PART IV.

DUODECIMALS;

Or, what is generally called Cross-Multiplication, and Squaring of Dimensions by ARTIFICERS and WORKMEN.

The foot is divided into 12 parts called seconds; the seconds into 12 parts called thirds; and the thirds into 12 parts called fourths. RULE. Write the Multiplier under the Multiplicand, feet under feet, inches under inches, &c.

1. Multiply the multiplicand, beginning at the lowest denomination, by the feet in the multiplier; and place each product under that denomination of the multiplicand from which it arises, always carrying at 12.

2. Next, multiply by the inches, and set each product a place towards the right hand.

3. Multiply by the parts, and set each product another place towards the right hand, and so on.

THE APPLICATION.

Artificers' work is computed by different measures, viz.:-1. Glazing and masons' flat work by the foot. 2. Painting, plastering, paving, &c., by the yard. 3. Partitioning, flooring, roofing, tiling, &c., by the square of 100 feet. 4. Brickwork, &c., by the rod, or 16 feet, whose square is 2724.

1.-MEASURING BY THE FOOT SQUARE, AS GLAZIERS' AND MASONS' FLAT WORK.

19. There is a house with three tier of windows, three in a tier, the height of the first tier is 7 feet 10 inches, the second is 6 feet 8 inches, and the third 5 feet 4 inches, the breadth of each is 3 feet 11 inches-what will the glazing come to at 14d. per foot?

20. What is the worth of 8 squares of glass, each measuring 4 feet 10 inches long, and 2 feet 11 inches broad, at 44d. per foot.

Ans. £2 2s. 3 d. 21. There are 8 windows to be glazed, each measures 1 foot 6 inches wide, and 3 feet in height-how much will they come to at Ans. £1 38. 3d. 7ąd. per foot.

22. What is the price of a marble slab, whose length is 5 feet 7 inches, and breadth 1 foot 10 inches, at 6s. per foot. Ans. £3 1s. 5d.

2.-MEASURING BY THE YARD SQUARE, AS PAVIERS, PAINTERS, PLASTERERS, AND JOINERS.

Divide the square feet by 9, and it will give the number of square yards. 23. A room is to be ceiled, whose length is 74 feet 9 inches, and width 11 feet 6 inches-what will it come to at 38 104d. per yard. Ans. £18 10s. 14d+. 24. What will the paving of a court-yard come to at 44d. per yard, the length being 58 feet 6 inches, and breadth 54 feet 9 inches? Ans. £7 Os. 10дd+. 25. A room painted 97 feet 8 inches about, and 9 feet 10 inches high-what does it come to at 2s. 8d. per yard?

Ans. £14 11s. 24d+.

26. What is the content of a piece of wainscotting in yards square, that is 8 feet 3 inches long, and 6 feet 6 inches broad, and what will it come to at 6s. 7 d. per yard? Ans. £1 19s. 5d+. 27. What will the paving of a court-yard come to at 3s. 2d. per yard, if the length be 27 feet 10 inches, and the breadth 14 feet 9 inches? Ans. £7 48. 51d+.

28. A person has paved a court-yard, 42 feet 9 inches in front, and 68 feet 6 inches in depth, and in this he laid a footway, the depth of the court, of 5 feet 6 inches in breadth; the footway is laid with Purbeck-stone, at 3s. 6d. per yard, and the rest with pebbles, at 3s. per yard-what will the whole come to ? Ans. £49 17s. 03d+.

29. What will the plastering of a ceiling, at 10d. per yard, come to, supposing the length at 21 feet 8 inches, and the breadth 14 feet Ans. £1 9s. 9d+.

10 inches?

30. What will the wainscotting of a room come to at 6s. per square yard, supposing the height of the room (taking in the cornice and moulding) be 12 feet 6 inches, and the compass 83 feet 8 inches, the three window-shutters each 7 feet 8 inches, by 3 feet 6 inches; and the door 7 feet by 3 feet 6 inches; the shutters and door being worked on both sides, is reckoned work and half work?

Ans. £36 12s. 23d+.

3.-MEASURING BY THE SQUARE OF ONE HUNDRED FEET, AS FLOORING, PARTITIONING, ROOFING, TILING, &C.

31. In 173 feet 10 inches in length, and 10 feet 7 inches in height of partitioning-how many squares?

Ans. 18 squares, 39 feet, 8 inches, 10 parts. 32. If a house of 3 stories, besides the ground-floor, was to be floored at £6 10s. per square, and the house measured 20 feet 8 inches, by 16 feet 9 inches; there are 7 fire-places, whose measures are 2 of 6 feet, by 4 feet 6 inches each, 2 of 6 feet, by 5 feet 4 inches each, and 2 of 5 feet 8 inches, by 4 feet 8 inches, and the seventh of 5 feet 2 inches, by 4 feet, and the well-hole of the stairs is 10 feet 6 inches, by 8 feet 9 inches-what will the whole come to ?

Ans. £53 13s. 3d+. 33. If a house measures, within the walls, 52 feet 8 inches in length, and 30 feet 6 inches in breadth, and the roof be of a true pitch-what will it come to roofing, at 10s. 6d. per square? Ans. £12 12s. 11d+.

NOTE. In tiling, roofing, and slating, it is customary to reckon the flat and half of any building within the walls, to be the measure of the roof of that building, when the said roof is of a true pitch, i. e., when the rafters are of a breadth of the building but if the roof is more or less than the true pitch, they measure from one side to the other with a rod or string.

34. What will the tiling of a barn cost, at 25s. 6d. per square, the length being 43 feet 10 inches, and breadth 27 feet 5 inches on the flat, the eave-boards projecting 16 inches on each side?

Ans. £24 9s. 53d+.

4.-MEASURING BY THE ROD.

