24. A ball 12 in. diameter weighs 30 lb., what will a ball weigh whose diam. is 18in.? Ans. 101 lb. 25. A cubic foot of marble weighs 2742 oz. ; find the weight of another cube whose side measures 25 in. Ans. 24793211 oz.

26. Required the side of a cubical vessel that will contain 100 imperial gallons. Ans. 30-267 in.

DUODECIMALS.

Duodecimals denote the division of the integer in a twelve-fold proportion.

TABLE OF LINEAL MEASURES.

//// 12 fourths 1 third.

=

" 12 thirds 1 second.

=

" 12 seconds 1 inch.

12 inches = 1 foot.

NOTE 1.-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, &c.

2. It is of the highest importance to remember that 12 1 lineal foot, 144 sq. in. 1 sq. ft., 1728 cub. in. =1 cub. ft., 3 lineal ft. = 1 lineal yd., 9 sq. ft. =

in.

27 cub. ft.

1 cub. yd.

=

1 sq. yd., and

MULTIPLICATION OF DUODECIMALS.

RULE. Place the multiplier under the multiplicand, feet under feet, inches under inches, &c.-Multiply each denomination of the length by the feet in the breadth, and place each product under the denomination of the multiplicand from which it arises, always carrying 1 for every 12.-Then multiply by the inches, and set each product one place farther to the right; next multiply by the seconds, and set each product another place toward the right, &c.-The sum of the several lines of products is the answer.

MENSURATION.

Find the product of

6 f. 3′ 2′′ x 7 f. 9'
12 f. 10' 1" x 11 f. 10'
6 f. 4' 7" x 6 f. 7′ 3′′
108 f. 7' x 5 f. 7' 8"
10 f. 4' 5" x 3 f. 10′ 3′′
6 f. 4′ 7′′ × 6 f. l′ 2′′
48 f. 7' x 36 f. 6'

56 f. 1' 4" x 48 f. 3′ 6′′

Ans. 48 f. 6′ 6′′ 6'"

151 f. 11' 3" 10" 42 f. 1' 9" 2""" ""

612 f. 3' 5" 8" 39 f. 11' 6" 3"" 3"""" 38 f. 10' 11" 4"′′ 2′′" 1773 f. 3' 6" 2709 f. 8' 4" 8"

To find the area of a rectangular surface. RULE—Multiply the length by the breadth.

To find the content of a rectangular solid. RULE.-Multiply the length, breadth, and thickness,

together.

1. How many sq. ft. in a deal 5 ft. 9' long and 1 ft. 3' broad? Ans. 7 ft. 2′ 3′′.

2. How many sq. ft. in a plank 57 ft. 8' long and 2 ft. 7' 3" broad. Ans. 150 ft. 2' 1".

3. How many sq. ft. in a window whose height is 7 ft. 8'6", and width 4 ft. 9′ 8′′? Ans. 37 ft. 6′′ 2′′".

4. Find the content and cost of a marble slab 5 ft. 7' long, and 3 ft. 8' broad, at 6s. per sq. ft. Ans. 20 ft. 5' 8"; cost £6, 2s. 10d.

5. Find the content and cost of a fir plank 31 ft. 7' long, and 1 ft. 2' broad, at 1s. 3d. per sq. ft. Ans. 36 ft. 10' 2"; cost £2, 68.0 d. §

6. Find the content and cost of 16 squares of glass, each measuring 2 ft. 11' by 2 ft. 5', at 44d. per sq. ft. Ans. 112 ft. 9' 4"; cost £2, 2s. 34d.

7. Find the cost of glazing 8 windows, each 6 ft. high and 3 ft. 5′ wide, at 84d. per sq. ft. Ans. 164 ft.; cost £5, 16s. 2d.

8. What is the value of a sash window 6 ft. 10' high and 3 ft. 8' wide, at 3s. per sq. ft.? Ans. 25 ft. 8"; cost £3, 15s. 2d.

9. Find the expense of paving a court 40 ft. 6 in. long, and 25 ft. broad, at 3s. 74d. per sq. yd. Ans. £20, 7s. 9 d.

10. How many roods of mason-work in a wall 50 ft. 6 in. long, and 24 ft. 3 in. high, and what will it cost at £2, 2s. per rood? Ans. 3 ro. 28 yd. 7′ 6′′ ; cost £7, 18s. 8 d. §.

