13. Find how much it will cost to gild the inner surface of a hemispherical bowl 2 feet 4 inches in diameter at 1d. per square inch. 14. A circular room has perpendicular walls 15 feet high, the diameter of the room being 28 feet; the roof is a hemispherical dome: find the cost of plastering the whole surface at 9 pence per square foot. 15. Find the cost of a string moulding round the springing of the dome in the preceding example at 15d. per foot. 16. A rectangular courtyard is 100 feet long and 90 feet broad; a footway goes through the length 6 feet broad; the footway is laid with stone at 4s. 6d. per square yard, and the remainder is covered with turf at 9d. per square yard: find the whole cost. 17. Required the cost of glazing the windows of a house at a shilling per square foot; there being three stories and three windows in each story; the height of the windows of the lower story is 8 feet, of the middle story 7 feet, and of the upper story 5 feet; and the common breadth of all the windows is 4 feet. 18. Find how many square feet of flooring there are in a house of three stories, measuring within the walls 58 feet by 34, deducting the vacancy for the stairs 15 feet 3 inches by 8 feet. 19. A room is 22 feet long, 20 feet wide, and 14 feet 6 inches high: find the expense of covering the walls with paper 30 inches wide at 11 d. a yard; allowing for two doors each 8 feet by 5 feet 3 inches, a fire-place 6 feet 6 inches by 6 feet, and a window 12 feet by 5 feet 7 inches. 20. A square court-yard is 36 feet long; in the middle of it is a circular basin 13 feet in diameter; and a flower-bed 4 feet wide is left round three sides: find the expense of paving the remainder of the court-yard at 8 shillings per square yard. XLI. ARTIFICERS' WORK. 360. Artificers compute their work in various ways, but in general a foot or a yard is the standard of length, and therefore a square foot or a square yard is the standard of area, and a cubic foot or a cubic yard is the standard of volume. 361. The work of flooring, roofing, plastering or tiling is often estimated by the number of squares, each square consisting of 100 square feet. 362. The measure of the roof of a house can be deduced from the measure of the base when the pitch of the roof is known. There are three pitches which have received names. (1) The common or true pitch. In this the length of the rafters is three-fourths of the breadth of the building; and hence the practical rule is to take the flat and half the flat of the house as the measure of the roof. (2) The Gothic pitch. In this the length of the rafters is equal to the breadth of the building, and consequently the roof is equal to twice the flat. (3) The pediment pitch. In this the perpendicular height is 2 9 of the breadth of the building. In this case the 11 length of the rafters will be nearly of the breadth of 20 11 the building, so that the roof will be nearly 10 of the flat. 363. Artificers of every kind have various special modes of estimating the charge for workmanship, which have the sanction of custom; but as these modes involve no principle of mensuration it is not expedient to detail them here. We will give as a specimen the mode in which the charge is made for doors. It is usual to add the thickness of the door both to the length and to the breadth, and to take the product of the length and the breadth thus increased for the area. If the door be panelled on only one side this area is increased by its half. If the door be panelled on both sides the area is doubled. Thus, for example, suppose that a door is 7 feet 5 inches high, 4 feet 3 inches wide, and 1 inch thick. Then the height is taken as 7 feet 6 inches, and the breadth as 4 feet 4 inches; and so the area in square feet is taken as 15 13 that is as 7x4, that is as X that is as 2 3 5 x 13 32. If the door be panelled on only one side the charge is for 48 square feet. If the door be panelled on both sides the charge is for 65 square feet. 364. Engineers always estimate brickwork by the cubic yard; but such brickwork as occurs in connexion with ordinary house-building is estimated in a peculiar way which we will now explain. 