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and then the ounces by 12, because 12 ounces make 1 pound. How do you reduce tuns to pounds? A. First multiply by 20, because each tun will make 20 hundred weight, and then multiply by 4, because each hundred contains 4 quarters, and lastly, by 28, because each quarter contains 28 pounds. How do you reduce guineas to pounds ? A. Multiply the guineas by 28, and the product will be shillings, and then divide the shillings by 20, and the quotient will be pounds. How do you reduce pounds to moidores? A. Multiply the pounds by 20, and the product will be shillings, and then divide the shillings by 36, and the quotient will be moidores. Suppose a barrel of wine is to be racked off, in pint bottles, quart bottles, and 2 quart bottles, and an equal number of each is required; how would you proceed to tell the number of bottles required to hold the wine ? A. Add, in one sum, the number of pints that would fill the bottles once, for the divisor, and then reduce the barrel to pints for a dividend, and the quotient would show how often the bottles could be filled.

COMPOUND ADDITION, Is collecting together two or more numbers of different denominations in one sum.

RULE.—Place the numbers, so that those of the same denominarion may stand directly under each other. Then add the right hand denomination the same as a sum in simple addition, and divide the amount by as many as it takes of that.denomination to make a unit in the next higher denomination ; set down the remainder under the denomination added, and carry the quotient to the next higher denomination;, and so proceed with all the denominations until you come to the left hand denomination, and there set down the whole amount the same as in simple addition.

PENCE TABLES.

s. d. 1. shilling is 120.
20
1 8 2

24
30
2 6 3

36
3 4 4

48
50
4 2 5

60
60
5 0 6

72
70
5 10 7

84
80
6 8 8

96
90
7 6 9

108
100
8 4 10

120 110 9 2 11

132 120

10
12

144 Note.—The principles in compound quantities do not essentially differ from those of abstract numbers, that is, simple, refined, pure, riot broken numbers. In the one case, we carry by 10; in the other, bv the number of units which it takes to equal a unit in thn

pence is

40

S.

d. yrs.

denomination; so that the student will find the work easy, if he has acquired a knowledge of the tables, and will only keep in mind the rule given for the operation of the work. Yet it is to be regretted, that the wisdom of our legislature, has never reduced compound quantities to the decimal system, which would greatly simplify the operations of work in arithmetick. The French have reduced all compound quantities to the decimal scale, except the division of time, which does not appear to be capable of change. A wise policy may dictate never to adopt hastily a new system ; but after the utility of a system has become obvious, neither national pride por narrow prejudices should prevent its adoption; no matter by what individual or individuals the system may have been simplified, or by what nation adopted, the benefits are the same.

EXAMPLES.

STERLING MONEY. 1. In £41 13s. 6d. 2qrs., £48 11s. 4d. 3qrs., £96 16s. 10d. 3qrs.; how many pounds, shillings, pence, and farthings, when added together? £

DEM.—We first add the denomina41 13 6 2

tion of farthings, and find it amounts

to 8, which we divide by 4, because 48 11 4 3

4 farthings are equal to one penny, 96 16 10 3 and we find that the quotient is 2, £187 1 10 O Ans.

and the remainder a cipher; so we.

set down the cipher and carry ? to the pence, the next higher denomination, because inė 8 farihings are equal to ? pence; by adding the pence, we find the amount 22, which we divide by 12, because it takes 12 pence to make a shilling, and the quotient is 1, and the remainder 10; we set down 10 under the column of pence, and carry the quotient, which is 1 shilling, tò the shillings; and in adding the shillings, we find they amount to 41, which we divide by 20, because it takes 20 shillings to make 1 pound, we find the quotient 2, and the remainder 1, which we set down under shillings, and carry the quotient, which is pounds, to the pounds; and in adding the left hand denomination, we carry the same as in simple work, and set down the whole amount in adding the left hand column. In all other sums in compound addition we observe the same rules ; always carrying by that number which is equal to’a unit in the next higher. Proof, the same as in simple work, only carry as in the first adding. 2. 3.

4.
£
d.

£
d.
£

d.
44 13 6
63 11 6

63 16 11 38 17 8 84 9 11

89 11 10
19 10 11
110 16 8

67 14 9
16
130 11 10

111

16 10 £120 0 11 Ans.

S.

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18

10

5. What is the amount of £47 !6s. 11d. 3qrs., £105 14s. 11d. 2qrs., £89 18s. 4d. Iqr., and £844 13s. 10d. Oqrs., when added ?

Ans. £1088 4s. 1d. 2qrs. 6. What is the amount of one hundred and five pounds, fourteen shillings, sixpence, one farthing; eighty-four pounds, ten shillings, four pence, three farthings; and five hundred pounds, fifteen shillings, ten pence, three farthings, when added together?

Ans. £691 Os. 9d. 3qrs. 7. What is the amount of 2s. 6d., 4s. 8d., 9s. 3d., 4s. 9d.?

Ans. £1 1s. 2d. 8. A man bought a wagon for £18 16s. 8d., a plough for 2 10s., a span of horses for £55 10s. 6d. ; what must he pay for the whole ?

Ans. £76 17s. 2d. 9. Three men found a prize, and having divided it equally among them, each man received £18 4s. Id.; what was the amount of the prize ?

Ans. £54 12s. 3d. TROY WEIGHT. 1, 16. oz. pwts. g1::

Note.„Observe to carry by 36 11 10 24 from grains to pennyweights, 34 5 8 15 and by 20 from pennyweights to

81 8 18 14 ounces, and by 12 from ounces to Ans. 1529 15

pounds.-Proof may be performed

by adding downwards.
2.
3.

