EXAMPLES. 1. Required the content of a floor, 48ft 6in long, and 24ft 3in broad? Ans. 11 sq. 76 ft. 2. A floor being 36ft 3in long, and 16ft 6in broad, how many squares are in it? Ans. 5sq 98 ft. 3. How many squares of partitioning are there in 173ft 10in in length, and 10ft 7in in height? Ans. 18.3973 sq. 4. What was the cost of roofing a house at 10s 6d a square; the length within the walls being 52ft 8in, and the breadth 30ft 6in; reckoning the roof of the flat? Ans. 127 128 113d. 5. Required the cost, at 6s per square yard, of the wainscoting of a room; the height, including the cornice and mouldings, being 12ft 6in, and the whole compass 83ft 8in; also the three window-shutters being each 7ft 8in by 3ft 6in, and the door 7ft by 3ft 6in, which being worked on both sides must be reckoned work and half work. Ans. 361 12s 24d. IV. SLATERS' AND TILERS' WORK. In this work, the content of a roof is found by multiplying the length of the ridge by the girt from eaves to eaves; making allowance in this girt for the double row of slates at the bottom, or for how much one row of slates or tiles is laid over another*. In roofing, the dimensions, as to length, breadth, and depth, are taken as in flooring joists, and the contents computed the same way. In floor-boarding, multiply the length by the breadth of the room. For stair-cases, take the breadth of all the steps, by making a line ply close over them, from the top to the bottom; and multiply the length of this line by the length of a step, for the whole area. By the length of a step is meant the length of the front and the returns at the two ends; and by the breadth is to be understood the girts of its two outer surfaces, or the tread and riser. For the balustrade, take the whole length of the upper part of the hand-rail, and girt over its end till it meet the top of the newel-post, for the one dimension; and twice the length of the baluster on the landing, with the girt of the hand-rail, for the other dimension. For wainscoting, take the compass of the room for the one dimension; and the height from the floor to the ceiling; making the string ply close into all the mouldings, for the other. For doors, multiply the height into the breadth, for the area. If the door be panneled on both sides, take double its measure for the workmanship; but if one side only be panneled, take the area and its half for the workmanship. For the surrounding architrave, girt it about the uppermost part for its length; and measure over it, as far as it can be seen when the door is open, for the breadth. Window-shutters, bases, etc. are measured in like manner. In measuring of joiners' work, the string is made to ply close into all mouldings, and to every part of the work over which it passes. Note. 64 cubic feet of fir, 60 of elm, 45 of ash, 39 of oak, make each a ton, at a medium. Battens are 7 inches, deals 9, and planks 11 inches wide. * When the roof is of a true pitch, that is, forming a right angle at the top; then the breadth of the building, with its half added, is the girt over both sides nearly. In angles formed in a roof, running from the ridge to the eaves, when the angle bends inwards, it is called a valley; but when outwards, it is called a hip. Deductions are made for chimney-shafts or window-holes. 1 square requires 760 plain tiles 6 inch gage, EXAMPLES. 1. Required the content of a slated roof, the length being 45ft 9in, and the whole girt 34ft 3in. Ans. 174 yds. 2. To how much amounts the tiling of a house, at 25s 6d per square; the length being 43ft 10in, and the breadth on the flat 27ft 5in; also the eaves projecting 16in on each side, and the roof of true pitch? Ans. 241 9s 84d. V. PLASTERERS' WORK. PLASTERERS' work is of two kinds, which are measured separately; namely, ceiling, which is plastering on laths; and rendering, which is plastering on walls *. EXAMPLES. 1. Find the content of a ceiling which is 43ft 3in long, and 25ft 6in broad. Ans. 122 yds. 2. Required the cost of the ceiling of a room at 10d per yd; the length being 21ft 8in, and the breadth 14ft 10in. Ans. 11 9s 83d. 3. The length of a room is 18ft 6in, the breadth 12ft 3in, and height 10ft 6in; what is the amount of ceiling and rendering, the former at 8d and the latter at 3d per yd: allowing for the door of 7ft by 3ft 8in, and a fire-place of 5ft square? Ans. 17 13s 3d. 4. Required the quantity of plastering in a room, the length being 14ft 5in, breadth 13ft 2in, and height 9ft 3in to the under side of the cornice, which girts 8in, and projects 5in from the wall on the upper part next the ceiling; deducting only for a door 7ft by 4. Ans. 53yds 5ft 3in of rendering, 18yds 5ft 6in of ceiling, and 39ft 0in of cornice. VI. PAINTERS' WORK. PAINTERS' work is computed in square yards. Every part is measured where the colour lies; and the measuring line is forced into all the mouldings and corners. Windows are painted at so much a piece: and it is usual to allow double measure for carved mouldings and other ornamental works. Five hundred feet in length of laths make a bundle; and is the quantity usually allowed to a square of tiling. A square of Westmoreland slates will weigh half a ton; of Welsh rag from 2 of a ton to a ton; and a square of pantiling weighs about 7 cwt. * The contents are estimated either by the foot or the yard, or the square of 100 feet. Enriched mouldings, etc. are rated by running or lineal measure. Deductions are made for chimneys, doors, windows, and other apertures. 