11. A rubble wall is 375 ft. long, and 13 ft. 7 in. high; find the expense of materials and workmanship at £3, 18s. per rood. Ans. £61, 6s 31d. §. 12. What is the expense of a pavement floor 27 ft. 9 in. long, and 16 ft. 6 in. broad, at 1s. 14d. per sq. ft.? Ans. £19, 16s. 3d. 32.

13. Find the price of 4 logs of wood each 35 ft. 6' long, and 1 ft. 10' the side of the square, at 2s. 6d. per cub. ft. Ans. £59, 13s. 24d. §.

14. Find the value of 100 logs of oak each 17 ft. l' long, and 1 ft. 8' the side of the square, at 4s. 6d. per cub. ft.? Ans. £1067, 14s. 2d.

MISCELLANEOUS QUESTIONS.

1. A merchant, who hadowing him £1000,8s. 9d. received at one time £103, 14s. 4d., at another £112, 10s. 6 d., and at a third time £258, 8s. 51d.; what remains due to him? Ans. £520, 15s. 4 d.

2. Bought 4 tons 6 cwt. 1 qr. of sugar, and sold at one time 1 ton 20 lb., and at another 1 ton 10 cwt. 1 qr. 4 lb. 14 oz.; what remains? Ans. 1 ton. 15 cwt. 3 qr. 3 lb. 2 oz.

3. Find the sum of 3 lb. 4 oz. 15 dwt.; 43 lb. 7 oz. 8 dwt.; 9 lb. 10 oz. 16 dwt.; 83 lb. 4 oz. 8 dwt.; 63 lb. 4 oz. 18 dwt. ; 50 lb. 1 oz. 19 dwt.; and 77 lb. 6 oz. 10 dwt. Ans. 331 lb. 4 Oz. 14 dwt.

4. Required the area of Fifeshire, if the cultivated lands amount to 206347 acres, the uncultivated to 79352 acres, and the unprofitable to 36861 acres. Ans. 322560 acres.

5. If the area of Fifeshire be 322560 acres, and the number of its inhabitants 129024, how many acres are there on an average to each person? Ans. 2 ac. 2 ro.

6. Bought a piece of muslin containing 24 yd., and sold to two young ladies 9 yd. 1 qr. 3 nl. each for a dress; what quantity remains? Ans. 5 yd. 2 nl.

7. Find the weight of 17 casks of sugar, each weighing 8 cwt. 3 qr. 11 lb. Ans. 150 cwt. 1 qr. 19 lb.

8. How many galls. in 47 casks, each containing 7 galls. 1 pt.? Ans. 334 galls. 3 qt. 1 pt.

9. Divide £11, 19s. 9d. equally among 12 men? Ans. 19s. 112d. to each.

10. A mason bought a hammer weighing 9 lb. at 7d. per lb., and 3 dozen of irons at 11d. each; required the cost of the whole? Ans. 1, 18s. 3d.

11. A builder paid 16 masons 18s. each, 4 apprentices 6s. each, and 3 labourers 14s. each, for their week's wages; how much money was paid in all? Ans. £17, 14s.

12. A certain person was born on 6th April 1810, and commenced to serve an apprenticeship on the 8th of June 1824; how old was he then, and how much money had been laid out for him, at the rate of 4. per day, for maintenance, and 3s. 6d. per quarter for the school fees of 10 years, with £3, 10s. 6d. for school books? Ans. 5177 days old, and £107, 11s. 104d. expended.

13. A tradesman's wages average 14s. 6d., and his expenses 9s. 3d. per week for 11 years; how much has he saved during that time? £150, 3s. saved.

Ans.

14. A gentleman has £560, 12s. a-year; how much is that a-month, a-week, and a-day? Ans. £46, 14s. 4d. a-month; £10, 15s. 74d. a-week; £1, 10s. 8 d. 188 a-day.

15. A gentleman distributed £6, 12s. among some poor people, and gave to each 5s. 6d.; how many poor were there? Ans. 24.

16. The revenues of an infirmary amount to £1152, 10s. 6d. ; how many patients will it maintain when each patient requires £9, 10s. 6d.? Ans. 121.

17. How long must a tradesman work, who gained 1s. 4d a-day, and spends 74d. in order to pay a debt of £20, 17s. 24d.? Ans. 589.

18. In £283, 9s. 6d., how many shillings, halfcrowns, and crowns, and of each an equal number? Ans. 667.

19. A grocer bought 2 cwt. 2 qr. 24 lb. of soap for £8, 13s. 4d. ; at how much must it be sold per lb. to gain £2, 2s. on the whole? Ans. 8d.

20. A merchant bought 4 tuns (each 252 galls.)