5. Price per metre given price per yd. Fixed number for yds. to metres = 0045568044. Multiply price in pence by rate of exchange and the product by the fixed number. Answer is in foreign units of rate. The methods of prediction (§ vi) apply and multiples of the fixed numbers may be constructed. Example 1. Price per kilo. =1.72 francs. Rate=25·21. Example 2. Price per Imp. qr.=37s. 9d. Rate=20.40. The modifications for a pfund (kilo.) are easily made. 10. Equivalent Prices with Sterling Rates by means of Fixed Numbers. The rules here given may be used in the case of all countries receiving a rate from London and using the Metric System. A. 1. Price = 4535926525. Multiply price by rate in pence and the product by the fixed number. Answer is in pence. PRICES BY FIXED NUMBERS. 2. Price per cwt. given price per kilo. Fixed number for kilos. to cwts. = 4.2335314. 111 Multiply price by rate in pence and the product by the fixed number. Answer is in shillings. 3. Price per gallon given price per litre. Fixed number for litres to gallons = 4.54345797. Multiply price by rate in pence and the product by the fixed number. Answer is in pence. = 4. Price per qr. given price per hectol. Fixed number for hectols. to qrs. 2423177583. Multiply price by rate in pence and the product by the fixed number. Answer is in shillings. 5. Price per yd. given price per metre. Fixed number for metres to yds. = 9143834807. Multiply price by rate in pence and the product by the fixed number. Answer is in pence. The methods of prediction (§ vi) apply and multiples of the fixed numbers may be constructed. B. 1. Price per kilo. given price per lb. Fixed number for lbs. to kilos. = 2.204621249. Multiply number by price in pence and divide by rate of exchange. Answer is in foreign units of rate. = •2362094. 2. Price per kilo. given price per cwt. Fixed number for cwts. to kilos. Multiply number by price in shillings and divide by rate of exchange. Answer is in foreign units of rate. 3. Price per litre given price per gallon. Fixed number for galls. to litres = 2200966768. Multiply number by price in pence and divide by rate of exchange. Answer is in foreign units of rate. 4. Price per hectol. given price per Imp. qr. Fixed number for qrs. to hectols. = 4.1268127. Multiply number by price in shillings and divide by rate of exchange. Answer is in foreign units of rate. 5. Price per metre given price per yd. = Fixed number for yds. to metres 1093633056. Multiply number by price in pence and divide by rate of exchange. Answer is in foreign units of rate. The methods of approximation apply-especially the methods of prediction (§ vi). The multiples of the fixed numbers may be constructed. Example 1. Price per metre = 1.61 pesetas at 434d. (Spain). Example 2. Price per cwt. = 17s. 10d. Rate=451d. (Lisbon). In the case of Spain the rate is quoted in pence per piastre. 1 piastre = 5 pesetas. The modifications for this and the half-kilo. are easily made. The Portuguese milreis is divided into 1000 reis – thus one more place is necessary than with other foreign moneys. Note. The Fixed Numbers are simply the invariable part of the work ready done in each case. They are obtained from the equi EQUIVALENT PRICES. 113 valents of the various units in a manner which is similar in all the cases, one example will therefore suffice. 6 B. 1 lbs. to kilos=00918592187. 1 kilo 2.204621249 lbs., .. if 1 lb. costs 1d., 1 kilo will cost 2-204621249 pence. The value in £ is thus 00918592187 (2·204621249 240) and the rule follows at once. Multiply £.00918592187 by price in pence and then by rate of exchange to convert the product in £ to the foreign price. A most valuable exercise for the Student would be to determine some of the remaining Fixed Numbers with due regard to the rules to which they are attached. EXAMPLES. 1. Find price per cwt. given price per kilo. and rate of exchange. (1) 1.23 m. at 20:40. (3) 1.72 fl. at 118.20. (2) 3:17 fl. at 11.95. (4) 3·17 pesetas at 493. (6) 1 rup. 12 annas at 172. 2. Find price per kilo. given price per lb. (1) 18. 2 d. at 25·171⁄2. (3) 28. 133d. at 18·43. (2) 11 d. at 20:37. (4) 18. 9 d. at 42g (Spain). (5) 28.3d. at 51% (Portugal). (6) 28. 1d. at 139 (Brazil). 3. Find price per litre given price per gallon. (1) 5s. 71d. at 26·18 (Italy). 10s. 9d. at 25-27 (Switzerland). (3) 68. 5d. at 471 (Spain). (4) 48. 61d. at 52 (Lisbon). 4. Find price per quarter given price per hectol. (1) 10.27 m. at 20:38. (3) 13.25 pesetas at 491. (2) 13.50 fl. (Dutch) at 12.15. (4) 1378 milr. at 51. 5. Find price per metre given price per yd. (1) 12s. 9 d. at 25.19. (3) 73d. at 20-36. (2) 58. 7 d. at 47 (Lisbon). 6. Find price per yd. given price per metre. (1) 10-35 m. at 20:41. (2) 2.350 milr. at 50. (4) 1·13 fl. at 12:05 (Amst.). SECTION V. PROPORTION AND PERCENTAGES. Proportion. 1. The Principle of Proportion, or in other words the Comparison of Ratios, underlies the vast majority of commercial calculations, but very rarely indeed does the statement of the question appear in a direct form such as a rule of three sum in ordinary text-books. In fact the usual proportion is "if 1 thing costs so much what will a given quantity cost?" and not "if 27 things cost so much what will the quantity cost?" None the less however is the principle of proportion involved, and the essential nature of such calculations cannot be too carefully remembered however much disguised the forms in which it occurs. It should also be noticed that the principle of Cancellation is of the utmost importance in reducing labour. Proportional parts, percentages, and some calculations in interest, together with questions of mixtures etc., involve the principle most plainly, but the shortest methods of solution even of these dispenses with the rule of three or the reduction to unity forms-both these forms being too cumbrous for actual work where time is valuable. We give an example of proportion to show the value of cancellation in reducing labour and also to show the |