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Ex. 1.–Find the value of .325 of £3. 10s. £3. 10s. = 70s.; proceeding then according to rule, we have:

.325

70
22.750s.

12
9:00d. Ans. : 22s. 9d. or £1. 2s. 9d.

Ex. 2.-Find the value of •546875 of 3 tons. -546875

3 1.640625 tons.

20 12.812500 cwt.

4

3.2500 qrs.

28 200 50

7.00 lbs. Ans.: 1 ton, 12 cwt. 3 qrs. 7 lbs. Ex. 3. Find the value of 6.66875 acres. 6.66875 acres.

4 2.67500 roods.

40 27-000 poles. Ans.: 6 acres, 2 roods, 27 poles. Ex. 4. Find the value of 316 of £1. First Method.

Second Method. £

-316 -3166667 nearly.

20 6.3333340s.

Then by rule for reduction 12

of fractions, 4.000008d. Ans. : 6s. 4d. £%% 6s. 4d. Ans.

The latter method is preferable when perfect accuracy is required.

316 - 31

900 15 X 19 =

15 X 60

2 85
900
19
60

Ex. X.

Find the value of 1. £375; £.98125; £.815625. 2. .416 of £3; 428571 of 6s. 5d. ; 8.571428 of 38. Ozd. 3. •625 of 1 ton; •046875 of 3 tons; 4:39 of 1 cwt. 53 lbs. 4. 1.6671875 acres; •3475 rood; •076923 of 5 acres, 6 poles. 5. •2083 of 1 ream; ·4583 quire; -383 of 3 reams, 12 sheets. 6. •3078125 pipe; •490625 tun; •37125 bushel.

7. Express in grains 142857 of 4 lbs. avoirdupois, and express the result in troy weight.

8. Express 10 oz. 3 dwt. 14 grs. as the decimal of 1 lb. avoirdupois.

9. What is the sum of 6 of 1 guinea, •083 of 1 crown, and 037 of £1. Os. 3d. 10. Find the value of

-20416 x 7.5) 4 ;

cwt. + (-95 ton – 769230 qrs.) * 26. .21875

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another Denomination of the same kind.

31. RULE. --Bring the given quantity to the fraction of the proposed denomination, and reduce this fraction to a decimal.

= 2 X 13

5 X 13

3 qrs. 21 lbs.

2 cwt. 3 qrs.

15 X 7 44 X 7

3.75 =
11

Ex. 1.—Reduce 3s. 3d. to the decimal of 8s. 17d.

3s. 3d. = 26 three-halfpence,

8s. 14d. = 65 three-halfpence, and the fraction

33 을 •4. Hence •4 is the decimal required. Ex. 2.-Reduce 3 qrs. 21 lbs. to the decimal of 2 cwt. 3 qrs.

105 lbs.

308 lbs. and the fraction to

•3409. Hence 3409 is the decimal required. Ex. 3.—Reduce 18s. 87d. to the decimal of £l.

The rule may be applied most concisely as follows :4 1: 12 8.25 20 18.6875

.934375 ... .934375 is the decimal required. The farthing is first reduced to the decimal of a penny, and the 8d. prefixed; then 8.25d. are reduced to the decimal of a shilling, and the 18s. prefixed; lastly, 18.6875s. are reduced to the decimal of £1.

Ex. 4.-Reduce 3 qrs. 21 lbs. to the decimal of 1 ton. 28

57
14 3:

4 3.75
20 .9375

•046875 Hence 046875 is the decimal required.

21

Ex. XI. Reduce

1. 128. 6d., 10s. 74d., 11s. lld., 18s. 64d., each to the decimal of £1.

2. 13s. O d., 10s. 8 d., 9s. 6d., each to the decimal of 15s. 54d.

3. 7s. 8 d. to the decimal of a guinea ; and 3s. 24d. to the decimal of a moidore.

4. 1

qr.

7 lbs. to the decimal of 1 ton; 3 cwt. 3 qrs. 20 lbs. to the decimal of 3 tons.

5. 3} lbs. to the decimal of lucwt. ; 14 oz. to the decimal of 3 cwt. 2 qrs.

6. 20 grs. to the decimal of 1 lb. Troy; 3 dwts. 16 grs. to the decimal of 4 oz. 11 dwts.

7. 1 rood, 10 poles to the decimal of 1 acre; 3 roods, 15% square yards to the decimal of 5 acres.

8. hours to the decimal of 10 weeks; 7 h. 18' to the decimal of 1 year (365 days).

9. Bring the sum of 14 of 9 hours, á of 12} days, 1 of 74 minutes, to the decimal of a week. 10. Express a pound troy as the decimal of a pound avoirdupois.

11. Reduce the sum of 6 lbs. 6. oz. avoirdupois, and 8 oz. 6 dwts. 16 grs. to the decimal of 1 ton.

12. Express 2:36 of 4s. -518 of 9s. 2d. + 1.4583 of 6d. as the decimal of £5.

CHAPTER IV.

THE METRIC SYSTEM.

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32.—The fundamental unit of the metric system is the

1 metre. A metre is the ten-millionth, or 10% part of 90° of the earth's meridian, and measures 39.3708 English inches. In order to express multiples and sub-multiples of this unit, and, indeed, of any unit in the metric system, we make use of one or more of the following prefixes :Deka, . 10 times. Deci,

10th. Hecto, 100 Centi,

100th. Kilo,. 1,000 Milli,

1,000th. Myria,

10,000 We will arrange these prefixes and the word unit in order according to their signification, thus

Myria, Kilo, Hecto, Deka, Unit, Deci, Centi, Milli. Now, as we read this line from left to right, it is evident

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Kilom.

Dekam.

Metres.

Decim.

Millim.

Kilom,

Metre.

Millim.

that the words have a signification decreasing tenfold in value; and as we read it from right to left, they have a signification increasing tenfold in value.

It therefore follows that figures placed under the above words have a local as well as an intrinsic value; and further, if when a figure is wanting to complete the series, its place be filled up by a cipher, it will be seen that the local value corresponds exactly with the ordinary decimal notation.

Moreover, we have only to place a mark in fact, a decimal point) at the right of the figure standing under any of the words of the above memorial line, and the given quantity is at once expressed in the denomination corresponding to that figure. Thus, taking the metre as our unit:

Myriam.

3 2 5 4 7 8 Myriam. Hectom. Dekam.

Decim. Centim.
3 2 0 5 4 7 0 8
= 3.2054708 myriametres.

32.054708 kilometres.
320-54708 hectometres.
3205·4708 dekametres.
32054.708 metres.
320547.08 decimetres.
3205470.8 centimetres.

32054708• or 32054708 millimetres. The following rule for expressing any quantity in terms of any one multiple or sub-multiple of the unit, or of the unit itself, is therefore evident :

RULE.—Put ciphers in the place of any multiple, unit, or sub-multiple absent in the series, and write the figures in close order, as in the ordinary decimal notation. Then place a decimal point at the right of the figure corresponding to the denomination in which we wish to express the given quantity.

Ex. 1.-Express 5 myriam. 3 hectom. 6 decim. as metres.
Filling up with ciphers the vacant spaces, we have-

Myriam.
5 0 3 0 0 6

50300-6 metres.

=

Kilom.

Hectom. Dekam. Metres.

Decim.

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