water) would determine the Avoir. Pound, and therefore also the Troy Pound. And a grain-obtainable from either of the two Pounds-would determine the Sovereign (5 dwts. 3 grs.): Besides the standards just mentioned, several local ones-retained under the influence of usage and prejudice, although not recognised by law-continue to be employed in different parts of the United Kingdom; and, what is still more perplexing, a local and a legal standard have the same name in some cases, so that the one is liable to be confounded with the other. In Ireland, up to the close of 1862, the Registrar-General used to express quantities of wheat, barley, and oats, in barrels of 20 st., 16 st., and 14 st. each, respectively-these being the three meanings attached to the word "barrel" in most parts of the country. In some places, however, "barrel" had other meanings. Thus, wheat was sold in Dublin by the barrel of 282 lbs. (20 st.), whilst barley and oats were sold in Sligo by the barrel of 24 stone. Grain was sold in Belfast by the hundred-weight, and in Limerick by the stone. The hundred-weight had two meanings in Belfast: 112 lbs. in the case of corn, and 120 lbs. in the case of pork. Moreover, the Belfast people sold flax by the stone of 163 lbs. in one part of the town, and by the stone of 24 lbs. in another part. A stone of flax meant 16 lbs. in Dublin, and 24 lbs. in Downpatrick. All these anomalies, and others into the details of which it is now unnecessary to enter, either have disappeared, or are gradually disappearing, under the operation of an Act of Parliament which took effect in the beginning of 1863. It is difficult to understand why this Act was not extended to Great Britain, where there are upwards of 50 different standards (including 18 varieties of bushel) for the measurement of grain; also, II different standards of length, and 16 of surface (for the measurement of land); and where BRICKWORK is measured by the perch of 22 cubic feet, the perch of 36 cubic feet, and the rod of 272 square feet × 1 bricks thick; POTATOES are sold by the measure of 84 lbs., the long measure of 90 lbs., the winch (Winchester bushel*), the load of 240 lbs., the sack of 10 pecks, the sack of 3 bushels, the bag of 140 lbs., and the hundredweight of 120 lbs. ; BUTTER is sold by the pound of 18 oz., the pound of 24 oz., the dish of 24 oz., the dish of 22 oz., the pint of 20 oz., and the roll of 24 oz. ; FLOUR is sold by the aigendale of 8 lbs., the gallon of 8 lbs. 1 oz., the pack of 240 lbs., and the sack of 5 bushels; COALS are sold by the long hundred-weight of 120 lbs., the peck of 1,209 cubic inches, the corf of 1 cwt., the corf of 3 cwts., and the corf of " 3 to 4" tons; &c. Grain is sold in Glasgow by the boll, of which there are four varieties-a boll of wheat being 240 lbs., a boll of barley 320 lbs., a boll of oats 264 lbs., and a bolt of Indian corn 280 lbs. In Liverpool, wheat is sold by the bushel of 70 lbs., barley by the bushel of 60 lbs., and oats by the bushel of 45 lbs. Wheat is sold in Bridgend (Wales) by the bushel of 168 lbs., and in Pwlheli (also in Wales) by the bushel of 252 lbs. In Saltash (Cornwall), wheat is sold by the bushel of 8 gallons, and oats by the bushel of 24 gallons. In Manchester, a bushel of English wheat means 60 lbs., and of American wheat 70 lbs. In Preston, barley is sold by the barrel, which means 224 lbs. or 240 lbs., according as the barley is * In 1697 the capacity of the Winchester bushel was fixed at 2150°42 cubic inches a capacity very slightly in excess of 7 Imperial gallons. "for malting" or "for grinding." Grain is likewise sold by the "bag" (7 varieties), by the "load" (6 varieties), by the "hobbet" (5 varieties), by the "weight" (3 varieties), by the "measure" (2 varieties), by the "stack," by the "coombe," by the "windle," by the "strike," &c. 66 It is difficult to reconcile this multiplicity of weights and measures with the fact that a uniform set of standards existed in England before the Conquest, or with the decree of Richard I.