EXERCISE XII. 1. Express a yard as a decimal of a metre; and a mile in the denomination of kilometres. 2. Express a dekametre in the denomination of yards; and a myriametre in the denomination of miles. 3. In 50 miles, how many kilometres? in 8 myriametres how many miles? 4. Express a furlong in metres. What is the least number of metres that contains an exact number of inches? 5. A traveller on the Continent paid the following Hotel bills in English money, reckoning 25 francs to the sovereign: (1) Hotel de France 22 frs., (2) Hotel de la Couronne 81.50, (3) Hotel de la Ville 91.50, (4) Hotel Belle Vue 252-25, (5) Hotel du Lac 69.50, (6) Schweizerhof 217-20. Find in each case the exact sum he paid. 6. Pay in francs the following English bills, reckoning 25 francs to the pound: (1) 17s. 6d., (2) £1. 8s. 3d., (3) £1. 13s. 9d., (4) £4. 16s., (5) £6. 16s., (6) £5., (7) £43. 8s. 7. Reckoning the pound sterling as 25-2215 francs, what is the value of 25000 francs? and what sum in francs is £50? 8. In accepting in English money the payment of a debt of 10000 francs, how many pounds, &c. did the creditor gain or lose by reckoning 25 instead of 25-2215 francs to the pound? 9. Express an acre in the denomination of hectares. 10. The docks at Hâvre covering 30 hectares, find their area in acres. 11. In a field of 13 acres, 3 roods, 17 poles, how many hectares? 12. If the area of a lake be 7·0457 acres, what is the equivalent in hectares? 13. How many gallons in a cask containing 100 litres ? 14. In 57 gallons, 3 pints, how many hectolitres ? 15. How many pounds, shillings, &c. would 4.732 hectolitres cost at 12 florins, 2 cents 5 mils per gallon? 16. If we take the litre as 12 pints, and allow that the bottles of the Litre Wine Company hold th more than the English reputed quart bottles, find how much short of a quart the attenuated English bottle now holds ? 17. In 100 kilolitres how many bushels ? 18. Express the lb. Troy in hectograms; and the lb. avoirdupois in kilograms. 19. What weight in avoirdupois is equivalent to 42:75 kilograms? 20. Find in myriagrams the weight of a gun of 4 tons, 19 cwt. 2 qrs. 19 lbs. 21. A gallon of water weighs 10 lbs.: express the weight of a litre of water in kilograms. 22. Express in kilograms the excess of 263 myriagrams over 2 tons, 9 cwt. 3 qrs. 24 lbs. 23. A French gun projected a shot of 31-6874 kilograms a distance of 5000 metres: express the weight and the distance in English measure. 24. An English gun threw a shot of 134 lbs. 5 oz. a distance of 33 miles: express the weight and the range in kilograms and metres. 25. The pendulum vibrating seconds in the latitude of London is 39′1393 inches: express that length referred to the metre. 26. The metre being the ten-millionth part of a line drawn along the meridian from the pole to the equator, what is the earth's circumference in miles ? 27. If the earth's polar diameter be 1271.057 metres, and the equatorial diameter 7924 miles, find the polar diameter in miles, and the equatorial diameter in metres. 28. Express a cubic yard as a stere. In 5028 45915 cubic feet, how many steres ? 29. An embankment contained 245-95994 steres: how many cubic yards and cubic feet were there in it? 30. In 3651 thalers, how many pounds, shillings, &c.? 31. Find the equivalents in English measures of 273 German "meiles," 87 "ruthe," and 139 "Schacht-ruthe." * 150 CHAPTER XI. PRACTICE. § 82. The rule of Practice does not involve any principles beyond the rules of compound multiplication and division, fractions and decimals. It depends for its use on the readiness with which the above rules can be applied, and on the dexterity and quickness which the calculator acquires by practice. It is the rule by which, when the price of an unit of any denomination is given, we can find the price of any quantity of the same kind of goods. 39 The method of its application is as follows: when the cost is required say of 90 yards at the rate of £2,, 16s.,, 6d. per yard, instead of reducing £2 16s. 6d. to pence, multiplying the pence so obtained by 90, and then dividing that result again by 12 and 20 to bring the result back into pounds, shillings and pence, we should by practice first multiply 90 by 2, to find what the 90 yards cost at £2 per yard; and we should then take the remainder of the money given as the cost price, and subdividing it so that each part may be a simple fraction of that which preceded it, we should find the cost separately of the 90 yards at each of these rates, and then add together the several results. The form of the process is as follows: § 83. The common difficulty in working examples in practice consists in finding out what are the proper fractional parts into which to subdivide either the money which is the price, or the quantities of the goods purchased; the tables given below will supply this information. An Aliquot part, (aliquoties, a certain number of times), sometimes called a submultiple, may be thus defined: One number or fraction is said to be an aliquot part of another number or fraction when the first is contained an exact number of times in the second. The first table contains the aliquot parts of £1, so arranged that the simple aliquot parts, or the aliquot part of an aliquot part, may be found at once by inspection. The figures written by themselves or before a semicolon are shillings; those after a semicolon are pence or fractions of a penny. Here the simple aliquot parts of a pound, the half, third, &c., are found in the left hand column, and in the upper column; the aliquot part of an aliquot part is found in the square opposite to the one and under the other part; thus opposite to eighth and under fourth is found; 7; which shows that 7d. is the eighth of a fourth of a pound. If now the price of 3107 yards at 74d. per yard be required, by dividing 3107 by 4 and the result by 8, we obtain the eighth of the fourth of £3107, and so find the cost required; thus Twentieth. Fortieth. |