365. A brick wall which is a brick and a half thick is said to be of the standard thickness. Brickwork of the standard thickness is estimated by the number of square yards in the area formed by its height and its length, or by the number of square rods, each square rod consisting of 30 square yards, that is of 2724 square feet. Thus a standard rod of brickwork is a mass of brickwork which has a surface of a square rod and is a brick and a half thick. 366. To find the number of standard rods of brickwork in a wall. RULE. Find the area of the surface in square feet, and divide it by 272; the quotient will be the number of rods if the wall be of the standard thickness; if not, multiply the quotient by the number of half bricks in the thickness, and divide the product by 3. In practice 272 is generally used instead of 2721. 367. Examples. (1) Find the number of standard rods of brickwork in a wall 105 feet long, 8 feet high, and 24 bricks thick. Thus the number of standard rods is nearly 5. T. M. 15 (2) Find the number of yards of brickwork of the standard thickness contained in a triangular gable-top which is 15 feet high, and the base of which is 20 feet, supposing the thickness 2 bricks. Thus the number of standard yards is 223. 368. A common brick is 8 inches long, 4 inches broad, and 2 inches thick; but, on account of the mortar, when laid in brickwork every dimension is to be taken half an inch greater thus the dimensions are to be taken as 9 inches, 4 inches, and 3 inches. The standarrd rod requires 4500 bricks of the usual size, allowing for waste. 1. Find the number of standard rods of brickwork in a wall 62 feet 6 inches long, 14 feet 8 inches high, and 2 bricks thick, 2. Find the number of standard rods of brickwork in a gable-end wall 2 bricks thick, 22 feet long, 27 feet high to the eaves, and 36 feet from the ground to the ridge of the roof. 3. Find the cost of a wall with a triangular gable-top of 10 feet high, the height of the wall being 36 feet, the breadth 24 feet, and the thickness 2 bricks, at 34s. per standard rod. 4. The end wall of a house is 30 feet long; it is 40 feet high to the eaves, and there is a triangular gable of 10 feet high; up to the height of 20 feet the wall is 2 bricks thick, between the height of 20 feet and 40 feet it is bricks thick, and the gable-top is 11⁄2 bricks thick; find. the number of standard yards. 5. Assuming that bricks cost £2 per thousand, that 4500 are required for a rod, that cartage and mortar cost together 22 shillings per rod, and labour £2 per rod: find the cost of building a wall 136 feet long, 18 feet high, and 2 bricks thick. 6. Find the cost of roofing a house of the common pitch at 15 shillings per square; the length being 40 feet, and the breadth 35 feet. 7. Find the cost of roofing a building of the Gothic pitch at 25 shillings per square; the length being 120 feet and the breadth 40 feet. 8. A building 30 feet long by 20 feet broad is to be covered with lead, so that the roof shall be eleven-tenths of the flat: find the cost supposing the lead to weigh 8 lbs. to the square foot and to cost 21 shillings per cwt. 9. A partition measures 45 feet 5 inches, by 8 feet 2 inches: find the cost at £6. 15s. per square. 10. The floor of a room measures 44 feet by 24: find the cost of flooring at £6. 5s. per square, allowing for two hearths each 7 feet by 4. 11. A room is 34 feet long, 18 feet 6 inches wide, and 12 feet high; find the cost of wainscoting the room at £10 per square. 12. The length of the roof of a house is 50 feet, and the length of a string stretched over the ridge from eaves to eaves is 60 feet: find the cost of the roof at £2. 7s. 6d. per square, 13. A garden wall is 180 feet long and 7 feet high; the wall is 1 brick thick, but there are 18 piers each 1 feet wide, and at these the whole thickness is 1 bricks: find the number of standard yards. 14. A room is 36 feet long, 18 feet broad, and 12 feet high: find the whole cost of plastering the walls at one shilling per square yard, and the ceiling at eighteen-pence. 15. Find the whole cost of flooring two rooms at £5 per square; one room measuring 28 feet by 16, and the other 24 feet by 15 feet 6 inches. 16. A room is 25 feet long, 20 feet broad, and 12 feet high; the walls are to have three coats of paint, each costing 10 shillings per square: find the whole cost. |