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 2724 square feet X 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 hundred-weight 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. I oz., the pack of 240 lbs., and the sack of 5 bushels; and 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 cwt., and the corf of " 3 to 4" tons.

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 boll 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 "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

In 1697 the capacity of the Winchester bushel was fixed at 2150.42 cubic inches-a capacity very slightly in excess of that of 7 Imperial gallons.

A new standard, called the centner, representing a weight of 100 lbs., was lately introduced into the Liverpool corn-market.

66

"stack," by the "coomb," by the "windle," by the strike,"

&c.

It is difficult to reconcile this multiplicity of weights and measures with the fact that a uniform set of standards existed 'n England before the Conquest, or with the decree of Richard 1.—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 nd measures of the United Kingdom have engaged the attenon 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 legalization, by Parliament, of what is called the Metric System, a detailed account of which will be found farther on.

REDUCTION.

70. The conversion of concrete numbers into others of higher or lower denominations (but of the same kind) is termed REDUCTION.

71. Reduction divides itself into two parts: (1.) Descending Reduction, or the reduction of numbers to lower denominations; and (2.) Ascending Reduction, or the reduction of numbers to higher denomi

nations.

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.

72. An exercise in Descending Reduction is 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 a particular application of Simple Divi

sion.*

In the reduction of perches to yards, or of yards to perches, both multiplication and division have to be employed.

DESCENDING REDUCTION.

EXAMPLE I.—How many farthings are there in 47 pounds?

£47

20

940s.

12

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 times 11,280-that is, 45,120. So that 47 pounds are equal in amount to 940 shillings, or to 11,280 pence, or to 45,120 farthings.

11280d.

4

45120f.

EXAMPLE II.-Reduce £28 14s. 5d. to farthings.

d.

£ s. 28 14 52

20

5748.

12

6893d.

In 28 pounds there are (28 x 20=)560 shillings; therefore, in 28 pounds and 14 shillings there are (560+14-)574 shillings. In 574 shillings there are (574X12=)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 X4 )27,572 farthings; therefore, in 6,893 pence and a halfpenny [2 farthings]— or in £28 14s. 5d.-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.

4

27574f.

EXAMPLE III.-Reduce 23 miles to yards.

23 m.

8

184 fur.

40

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 184that 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: 5 times 7,360 36,800; one-half of 7,360(7,360+2)3,680; 5 times7,360 (368,800 +3,680=)40,480. So that 23 miles are equal in length to 184 furlongs, or to 7,360 perches, or to 40,480 yards.

7360 per.

52

36800

3680

40480 yds.

m. fur. per. yds.

17 6 28 4 8

EXAMPLE IV.-Reduce 17 m. 6 fur. 28 per. 4 yds. to yards. In 17 miles there are (17X8=) 136 furlongs; therefore, in 17 miles and 6 furlongs there are (136+6=) 142 furlongs. In 142 furlongs there are (142X40=) 5,680 perches; therefore, in 142 furlongs and 28 perches-or in 17 m. 6 fur. 28 per.there are (5,680+28=) 5,708 perches. In 5,708 perches there are (5,708 × 53—) 31,394 yards; therefore, in 5,708 perches and 4 yards—or in 17 m. 6 fur. 28 per. 4 yds. there are (31,394+4=) 31,398 yards. In practice, we add the 4 yds. to 5 times 5,708, and then add the half of 5,708 to the result.

142 fur.
40

5708 per.

51

28544

2854

31398 yds.

73. Rule for Descending Reduction: Reduce the highest denomination to the next lower, by multiplying by the number indicating how many units of the lower denomination are contained in one of the highest; and to the product add as much of the given number as belongs to this lower denomination. Treat the result in the same way, and continue the process until the required denomination is obtained.

ASCENDING REDUCTION.

EXAMPLE I.-Reduce 45,120 farthings to pounds.

4)45120f.

12)11280d.

We first reduce the farthings to pence, by dividing by 4; next, the pence to shillings, by dividing by 12; and then the shillings to pounds, by dividing by 20. If the farthings were formed into penny packages, each package would contain 4, and the total number of such packages would be (45,120÷4=)11,280; so that 45,120 farthings are worth 11,280 pence. Again: if the pence were formed into shilling packages, each package would contain 12, and the total number of such packages would be (11,280÷12=) 940; so that 11,280 pence are worth 940 shillings. In like manner, if the shillings were formed into pound packages, each package would contain 20, and the total number of such packages would be (940÷20= so that 940 shillings are worth 47 pounds. We thus find that 45,120 farthings, 11,280 pence, 940 shillings, and 47 pounds are all equal in amount.

201940s.

£47

EXAMPLE II.-Reduce 27,574 farthings to pounds.

4)27574ƒ.

=)47;

12)68931⁄2d.

Dividing by 4, we find that in 27,574 farthings there are 6,893 pence, and two farthings or one halfpenny over. Dividing by 12, we next find that in 6,893 pence there are 574 shillings, and 5 pence over. Lastly, dividing by 20, we find that in 574 shillings there are 28 pounds, and 14 shillings over. So that 27,574 farthings are equal in amount to 6,893 pence, or to 574 shillings and 51⁄2 pence, or to £28 14s. 5d.

20)5748. 5 d.

£28 148. 5d.

NOTE. We reduce shillings to pounds in this way we first convert the shillings into half-sovereigns, by dividing by 10; and then the half-sovereigns into pounds, by dividing by 2. In dividing by 10, we simply "cut off," for remainder, the most right-hand figure of the dividend, and take the remaining figure or figures for quotient. Thus, 940 shillings [Ex. I.] are equal in amount to (940÷10=) 94 half-sovereigns, which are equivalent to (94÷2=) 47 pounds. In like manner, 574 shillings [Ex. II.] are equal in amount to (574÷10) 57 halfsovereigns and 4 shillings, or to £28 14s.,-57 half-sovereigns being equivalent to (57÷2) 28 pounds and I half-sovereign, or to £28 10s.