5. Reduce 3h. 30m. 10sec. to the decimal of a day. Ans. 0.145949074074, &c., of a day.

6. Reduce £3 5s. Od. 2far. to the value of a £.

head.

Ans. £3.252083333, &c.

7. Reduce 28 gallons of wine to the decimal of a hogsAns. 0.4444, &c., of a hogshead. 8. Reduce 4s 6d. to the decimal of a £.

Ans. £0-2270833, &c.

9. Reduce 18s. 34d. to the decimal of a £.

Ans. £0.915625.

10. Reduce 3 pecks, 5 quarts and 1 pint to the decimal of a bushel. Ans. 0.921875 of a bushel.

11. Reduce 11hr. 16m. 15sec. to the decimal of a day. Ans. 0.469618055, &c., of a day. 12. Reduce 20 rods, 4 yards, 2 feet and 6 inches to the decimal of a furlong.

Ans. 0.521969696, &c., of a furlong. 13. Reduce 42m. 36sec. to the decimal of an hour.

Ans. 0·71, of an hour. 14. Reduce 30 days, 3 hours, 27 minutes, 30 seconds, to the decimal of a year of 365-24224 days.

Ans. 0.0827617, &c., of a year.

15. Reduce 5hr. 48m. 49-536sec. to the decimal of a Ans. 0.24224 of a day.

day?

CASE II.

To find the proper value of denominate decimals.

Find the value of 0.778125 of a £.

We first multiplied the decimal of a £ by 20, because 20 shillings make 1 pound; pointing off by the rule for decimals, we found 15s. and 0.5625 of a shilling. Then we multiplied this decimal of a shilling by 12, because 12 pence make 1 shilling; pointing off, we found 6d. and 0·75 of a penny, which being multiplied by 4, because 4 farthings make 1 penny, gave just 3 farthings.

By carefully considering the above operation, we deduce this

RULE.

Multiply the decimal by the number expressing how many of the next lower denomination make a unit of the denomination of the decimal; point off by the usual rule for decimals; multiply the decimal part, thus pointed off, as

before; and so continue to the lowest denomination; the several denominate values sought will appear at the left of the decimal point of the successive products.

Repeat this Rule.

EXAMPLES

1. What is the value of 0.9075 of an acre?

4. What is the value of 0.375 of a hogshead of wine? Ans. 23gal. 2qt. 1pt.

5. What is the value of 0·121212 of a year of 365 days? Ans. 44da. 5hr. 49m. 1.632sec.

6. What is the value of 0.3355 of a pound avoirdupois ? Ans. 5oz. 5·888dr.

7. What is the value of 0.3322 of a ton?

Ans. 6cwt. 2qr. 16lb. 2·048oz.

8. What is the value of 0.2525 of a mile?

Ans. 2fur. Ord. 4yd. 1ft. 2·4in.

9. What is the value of 0.345 of a £?

Ans. 6s. 10d. 3.2far.

10. What is the value of 0·121212 of a day?

Ans. 2hr. 54m. 32-7168sec.

11. What is the value of 0.3456 of a £?

Ans. 6s. 10d. 3·776far.

12. What is the value of 0.9875 of a £?

Ans. 19s. 9d.

13. What is the value of 0·24224 of a solar day?

Ans. 5hr. 48m. 49-536sec.

DUODECIMALS.

100. IN decimals we have seen that the figures decrease in a tenfold ratio, from the left towards the right.

In duodecimals, this decrement goes on in a twelvefold ratio.

The different denominations are the foot (f.) the prime, or inch ('), the second ("), the third (""), the fourth ("""), the fifth (''''''), and so on.

Thus, 7f., 6', 3", 4"", 5'''', is read 7 feet, 6 primes, 3 seconds, 4 thirds, 5 fourths.

The accents used to distinguish the denominations below feet, are called indices.

Taking the foot for the unit, we have the following relations:

ADDITION AND SUBTRACTION OF DUODECIMALS.

101. ADDITION AND SUBTRACTION of duodecimals, are performed like addition and subtraction of other denominate numbers, remembering that 12 of any denomination make one of the next greater denomination.

In decimals how do figures decrease from the left toward the right? In duodecimals how do they decrease? What are the different denominations of duodecimals? What are the accents called which are used to distinguish the different denominations below the foot? How is addition and subtraction of duodecimals performed?

3. What is the sum of 3f. 6' 4", 8f. 3′ 4′′, 9f. 1'′ 3′′, and 10f. 10' 10"? Ans. 31f. 9' 9". 4. What is the sum of 100f. 8' 8", 135f. 0' 1", 65f. 9 2", 45f. 3' 3", and 200f. 6'-6"?

(5.)

Ans. 547f. 3′ 8′′.

(6.)

7. From 25f. 6' 6" subtract 18f. 9' 10".

8. From 100f. subtract 58f. 2′ 1′′.

Ans. 41f. 9′ 11′′.

Ans. 6f. 8′ 8′′.