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In some places, double measure is allowed for hips, rallics, gutters, &c. and no deduction for chimneys.

EXAMPLE I.

A Nate roof is 30 feet long and 26 feet over,-how many squares are in it?

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Ex. 2. How many squares tiling in a roof 351 feet deep, and whose length is 48 ?

An. 16 squares 92 feet. Ex. 3. How much Nating in a pavilion roof, with a platform 50 feet long and 30 broad at the eaves, and 30 feet long by to at the platform ; 14. feet from the platform to the eaves, taken the shortest way, and 17 along the hips?

Anf. 5 roods 31 yards.

GLAZIERS WORK.

Glaziers take their dimensions in feet, inches, and parts. All circular, triangular, &c. windows, are 'measured as if they were squares; and the greatest lengths and breadths are taken on account of the trouble and waste of glass attending the cutting

EXAMPLE.

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A house with 3 rows of windows, 5 in a row, the dimenfions of the first row is 6 feet 4 inches by 4 feet 2 inches; of the second row, 5 feet 9 by the same breadth ; of the third, 5 feet 3 inches, same breadth ; also a semicircular window above the door, whose height is 2 feet;- required the expence of glazing, at 1s. per square foot.

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369 4 Which, at 1s. per square foot, amounts to 181. gs. 1 d.

PAINTERS Work.

PAINTERS work is measured in the same manner as that of carpenters; and, in taking the dimensions, the line must be bent into all the hollows, and over all the projections, in order

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to ascertain the surface which has been touched with the brush. The painting of the bars of windows is reckoned whole work, it being troublesome; and railing a whole furface painted on both sides. Doors, window-fhutters, &c. are reckoned double work. Deductions are w be made for chimnies, casements, &c.

EXAMPLE I.

The height of a room is 12 feet 9 inches, circumference 60 feet ;-how many square yards of painting ?

12.75

60

9)765.00
Anf. 85 sq. yards.

Ex. 2. The height of a room is 11 feet 7 inches, circumference 74 feet 10 inches, the door 7 feet 6 inches by 3 feet 9 inches, 5 window-shutters, each 6 feet 8 inche's by 3 feet 4 inches, the breaks in the windows 14 inches deep and 8 feet high, the chimney 6 feet 9 inches by 5 feet; a closet, the height of the room, 3 : feet deep and 4 feet 9 inches in front, with shelving, at 22 feet 6 inches by ro inches, painted on both fides-what will the whole amount to, at 6d. per square yard ?

Anf. 31. 145. 0 d.

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MISCELLANEOUS QUESTIONS.

Question 1.

What will the side of a cube be, when the surface and folidity are expressed by the same number?

Anf. 6.

Anf. 4.

2. A cistern 25 feet long, 15 broad, and 10 feet deep, is to be enlarged, so as to contain four times the quantity, its depth will be 7 feet, and the sides in the proportion of 3 to 5 ;-required the sides. Anf. 34.641013, and 57-735020 feet.

3. Required the diameter of a globe equal to a cube, whose fide is 6.

Ans. 7.43. 4. Three men, Wright, Smith, and Turner, bought a grinding stone of 60 inches diameter; Wright and Smith paid equal shares, and Turner one-half share ; each partner is to grind the stone in his turn, first Wright, then Smith, and Turner last. How much of the diameter ought each to grind down for his share ?

Wright=13.525 inches Ans. Smith =19.640

Turner=26.835 5. What is the diameter of a cylinder when the cylindric area is expressed by the same number with the solidity ?

6. My wright made me a ladder of such a length, that, by planting it on a street 70 feet wide, it will reach a window on one side 40 feet high; by turning it over, without moving the foot, it will do the same by a window 30 feet ;-required the length of the ladder,

Ans. 50 feet. 7. My coppersmith agreed to make me a flat-bottomed kettle, that should contain 137} ale gallons : The depth of the kettle is 12 inches, the top and bottom diameters are in the proportion of 5 to 3 ;-required the diameters.

head The bottom

15 8. What ought to be the depth of a tub whose base and head diameters are 20 and 10, to contain 9163 solid inches?

Anf. 50 inches. 9. There is a wall containing 18225 folid feet, the height is 5 times the thickness, the length is 8 times the height ;-required the thickness of the wall.

Anf. 4.5 feet. . ļo. A tree 100 feet high, standing on a horizontal plane,

was

was broke by a tempestuous wind, so that the upper part of it struck the ground 30 feet from its root ;-required the length of the part broke off.

Anf. 54 feet. 11. A square within a circle contains 16 square yards ;-required the area of a square circumscribed about the same circle.

Anf: 32 square yards. 12. The cubical altar at Delphos was i cubit ;-required the fide of the new altar, which was to be twice that size, and of the same form.

Ans: 1.259921 cubits. 13. The ceiling of a room, at 6d. per square yard, amounted to 21. 10s. ; the breadth is 22 feet ;-required the length.

Anf. 40 feet. 14. A man left two daughters ; ordered by his will that the eldest should have annually the rent of a square field, and the younger the rent of a circular one; the rent of each field, at 205. per acre, would exactly surround it in shillings, allowing one inch to each shilling ;-required the portion of each of the daughters.

The first's annual income is 250905l. 125.
Anf
The second,

-197061l. 55. 2d. 15. A gentleman had a garden surrounded by a terrace walk; the length of the garden is 500 yards, and the breadth 400 yards; the walk was equal to of the garden ;-required the breadth of the walk.

Anf. 13.6809 yards. 16. A gentleman has a garden 100 feet long and 80 broad, but intends to make a walk half round it that shall take up half the ground ;--required the breadth of the walk.

Anf. 25.96876. 17. The length of a room is 40 feet, and breadth 30 feet; the expence of painting the walls, at 6d. per square yard, is 7!. -required the height of the room. Anf. 18 feet high.

13. The diameter of a malt bushel is 18 inches, and its depth 8,5 inches; what ought to be the depth when the diameter is 19 inches ?

Anj. 6.8448 inches.

19. Three

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