When the bill is not payable until the expiry of some months, the course of exchange is further affected by the deduction of interest due to deferred payment. When the course of exchange involves interest it is said to be long; when it does not involve interest it is said to be short. Suppose that the course of exchange between Paris and London is 25.50 franc = £. Since the par of exchange is 25.22 franc = £, we deduce 25.50 – 25·22, i.e., ·28 franc premium = £. If the course of exchange is less than the par, for example, 25.15 franc = £; then 07 franc discount = £. When the course of exchange is equal to the par of exchange, the exchange is said to be at par. ART. 53. Indirect or Arbitrated Rates of Exchange. The indirect rate of exchange between two places is the rate deduced from the direct rate of each with respect to a third place. There may be more than one intermediate place. For example.-The direct rate of exchange between London and Berlin is 20·66 marks = £, and the direct rate between Berlin and Paris is 81 marks = 100 francs; deduce the indirect rate of exchange between Paris and London, 20.66 marks £, 100 francs = 81 merks; 2066 francs = £, i.e., 25.50 francs = £. EXAMPLES. Ex. 1. Convert 10,000 francs into sterling money, when exchange Ex. 2. Express 1,000 dollars in francs; given that 1 dollar is equivalent to 4s. 1d., and one franc to 91d. Ex. 3. The fineness of English silver coin is 37 parts by weight of silver to 3 parts by weight of alloy; express its fineness in millièmes. Let M denote any unit of weight (see Art. 54), then 37 M silver + 3 M alloy 40 M standard; 37 × 100 4 i.e., = 1. A German 20-mark piece is worth 9791.; find to the nearest farthing the value in English money of 3725 39 marks. 2. Given that the United States dollar is equivalent to 4s. 13d.; find the equivalent in American money of the several current British coins. 3. Reduce 40,000 dollars to pounds sterling and to francs, taking par of exchange. 4. From the table of pars of exchange deduce the par of exchange between Paris and New York, and between Berlin and Paris. 5. Exchange 781. 68. 8d. into francs at 25.241. 7. Exchange 1,000 marks into pounds sterling at 20:45 marks per £. 10. Exchange 10,000 dollars into pounds at 48g dollars per £10. 11. The direct exchange between St. Petersburgh and Berlin is 215 marks = 100 roubles, and that between Berlin and Vienna is 175 marks = 100 florins; what is the arbitrated rate between St. Petersburgh and Vienna? 12. A money-changer buys francs for 94d. each, and sells them at the rate of 25 for a sovereign. How much money must pass through his hands in this way in order that he may gain £150? 13. A Canadian Company borrows in Paris 294,000 francs for which it pays an annual interest of 2,920 dollars. This loan is transmitted through London when exchange in London is quoted at 25.30 francs, and sterling exchange is 1093. Find what rate of interest the Company pays on the money actually received. 14. A quantity of sugar, valued at 42, 134 dollars Spanish gold, was entered for duty at 30 per cent. In consequence of Spanish gold having been taken at par, whereas. it was only worth 92 cents on the dollar, a refund of duty was afterwards claimed. Calculate the amount. 15. The full weight of the sovereign is 123 274 grains; its fineness is 22 carats. What is the weight of gold in a sovereign? 16. The value of an ounce of the gold of which sovereigns are made is 37, 178, 103d.. What is the weight in pounds troy of 46,725 sovereigns? 17. How many "Napoleons" are required to weigh a kilogramme? 18. At New York a bill of exchange on Dublin for £720 cost 3,472 dollars; find the course of exchange. 19. A Glasgow merchant ships to his Montreal agents for sale goods for which he pays £616 sterling in Glasgow. He pays an ad valorem duty of 12 per cent. upon the goods, and a commission of 7 per cent. to his agents for their services. The goods realize in Montreal 7,800 dollars. Find the merchant's net gain, a pound sterling being equal to 4.86 dollars. CHAPTER SECOND. GEOMETRICAL. SECTION IX.-LENGTH. ART. 54.-General Unit. The idea of length is one of the fundamental ideas of exact science. We shall denote, following Clerk-Maxwell in the choice of a letter,' any unit of length by the capital letter L. It denotes any unit of length in the same way as n denotes any number. We have chosen a bold and simple form of the letter in order that there may be a clear contrast between it and any italic letter used to denote a numerical value. ART. 55.-Imperial Standard of Length. In the Imperial System of Weights and Measures 2 the standard unit of length is determined by means of a bronze bar, constructed in 1845 and now deposited in the Standards Department of the Board of Trade in the custody of the Warden of the Standards. In a small hole near each end of the bar there is a gold plug, and across each plug there are drawn three transverse lines. The distance between the centres of the middle transverse lines, when the bar is at the temperature of 62° Fahrenheit, is the standard yard. The previous standard yard, constructed in 1760, was lost in the fire which destroyed the Houses of Parliament in 1834. It had been defined as bearing at 62° Fahr. the proportion of 36 1 Electricity and Magnetism, vol. 1, p. 3. 2 Weights and Measures Act, 1878. inches to 39-1393 inches, the length of a pendulum vibrating seconds in a vacuum in the latitude of London and at the level of the sea. Exchequer yard of Henry VII., left-hand end, showing sixteenths of yard. Right-hand end, showing inches. |