The 65 shillings are then divided by 20, the number of shillings in a pound, the quotient is £3 and a remainder of 5 shillings. Hence, £3 5s 4d 2 far. is the value of 3138 farthings.

NOTE. The same rules apply to all the denominate numbers.

2. Reduce 3658 inches to yards?

Ans. 101 yards, 1 foot, 10 inch.
Ans. £84.

3. In 80 guineas, how many pounds?
4. In 1549 farthings, how many pounds shillings and

pence?

5. Reduce 1046 pence to pounds. 6. Reduce 4704 pence to guineas. 7. In 6169 pence, how many £?

Ans. £1 12s 31d.

Ans. £4 7s 2d. Ans. 18 guineas 14s. Ans. £25 14s 1d.

PROOF OF REDUCTION.

§ 58. After a number has been reduced from a higher denomination to a lower, by the first rule, let it be reduced back by the second; and after a number has been reduced from a lower denomination to a higher, by the second rule, let it be reduced back by the first rule. If the results agree the work is supposed right.

EXAMPLES.

1. Reduce £15 7s 6d to the denomination of pence.

2. In £31 8s 9d 3 far.; how many farthings? Also the proof.

3. In £87 14s8d: how many farthings? Also the proof. 4. In £407 19s 113d: how many farthings? Also the proof.

TROY WEIGHT.

§ 59. Gold, silver, jewels, and liquors, are weighed by this weight. Its denominations are pounds, ounces, pennyweights, and grains.

Q. What things are weighed by Troy weight? What are its deno minations? Repeat the Table.

EXAMPLES.

1. Reduce 1676. 11oz. 15pwt. to pennyweights.

2. In 25lb. 9oz. Opwt. 20gr.: how many grains?

3. Reduce 6490gr. to pounds.

We first divide by the number of grains in a put.; then by the pwts. in an oz.; then by the ounces in a lb.

Ans. 148340.

OPERATION.

24) 6490

20)270 10gr. remainder. 12)13.. 10pwt. remainder

1.. 1oz. remainder. Ans. 1lb. 1oz. 10pwt. 10gr.

4. In 678618 grains, how many pounds?

Ans. 1177b. 9oz. 15pwt. 18gr.

5. Reduce 8794pwt. to pounds.

Ans. 867b. 7oz. 14pwt.

APOTHECARIES' WEIGHT.

§ 60. This weight is used by apothecaries and physicians in mixing their medicines. Its denominations are pounds, ounces, drams, scruples, and grains. The pound and ounce are the same as the pound and ounce in the Troy weight; the difference between the two weights consists in the different divisions and subdivisions of the

ounce.

TABLE.

20 grains, gr. make 1 scruple, marked 9.
3 scruples - 1 dram,

3.

Q. What is the use of the Apothecaries' weight? What are its denominations? Of what value are the pound and the ounce? Repeat the Table.

EXAMPLES.

1. Reduce 9 83 63 29 12gr., to grains.

We first multiply by the number of ounces in a lb., and at the same time add in the ounces. We next multiply by the number of drams in an ounce and add in the drams: we then multiply by the number of scruples in a dram and add in the scruples; and lastly, we multiply by 20 and add in the grains.

OPERATION.

9

12

116 ounces.
8

934 drams.
3

2804 scruples.
20

Ans. 56092 grains.

2. Reduce 27 93 63 19 to scruples.

8. Reduce 94 113 13 to drams.

Ans. 8011 scruples.

Ans. 9113 drams.

4. In 56092 grains, how many pounds?

We first divide by 20, the number of grains in a scruple: then by 3 the number of scruples in a dram then by 8 the number of drams in an ounce; and lastly by 12, the number of ounces in a pound.

OPERATION.

20)560912
3)2804.. 12gr
8) 934..29.
12) 116.. 63.
91 83.

Ans. 91 83 63 29 12gr.

5. Reduce 24033 grains to pounds.

Ans. 4 23 0z 19 13gr.

6. Reduce 32044 scruples to pounds.

Ans. 111 33 13 19.

AVOIRDUPOIS WEIGHT.

§ 61. By this weight are weighed all coarse articles, such as hay, grain, chandlers' wares, and all the metals, excepting gold and silver.

Its denominations are tons, hundreds, quarters, pounds, ounces, and drams.

In this weight the words gross and net are used. Gross is the weight of the goods, with the boxes, casks, or bags, in which they are contained. Net is the weight of the goods only; or what remains after deducting from the gross weight, the weight of the boxes, casks, or bags.

A hundred weight is 112 pounds, as appears from the Table. But at the present time, the merchants in our principal cities, buy and sell by the 100 pounds.

TABLE.

16 drams dr. make 1 ounce, marked 0%.

Q. What articles are weighed by this weight? What are its denominations? What does gross mean? What does net mean? What is a hundred weight? How do they buy and sell in the principal cities? Repeat the Table.

EXAMPLES.

1. Reduce 5T. 8cwt. 3qr. 24lb. 13oz. 14dr. to drams.

2. Reduce 27T. 17cwt. 29qr. 21lb. to ounces.

3. Reduce 94T. 19cwt. 1qr. to quarters. 4. Reduce 3124446 drams to tons.

Ans. 1011472oz.
Ans. 7597gr.

3X4+2-14dr.

4)48819 1

4x4=16

{

4x7=28

{

7)3051

4)12204...3×4+1=130%.

4)435...6×4=247b.

20)1018...3qr.

5 ... 8cwt.

Ans. 5T. 8cwt. 3qr. 24lb. 13oz. 14dr.

5. Reduce 108910592 drams to tons.

Ans. 189T. 18cwt. 2qr.

6. Reduce 2998128 ounces to tons.

Ans. 83T. 13cwt. Oqr. 7lb.