounds,

70lb. Sashen,

Tonna,

9.38gal. PRUSSIA. Salma grossa,

9.48bu. Pound, 1.03lb. Salma generale,

7.62bu. 100 pounds, Dantzic, 103.3lb. Conna or yard,

38.40in. Quintal = 110 pounds, 113.421b.

GENOA.
Eimer of wine,

18.14gal.
Cantaro grosso,

76.871b. Ahm,

39.66gal. Scheffel of grain,

69.891b. 1.52bu.

Cantaro sottile,
Last of grain,

91bu.
Mezzarola,

39.25gal. Mina of grain,

3.50bu. Berlin Ell,

25.5in. Prussian Ell,

Camna picco'a,

87.50in. 26.28in. Canna grossil,

116.70in. PORTUGAL.

VENICE. Pound or arratel,

1.01lb. Arroba 22 arratels, 22.26]b. 100 pounds, pesso grosso,

105.18lb. Quintal = 4 arrobas,

89.05lb. 100 pounds, pesso sottile, 66.421b. 100 pounds or arratels, 101.191b. Miro of oil,

4.02gal. Almude of wine, 4.37gal. Anfora of wine,

1.37gal. Tonelado = 52 almude, 227.25gal. Staja of grain,

2.27bu. Moyo, 23.03bu. Moggio

9.08bu.

4 staji, Vara, 43.20in. Braccio for silks,

24.84in. Braccio for woollens,

26.64in. SPAIN. Pound,

1.01lb.

CHINA. Arroba 25 pounds, 25.381b. Catty,

1.33lb. Quintal = 4 arrobas, 101.521b. Pecul,

133.33lb. Cantaro or arroba of oil, 3.75gal. Covid,

14.62in.

7ft.

NOTE. The weights and measures of Mexico, Central America, and of the republics of South America are the same generally as those of Spain; of Brazil, the same as those of Portugal; of the British North American Provinces, the same, in general, as in England; and of Hayti, the weights are the same as in the United States, except abcut 8 per cent. heavier, and the measures the same as in France.

504. To compute arbitration of exchanges.

Ex. 1. When the exchange between New York and London is at a premium of 9 per cent., and that between London and Paris 25 francs to a pound sterling, how much must be paid in New York for a bill on Paris for 1000 francs ? OPERATION.

Since $45 $40 9 £.

1£. of the nomi109 £. 100 £.

nal par of ex1 £. 2 5 fr.

change (Article 10 0 0 fr. =

497), $40=9£.; 16

and 109£. of the

same value 40 x 109 x 1 x løøø

100£. at 9 per

$ 193.77+ Ans. 9 X 100 x 25

cent. premium. We write the terms of equivalent value as antecedent and consequent, and proceed as in conjoined proportion (Art. 341).

NOTE. When it is required to find which of several routes of exchange is the most advantageous, the rate of exchange by each route may be determined first, and the results then compared.

10

EXAMPLES.

2. When exchange at Lisbon on Paris is at the rate of 5 francs 95 centimes per millrea, and at Paris on the United States at 5 francs 20 centimes per dollar, how much must be paid in Lisbon to cancel a demand in New York for $ 3500 ?

Ans. 3058 millreas 823 17 reas. 3. A merchant in Boston wishes to pay 2000£. in Liverpool. Exchange on Liverpool he finds is at 10 per cent. premium, on Paris 5 francs 20 centimes to a dollar, and on Hamburg 35 cents to a mark banco; and the exchange between France and England at the same time is 24 francs to a pound sterling, and that of Hamburg on England 13marks banco to a pound sterling. Which is the most advantageous course of remittance, that direct to Liverpool, or that through Paris or Hamburg?

4. A merchant of St. Louis wishes to pay a debt of $ 5000 in New York. The direct exchange is 11 per cent. in favor of New York, but on New Orleans it is } per cent. discount; and between New Orleans and New York at per cent. premium. How much would he save by the circular exchange compared with the direct ?