—a decree subsequently confirmed by Magna Charta-that there should be but one weight and one measure throughout the realm." Since the middle of the last century, the weights and measures of the United Kingdom have engaged the attention of no fewer than eight Parliamentary Committees, as well as of one or two Royal Commissions, and have been the subject of several legislative enactments. The labours of the last Committee, that sat in 1862, have resulted in the legalisation, by Parliament, of what is called the Metric System, a detailed account of which will be found elsewhere (p. 125). The following couplet, translated (somewhat freely) from the Latin, will hardly be considered an inappropriate termination to this chapter: "One Faith, one Weight, one Measure, and one Coin *The couplet, which is attributed to Budelius, runs thus in the original "Una Fides, Pondus, Mensura, Moneta sit una, 72. The conversion of concrete numbers into others of higher or lower denominations (but of the same kind) is termed REDUCTION. 73. Reduction divides itself into two parts: (a) Descending Reduction, or the reduction of numbers to lower denominations; and (b) Ascending Reduction, or the reduction of numbers to higher denominations. Under the head of Descending Reduction would come the reduction of pounds to farthings, of miles to yards, of acres to perches, &c.; whilst under the head of Ascending Reduction would come the reduction of farthings to pounds, of yards to miles, of perches to acres, &c. 74. An exercise in Descending Reduction is, in most cases, merely a particular application of Simple Multiplication, or of Simple Multiplication and Simple Addition-according as the number to be reduced is simple or compound. An exercise in Ascending Reduction is, in most cases, merely a particular application of Simple Division. DESCENDING REDUCTION. EXAMPLE I.-How many farthings are there in 47 pounds? £47 20 9408. We first reduce the pounds to shillings, by multiplying by 20; next, the shillings to pence, by multiplying by 12; and then the pence to farthings, by multiplying by 4. The number of shillings in one pound being 20, the number in 47 pounds must be 47 times 20, or 20 times 47-that is, 940. The number of pence in one shilling being 12, the number in 940 shillings must be 940 times 12, or 12 times 940-—that is, 11,280. And, the number of farthings in one penny being 4, the number in 11,280 pence must be 11,280 times 4, or 4 45120f. times 11,280-that is, 45,120. So that 47 12 1128od. 4 pounds are equal in amount to 940 shillings, or to 11,280 pence, or to 45,120 farthings. EXAMPLE II.-Reduce £28 148. 5d. to farthings. In 28 pounds there are (28x20=) 560 shillings; therefore, in 28 pounds and 14 shillings there are (560+ 14=) 574 shillings. In 574 shillings there are (574 X 12=) 6,888 pence; therefore, in 574 shillings and 5 pence -or in £28 148. 5d.—there are (6,888 +5) 6,893 pence. In 6,893 pence there are (6,893 X 4 ) 27,572 farthings; therefore, in 6,893 pence and a halfpenny [2 farthings] or in £28 148. 5d. £ s. d. 28 14 5/ 20 5748. 12 6893d. 4 27574f. there are (27,572+2=) 27,574 farthings. The work is shown in the margin. Instead of first setting down the product of 28 by 20, and afterwards adding 14, we as it were combine the two operations-writing 4, the units' figure of the given number of shillings, instead of the units' figure (0) of the product, and adding 1, the tens' figure of the shillings, to the tens' figure (6) of the product. In like manner, when multiplying 574 by 12, we add 5 to the product; "12 fours=48; [48] and 5=53;" &c. And when multiplying 6,893 by 4, we add 2 (the number of farthings in the halfpenny) to the product: "4 threes=12; [12] and 2 =14;" &c. 23 m. 23 8 184 fur. 40 EXAMPLE III.-Reduce 23 English miles to yards. We first reduce the miles to furlongs, by multiplying by 8; next, the furlongs to perches, by multiplying by 40; and then the perches to yards, by multiplying by 5. The number of furlongs in one mile being 8, the number in 23 miles must be 23 times 8, or 8 times 23-that is, 184. The number of perches in one furlong being 40, the number in 184 furlongs must be 184 times 40, or 40 times 184-that is, 7,360. And, the number of yards in one perch being 5, the number in 7,360 perches must be 7,360 times 5, or 5 times 7,360-that is, 40,480: 7360 per. 53 36800 3680 40,480 yds. |