4.
lb. oz. put. gr.
16. oz. pvt. gr.

16. oz. prot. gr. 39 8 10 21 81 10 18 22 63 10 11 19 84 9 11 18 18 11 10 19 18 10 9 3 13 6 15 17 66 10 15 16 6 7 4 4

18

5. Bought a set of silver spoons weighing ilb. 1oz. 9pwts. 17 grs., a silver cup weighing 5oz. 10pwts. 14grs., and a silver tankard weighing ilb. 11oz. 7grs.; what was the weight of the whole ?

Ans. 3}b. 6oz. Opwts. 14grs. AVOIRDUPOIS WEIGHT. 1. T. cwt. qr. lb.

oz. dr.

Note.--We carry from 13 12 1 15 6 11

drachms to ounces by 16, be

cause 16 drachms make an 14 14 3 24 9 10

ounce, and from ounces to 18 15 2 11 15 11

pounds by 16, because 16 ounAns. 47 2 3 24 0 0

ces make a pound; and from pounds to quarters by 28, be

cause 28 pounds make a quarter; and from quarters to hundreds hy 4,
because 4 quarters make a hundred; and from hundreds to tuns by 20,
because 20 hundred make a tun.
2.

3
16.
oz. dr.

cwt. qrs. lb. oz. dr.
18 3 16 5 14

180 1 16 11 12 105 2 26 14 13

14 2 15 10 13 .108 3 16 11 11

14 1 15 15 14 64 1 13 10 15

2 27 11 15

cwt. qrs.

4. Bought 4 fat oxen, weighing as follows, viz., 12cwt. 3qrs. 161b., 13cwt. 2qrs. 12lb. 13oz., 15cwt. lqr. 21 lb. lloz., 16cwt. 1qr: 241b. 8oz.; what was the weight of the whole in tuns?

Ans. 2T. 18cwt. lqr. 19lb. APOTHECARIES' WEIGHT. 1. 2.

3. oz. dr. sc. gr.

Ib. oz. dr. sc. gr. 5 1 15 10 7 2 18 10 11 6 1 14 6 2 18

9. 6 1 19 13 10 5 2 18 4 0 17 11 3 2 18 11. 11 4 1 11 oz. 6 2

11 10 5 1 17 7 9 3 0 10 Ans. 2 7

1

dr. sc. gr.

CLOTH MEASURE. 1.

2.

DEM.--It is evident, yds. qrs. No yds. qrs. n. that we must carry by 44 3 2 546 2 3

4 from nails to quar53 1 1

1
2 ters, because 4 nails

make a quarter; and 11 3 3 36 2 1

by 4 from quarters to 14 1 3

1 3 1

-yards, because 4 quar

ters make a yard. Ans. 124 2 1

46

6.

E. Fr. qr. n.

3.

4. Yds. a. . E, F. TT. .. 36 1 3 41 2 3 44 2 1 36 1 2 55 2 3 44 2 1 68 1 2 36 1 3

5. E.E. gr. n.

84 3 3 68 3 2

1 4 1 6 1 3

38 3 3 98 5 2 36 3 2 54 4 3

7. Bought 4 pieces of cloth, the first 96yds. 3qrs. 2n.;

the second 84yds. 3qrs. 3n.; the third 75yds. Igr. 2n. ; the fourth 96yds. Iqr. 1n.; how much did the four pieces contain ?

Ans. 353 yards.
LONG MEASURE.
1.

2
Deg. m. fur.rd. ft. in. b.C. Deg. m. fur. rd.ft. in. 6.c.

63 44 30 14 10 2 79 65 7 13 11 10 1
56 54 7 35 11 6 2 34 65 6 35 14 11 2

10 57 6 16 7 8 I 84 55 6 14 15 11 2
Ans. 131 18 5 3 1 1 2
3.

Note.—When halves or fracDeg. m.fur. rd.yds. ft. in. b.c.

tions occur with the remainder

after the division, they must be 84 65 6 35 4 2 6 2

carried back in the inferiour de95 55 7 14 5 1 11 1

nominations according to the 37 1 2 0 0 2 3 2 value; and if by carrying back

it increases the inferiour de

nominations so as to equal a unit, or exceed a unit, at the left, a unit must then be added to the superiour, and the excess set down in its proper place; for fractions must never be placed in a sum, when there are denominations at the Fight.

LAND, OR SQUARE MEASURE.
1.

DEM.—In adding the inches, we
Pol. ft. in.

find they amount to 340 inches, which

contain 144 twice, and 52 remain, 19 180 135

which we retain, and carry the 2 to the 25 250 120 feet; we find the feet amount to 523, Rood. 13 90 85 which we divide by 2721, which we Ans. 1

find contained once, and 2491 remain, 18 250 16 and as we cannot set down a fraction

in the superior denominations, we reduce the of a foot to inches, which produce 108 inches, and the 52 inches added which was our remainder in inches, we have 160 inches, which are equal to 1 foot and 16 inches; we then set down the 16in. under inches, and add the foot to 249 feet, which gives 250 feet, which we place under feet, and carry 1 to the poles, and by adding we nnd the poles amount to 58, which divided by 40, the number of poles in a rood, gives 1 rood and 18 poles.

A. rds. pol. ft. in. A. rds. pol. ft.
75 3 37 245 30

87 2 39 150 87 1 37 75 114

185 3 36 27 415 3 18 69 135

19 1 7 9

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