7. Exchange 1,000 marks into pounds sterling at 20:45 marks per £. 8. Exchange 1,000 milreis into sterling money at 52d. per milreis. 9. Exchange £100 into roubles at 26d. per rouble. 10. Exchange 10,000 dollars into pounds at 48g dollars per £10. = 100 florins; what is 11. The direct exchange between St. Petersburgh and Berlin is 215 marks = 100 roubles, and that between Berlin and Vienna is 175 marks 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, 104d.. 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. stroyed, four copies (called the New Palace at Westminster. The recent Act provides for the construction of a fifth parliamentary copy. From these copies are derived the Board of Trade standards, and from the latter the local standards for testing measures used in trade. The oldest standard yard now existing is the exchequer yard of Henry VII. It falls short of the existing standard by only the one hundredth part of an inch. It is represented in the accompanying illustrations. In form it is an end-measure, the present standard being a line-measure. Exchequer yard of Henry VII., left-hand end, showing sixteenths of yard. Right-hand end, showing inches, ART. 56.-Derived Units of Length. The other units of length in the Imperial system having a special name, such as the inch, the foot, the mile, are defined as a multiple or submultiple of the yard. Originally, no doubt, they were defined independently of one another, but the definitions were rough. The "foot meant the length of a man's foot, the "yard " the length of a man's arm, and the "inch" the breadth of a man's thumb; and three feet were equivalent to one yard, and 12 inches to one foot, with the same amount of accuracy. The present legal definitions owe their unsystematic character to the fact that they are ultimately based upon these rough equivalences. In the table appended I have given all the special units defined by or under the Act; a denomination within parentheses is not an Imperial denomination. The Act also allows a length to be specified in terms of any Imperial denomination and its decimal multiples and submultiples. ART. 57. The F.P.S. System. For scientific purposes the foot is the principal unit of length; and it is exclusively adopted in what is called the British system of absolute units. In that system the foot, pound, and second are used to define all the other dynamical units. Hence, for shortness, it is sometimes called the F.P.S. system. ART. 58.-Metric Standard of Length. In the metric system of weights and measures, instituted in France in 1795, the stan dard unit of length is the distance between the ends of a rectangular bar of platinum called the metre des Archives preserved at Paris, the bar being at the temperature of melting ice. That standard distance is denominated the metre. Originally, the metre was defined as the ten-millionth part of a quadrant of the earth's meridian through Paris. To determine that length the arc from Dunkirk to Barcelona (9° 40′ 45′′) was measured in terms of the then existing French standard of length, called the toise of Peru, and it was found to contain 551,584.72 toises. The meridian is not an exact circle, but an ellipse with the polar axis for the shorter axis. From measurements previously made the ellipticity was taken to be ; and by computing from these data the length of the quadrant was found to be 5,130,740 toises. The platinum bar was constructed to equal the ten-millionth part of 5,130,740 toises, when at its standard temperature of melting ice. Another standard metre was deposited in the Observatory at Paris, and twelve iron copies were distributed to other countries. Former French Standard, called the "Toise of Peru." The toise de Perou was so called from its having been constructed to measure an arc of the meridian in Peru. The breadth, thickness, and ends of the measure are represented in the illustration. The toise is given by the distance on the bar between the points of the arrows a and b. ART. 59. Relation of the Standard Metre to its Primary Definition. According to Colonel Clarke's determinations of the size and figure of the earth, which are at present the most authoritative, the length of a quadrant of the meridian through Paris is 10,001,472 metres, and thus the standard metre is slightly less than the distance upon which it was founded. A difference of |