2. What is the present worth of a freehold estate of 290 dollars per annum, to continue for ever, allowing 4 per cent. to the purchaser? Ans. 7250dols.

PERPETUITIES IN REVERSION.

CASE 1.

The rent of a freehold estate, time of reversion, and rate per cent. given, to find the present worth:

RULE.

Multiply the ratio involved to the time of reversion, by the ratio, less one, for a divisor; by which divide the yearly payment, the quotient will be the answer..

EXAMPLES.

1. If a freehold estate of 50L. per annum, to commence 4 years hence, be put up at sale, what is the present worth, allowing the purchaser 5 per cent.?

Ans. 822L. 14s. 1d. 2qrs. +

Ratio involved to the time? of reversion, viz. 4 years S

1.2155062

.05 ratio less one.

.060775310)50(8227. 14s. 1d. 2q.+ 2. What is an estate of 696dols. per annum, to continue for ever, but not to commence till the expiration of 4 years, worth in present money, allowance being made at 4 per cent. Ans. 14873.594dols.

PERMUTATION.

Permutation is a rule for finding how many different ways any given number of things may be varied in position, place, or succession; thus, a b c, ac b, ba c, bca, cab, cb a, are six different positions of three letters.

RULE.

Multiply all the terms of the natural series continually from one to the given number inclusive; the last product will be the answer required.

R

EXAMPLES.

1. In how many different positions can 6 persons place themselves at a table? 1x2×3×4x5x6-720. Ans. 2. How many days can 7 persons be placed in a different position at dinner? Ans. 5040 days. 3. What number of changes may be rung upon 12 bells, and in what time may they be rung, allowing 3 seconds to every change.

Ans.

S479001600 changes.

45 years, 195 days, 18 hours.

COMBINATION.

• Combination is a rule for discovering how many different ways a less number of things may be combined out of a greater; thus out of the letters a, b, c, are three different combinations of two; viz. ab, ac, bc.

RULE.

Take a series proceeding from and increasing by a unit, up to the number to be combined; and another series of as many places decreasing by a unit, from the number out of which the combinations are to be made, multiply the former continually for a divisor, and the latter for a dividend, the quotient will be the answer.

EXAMPLES.

1. How many combinations can be made of 5 letters out of ten?

10x9x8x7x6

-252. Ans.

1×2×3×4x5

2. How many combinations can be made of 6 letters out of 10?

Ans. 210.

3. What is the value of as many different dozens as may be chosen out of 24, at 1d. per dozen.

Ans. 11267L. 6s. 4d.

DUODECIMALS.

Duodecimals are fractions of a foot, or of an inch, or parts of an inch, &c. having 12 for their denominator.

The denominations are, foot, inch, second, third,

4. Four floors in a certain building contain each 1084 feet, 9in. 8"; how many feet are there in all?

Ans. 4339ft. 2in. 8".

5. There are six mahogany boards, the first measures 27ft. 3in. the second, 25ft. 11in. the third, 23ft. 10in. the fourth, 20ft. 9in. the fifth, 20ft. 6in. and the sixth, 18ft. 5in.; how many feet do they contain? Ans. 136ft. 8in.

SUBTRACTION OF DUODECIMALS.

4. If 19ft. 10in. be cut from a board which contains 41ft. 7in. how much will be left?

Ans. 21ft. 9in.

5. Bought a raft of boards containing 59621ft. 8in. of which are since sold three parcels, each 14905ft. 5in. many feet remain? Ans. 14905ft. 5in. MULTIPLICATION OF DUODECIMALS.

how

CASE 1.

When the feet of the multiplier do not exceed 12.

RULE.

Set the feet of the multiplier under the lowest denomination of the multiplicand, as in the following example; then multiply as in Compound Multiplication by each denomination of the multiplier separately, observing to place the right hand figure, or number, of each product, under that denomination of the multiplier by which it is produced.

Note 1.-If there are no feet in the multiplier, supply their place with a cipher; and in like manner supply the place of any other denomination between the highest and lowest."

2. Feet multiplied by feet, give feet.

Feet multiplied by inches, give inches. Feet multiplied by seconds, give seconds. Inches multiplied by inches, give seconds. Inches multiplied by seconds, give thirds. Seconds multiplied by seconds, give fourths. *** It may be remarked that though the feet obtained by this rule are square feet, the inches are not square inches, but twelfth parts of a square foot.

CASE 2.

When the feet of the multiplier exceed 12.

RULE.

Multiply by the feet of the multiplier as in Compound Multiplication, and take parts for the inches, &c.

EXAMPLES.

1. Multiply 112ft. 3in. 5" by 42ft. 4in. 6".

1. A certain board is 28ft. 10in. 6" long, and 3ft. 2in. 4" wide; how many square feet does it contain? Ans. 92ft. 2in. 10" 6". 2. If a board be 23ft. 3in. long, and 3ft. 6in. wide, how many square feet does it contain?

Ans. 81ft. 4in. 6". 3. A certain partition is 82ft. 6in. by 13ft. 3in. how many square feet does it contain? Ans. 1093ft. lin. 6". 4. If a floor be 79ft. 8in. by 38ft. 11in. how many square feet are therein? Ans. 3100ft. 4in. 4". Note.-Divide the square feet by 9, and the quotient. will be square yards.

5. If a ceiling be 59ft. 9in. long, and 24ft. 6in. broad, how many square yards does it contain?

Ans. 162yd. 5ft. + 6. What will the plaistering of a ceiling come to, at 10d. per yard, supposing the length 21ft. Sin. and the

breadth 14ft. 10in.?

Ans. 1L. 9s. 9d.