10. What is the value of 0.121212 of a day?

Aps. 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 quodecimals? 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", 8ƒ. 3′ 4′′, 9f. 1′ 3′′, and .Of. 10' 10"?

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

Ans. 547f. 3′ 8′′.

10f. 4

Remainder 51f. 6′ 7′′

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

8. From 100f. subtract 58f. 2′ 1′′.

Ans. 6f. 8′ 8′′. Ans. 41f. 9' 11".

MULTIPLICATION OF DUODECIMAL 8.

102. SUPPOSE we wish to multiply 14f. 7' by 2f. 3 we should proceed as follows:

14f. 7'

2f. 3'

3f. 7' 9" 29f. 2'

Ans. 32f. 9′ 9′′=32f+1 of a foot+ of a fool

EXPLANATION.

We begin on the right hand, and multiply the multiplicand through, first by the primes of the multiplier, then by the feet of the multiplier, thus: 3'x7'-x=2 of a foot, which is 21"-1′9′′; we write down the 9′′, and reserve the 1' for the next product; again, 14f. x3'=14x

of a foot, which is 42'; now adding in the 1', which was reserved from the last product, we have 43′= 3f. 7', which we write down, thus finishing the first line of products.

Again, we have 2f. x7'=2x

of a foot, which

is 14'1f. 2'; we write the 2' under the primes of the line above, and reserve the 1f. for the next product; 2f.× 14f. 28f., to which, adding in the 1f. reserved from the last product, we have 29f, which we place underneath the feet of the line above. Taking the sum, we find 32f. 9'9", for the answer.

From the above we infer, that if we consider the index

of the feet to be 0, then the denomination of each product will be denoted by the sum of the indices of the factors.

Thus, feet by feet, produces feet; feet by primes, produces primes; primes by primes, produces seconds, &c. Hence, to multiply a number consisting of feet, inches, seconds, &c., by another number consisting of like quan tities, we have this

RULE.

Place the several terms of the multiplier under the cor responding ones of the multiplicand. Beginning at the right hand, multiply the several terms of the multiplicand by the several terms of the multiplier successively, placing the right-hand term of each of the partial products under its multiplier; then add the partial products together, observing to carry one for every twelve, both in multiplying and adding. The sum of the partial products will be the answer,

Repeat this Rule.

EXAMPLES.

1. What is the product of 3f. 7' 2" by 7f. 6' 3"?

2. Multiply 7f. 8' by 6f. 4′ 3′′?

Ans. 48f. 8' 7". Ans. 28f. 3′ 11′′ 2′′".

3 Multiply 6f. 9′ 7′′ by 4f. 2' ? 4. What is the area of a marble slab, whose length is 7f. 3', and breadth 2f. 11'? Ans. 21f. 1′ 9′′. 5. How many square feet are contained in the floor of a hall 37f. 3' long, by 10f. 7' wide? Ans. 394f. 2′ 9′′.

6. How many square feet are contained in a garden 100f. 6′ in length, by 39f. 7′ in width? Ans. 3978f. 1′ 6′′. 7. How many yards of carpeting, one yard in width, will it require to cover a room 16ƒ. 5′ by 13ƒ. 7' ? Ans. 24yd. 6f. 11′ 11′′.

REDUCTION OF CURRENCIES.

103. Before the adoption of Federal money in this country, accounts were generally kept in the denominations of English money. Different States considered the pound as having different values, as given in the following

TABLE.

$1 in England 4s. 6d. £, called Sterling money. 5 South Carolina 4s. 8d.£, called Georgia

81 in {Georgia

$1 in

Canada
Nova Scotia S

}

=

currency.

5s., called Canada cur

rency.