Ans. $87.561

5. A merchant in Boston owes a debt of 9760 thalers in Bremen, to pay which he purchases a bill on London, at a premium of 9 per cent., and remits the same to his agent in England, on whom his creditor is requested to draw.

If the exchange between London and Bremen be at the rate of 34d. sterling per thaler, and the charges for brokerage { per cent., how much must have been the cost of the bill in New York ?

Ans. $ 6731.74+ 6. When exchange between New Orleans and Hamburg is at 34 cents per mark banco, and between Hamburg and St. Petersburg is 2 marks 8 schillings per ruble, how much must be paid in St. Petersburg for a bill on New Orleans for $ 650 ?

Ans. 764 rubles 7014 kopecks. 7. When exchange in Philadelphia on Boston is at & per cent. premium, and on Chicago at 2 per cent. discount, if the exchange between Chicago and Boston is at par, how much better is the circuitous ruute of exchange between Philadelphia and Boston than the direct ?

8. A merchant, about to import broadcloth, finds he can obtain the quality desired in Amsterdam at 8 guilders per Amsterdam ell; in Berlin, at 3 thalers 15 groschen per Berlin ell ; and in England, at 15 shillings per yard. Exchange being on Amsterdam at 40 cents per guilder, on Berlin at 66 cents per thaler, and on England at 91 per cent. premium, and the freight being the same in each case, from which place can he make the importation to the best advantage ?

Ans. Berlin. 9. When exchange between Washington and London is at 8 per cent. premium, and between London and Paris 25.25 francs per pound sterling, what sum in Washington is equal to 7000 francs in Paris ?

10. A merchant in London remits to Amsterdam 1000£. at the rate of 18d. per guilder, directing his correspondent at Amsterdam to remit the same to Paris at 2 francs 10 centimes per guilder, less į per cent. for his commission ; but the exchange between Amsterdam and Paris happened to be, at the time the order was received, at 2 francs 20 centimes per guilder. The merchant at London, not apprised of this, drew upon Paris at 25 francs per pound sterling.

Did he gain or lose, and how much

per

cent. ? Ans. Gain, 165 per cent,

ALLIGATION.

505. ALLIGATION is a process employed in the solution of questions relating to the compounding or mixing of articles of different qualities or values.

It is of two kinds : Alligation Medial, and Alligation Alternate.

ALLIGATION MEDIAL.

506. ALLIGATION MEDIAL is the process of finding the mean or average rate of a mixture composed of articles of different qualities or values, the quantity and rate of each being given.

507. To find the average value of several articles mixed, the quantity and rate of each being given.

Ex. 1. A grocer mixed 2cwt. of sugar worth $ 9 per cwt. with lcwt. worth $ 7 per cwt. and 2cwt. worth $10 per cwt. ; what is lcwt. of the mixture worth?

Ans. $ 9. $ 9 x 2 $18

Since 2cwt. at $ 9 per cwt. is worth 7 x 1

7 $ 18, 1cwt. at $ 7 per cwt. is worth $ 7, 10 X 2 20 and 2cwt. at $ 10 per cwt. is worth $ 20;

2cwt. + lcwt. + 2cwt. = 5cwt. is worth 5) $ 4 5 $ 18 + $ 7 + $ 20 = $ 45; and lcwt. is $9 Ans.

worth as many dollars as 45 contains times

5, or $ 9. RULE. Find the value of each of the articles, and divide the sum of their values by the number denoting the sum of the articles. The quotient will be the average value of the mixture.

EXAMPLES. 2. If 19 bushels of wheat at $ 1.00 per bushel should be mixed with 40 bushels of rye at $0.66 per bushel, and 11 bushels of barley at $ 0.50 per bushel, what would a bushel of the mixture be worth?

Ans. $ 0.7274. 3. If 3 pounds of gold of 22 carats fine be mixed with 3 pounds of 20 carats fine, what is the fineness of the mixture?

Ans. 21 carats. 4. If I mix 20 pounds of tea at 70 cents per pound with 15 pounds at 60 cents per pound, and 80 pounds at 40 cents per pound, what is the value of 1 pound of this mixture ?

Ans. $ 0.4715.

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