NOTE.-Bricklayers always value their work at the rate of a brick and a half

thick: and if the thickness of the wall be more or less, it must be reduced to that thickness by this rule.

RULE.-Multiply the area of the wall by the number of half bricks the thickness the wall is of; the product divided by 3, gives the area. 35. If the area of a wall be 4085 sq. feet, and the thickness two bricks and a half-how many rods doth it contain ? Ans. 25+rods. 36. If a garden wall be 254 feet round, and 12 feet 7 inches high, and 3 bricks thick-how many rods doth it contain?

Ans. 23 rods, 130 feet, 7 inches. 37. How many square rods are there in a wall 62 feet long, 14 feet 8 inches high, and 2 bricks thick?

Ans. 5 rods, 166 feet, 6+inches. 38. If the side walls of a house be 28 feet 10 inches in length, and the height of the roof from the ground 55 feet 8 inches, and the gable, or triangular part at the top, to rise 42 course of bricks, reckoning 4 course to a foot: now 20 feet high is 2 bricks thick, 20 feet more at 2 bricks thick, 15 feet 8 inches more at 1 brick thick, and the gable at 1 brick thick-what will the whole work come to at £5 16s. per rod? Ans. £48 12s. 7d+.

PART V.

A Collection of Questions set down promiscuously, for the greater trial of the foregoing Rules.

1. Write down three millions, five hundred and two thousand, two hundred and five.

2. What is the value of 21 barrels of soap, at 44d. per lb., each barrel containing 254 lb.? Ans. £100 0s. 3d.

3. If £100 principal gain £5 interest in 12 months--what principal will gain £40 in 8 months? Ans. £1200. 4. What number is that from which, if the square of 14 be deducted, and to the remainder the square of 12 be added, the sum will be 250?

Ans. 302.

5. A and B trade together; A advanced £220 for 6 months, B £340 for 4 months, and they gained £100-what must each man receive? Ans. A £49 5s. Od.15, B £50 14s. 11d.6. How many yards of cloth, at 17s. 6d. per yard, can I have for 13 cwt. 2 qrs. of wool, at 14d. per lb.? Ans. 100 yds. 31qrs.

7. Gave 215 lb. of chocolate for 125 yards of cloth, at 5s. 6d. per yard; required the price of the chocolate. Ans. 3s. 24d..

8. What number, added to the cube of 21, will make the sum equal to 113 times 147 ? Ans. 7350. 9. Sold 3 pieces of cloth, each 27 yards, at 17s. 3d.; and 5 pieces narrow ditto, each 31 yards, at 11s. 7d., allowing 5 per cent. discount for prompt payment-what did I receive? Ans. £151 13s Old.

10. If I buy 1000 ells of linen, Flemish, for £90-what may I sell it at per ell in London, to gain £10 by the whole? Ans. 3s. 4d. per ell.

11. If cotton wool be bought at 3s. 1d. per lb., and sold at 28. 11d. per lb.-what is the loss per cent.? Ans. £5 8s. 1d.y. 12. An oilman bought 417 cwt. 1 qr. 15 lb. gross weight of train oil, tare 20 lb. per 112 lb.-how many nett gallons were there, allowing 7 lb. to a gallon? Ans. 5120 gallons.

13. I bought three score pieces of Holland for three times as many pounds, and sold them again for four times as much; but if they had cost me as much as I sold them for-what should I have sold them for to gain after the same rate ? Ans. £320.

14. Find the present worth of a bill of £39 5s., due September 1st, but paid on the 3rd of July last, discount at 5 per cent. per annum. Ans. £38 188. 63d. 15. What number, taken from the square of 54, will leave 19 times 46? Ans. 2042 16. If I buy a yard of cloth for 14s. 6d., and sell it for 16s. 9d.what do I gain per cent. ? Ans. £15 10s. 4d. 24.

17. If 40 gallons of porter serve 17 men 5 days, how many gallons will serve 9 persons for a year, at the same rate? Ans. 15451 gallons. 18. If of an ounce avoirdupois cost of a shilling-what will of a lb. cost? Ans. 17s. 6d.

19. A young man received £210, which was of his elder brother's portion; now three times the elder brother's portion was half of the father's estate-how much was the estate? Ans. £1890. 20. Required the value of 3945 of a day in hours, minutes, &c. Ans. 9 hours, 28 min., 4 sec., 48 thirds. 21. If the salary of an officer be £48 per annum-what must he receive for 232 days Ans. £30 10s. 2d.

22. A gentleman spends daily £1 7s. 104d., and at the year's end layeth up £340-what is his yearly income? Ans. £848 148. 4jd. 23. A lady's fortune consisted of a cabinet worth £200, containing 16 drawers, each having two partitions, each of which contained £37 and two crowns-what was her portion? Ans. £1400.

24. What cost 847 yards of muslin, at 2s. per yard? Ans. £84 148.

The price of any number of articles, at 2s. each, is found by doubling the figure of the number for shillings, and taking the number expressed by the preeeding figures as pounds.

25. If a person walk 30 miles in 10 hours, 42 minutes-in what time will he walk, at the same rate, 80 miles? Ans. 28 hours, 32 min. 26. If a family of 8 persons cost £42 in 16 weeks, how long will £100 support a family of 6 persons at the same rate? Ans. 50 weeks. 27. A captain and 160 sailors took a prize worth £1360, of which the captain had for his share, and the rest was equally divided among the sailors-what was each man's part?

Ans. The captain had £272, and each sailor £6 16s. 28. What number is that to which if you add 73 the whole will be 124? Ans. 4. 29. I put out £75 for 12 months, and received for principal and interest £81-at what rate per cent. did I receive interest?

Ans. 8 per cent. 30. What will £956 amount to in 7 years, at 5 per cent. simple interest? Ans. £1314 10s.