3 cwts. of lime, 4 loads of sand, and 10 bushels of hair, are allowed to 200 yards of rendering. 1 bundle of laths, and 500 of nails, are allowed to cover 4 square yards. 1 barrel of cement is 5 bushels, and weighs 3 cwt. 1 rod of brickwork in cement requires 36 bushels of cement and 36 bushels of sand. EXAMPLES. 1. How many yards of painting are there in a room which is 65ft 6in in compass, and 12ft 4in high? Ans. 89 yds. 2. The length of a room being 20ft, its breadth 14ft 6in, and height 10ft 4in: how many yards of painting are there, deducting a fire-place of 4ft by 4ft 4in, and two windows, each 6ft by 3ft 2in? Ans. 73 yds. 3. Required the cost of painting a room of the following dimensions at 6d a yd: viz. the length 24ft 6in, the breadth 16ft 3in, and the height 12ft 9in; the door 7ft by 3ft 6in, and the fire-place 5ft by 5ft 6in; also the shutters to the two windows each 7ft 9in by 3ft 6in, the breaks of the windows 8ft 6in high by 1ft 3in deep, and the window-cills and soffits determinable from the dimensions already given. Ans. 31 38 10 d. VII. GLAZIERS' WORK. GLAZIERS take their dimensions, either in feet, inches, and parts, or feet, tenths, and hundredths; and they compute their work in square feet *. EXAMPLES. 1. How many square feet are there in the window which is 4.25ft long, and 2.75ft broad? Ans. 11 ft. 2. What will the glazing a triangular sky-light cost at 10d per foot; the base being 12ft 6in, and the height 6ft 9in? Ans. 17 15s 13d. 3. There is a house with three tiers of windows, three windows in each tier, their common breadth 3ft 11in: and their height are 7ft 10in, 6ft 8in, and 5ft 4in respectively. Required the expense of glazing at 14d per foot. Ans. 131 11s 103d. 4. Required the expense of glazing the windows of a house at 13d a foot; there being three stories, and three windows in each story; the heights of which are respectively 7ft 9in, 6ft 6in, and 5ft 3in, and of an oval window over the door 1ft 10in also the common breadth of all the windows 3ft 9in. : VIII. PAVERS' WORK. Ans. 127 5s 6d. PAVERS' work is done by the square yard: and the content is found by multiplying the length by the breadth. EXAMPLES. 1. What cost the paving a foot-path, at 38 4d a yard; the length being 35ft. 4in, and breadth 8ft 3in? Ans. 51 7s 11 d. In taking the length and breadth of a window, the cross bars between the squares are included. Windows also of round or oval forms are measured as square, measuring them to their greatest length and breadth, on account of the waste in cutting the glass. 2. What was the expense of paving a court, at 3s 2d per yd; the length being 27ft 10in, and the breadth 14ft 9in ? Ans. 71 48 54d. 3. What will be the expense of paving a rectangular court-yard, whose length is 63ft, and breadth 45ft; in which there is laid a foot-path of 5ft 3in broad, running the whole length, with broad stones, at 3s a yd; the rest being paved with pebbles at 2s 6d a yd? Ans. 401 5s 10 d. IX. PLUMBERS' WORK. PLUMBERS' work is rated at so much a pound; or else by the hundred weight of 112 pounds*. EXAMPLES. 1. Required the weight of the lead which is 39ft 6in long, and 3ft 3in broad, at 84lbs to the square foot. Ans. 1091 lbs. 2. Find the cost of covering and guttering a roof with lead, at 18s per cwt; the length of the roof being 43ft, and breadth, or girt over it, 32ft; the guttering 57ft long, and 2ft wide; the former 9.8311b, and the latter 7.373lb to the square foot. Ans. 1157 9s 1d. X. TIMBER MEASURING. PROBLEM I. To find the area, or superficial content, of a board or plank. MULTIPLY the length by the mean breadth, when the breadths of each end are equal; but when the board is tapering, add the breadths at the two ends together, and take half the sum for the mean breadth; or, if convenient, take the breadth in the middle. By the sliding rulet. Set 12 on B to the breadth in inches on A; then against the length in feet on B, is the content on A, in feet and fractional parts. * Sheet lead, used in roofing, guttering, &c. weighs from 6lb. to 10lb. to the square foot; and pipe of an inch bore is commonly 13 or 14lb. to the yard in length. A square foot an eighth of an inch thick, weighs 7.38 or 741b. nearly; a quarter of an inch thick 1431b., and so on. The Carpenter's or Sliding Rule is an instrument much used in measuring of timber and artificers' works, both for taking the dimensions, and computing the contents. The instrument consists of two equal pieces, each a foot in length, which are connected together by a folding joint. One side or face of the rule is divided into inches, and eighths, or half-quarters. On the same face also are several plane scales divided into twelfth parts by diagonal lines; which are used in planning dimensions that are taken in feet and inches. The edge of the rule is commonly divided decimally, or into tenths; namely, each foot into ten equal parts again; so that by means of this last scale, dimensions are taken in feet, tenths, and hundredths, and multiplied as common decimal numbers, which is the best way. On EXAMPLES. 1. What is the value of a plank, at 14d per foot, whose length is 12ft 6in, and mean breadth 11in? Ans. 1s 5d. 2. Required the content of a board, whose length is 11ft 2in, and breadth 1ft 10in. Ans. 20ft 5in. 3. What is the value of a plank, which is 12ft 9in long, and 1ft 3in broad, at 24d a ft? Ans. 3s 3 d. 4. Required the value of 5 oaken planks, at 3d per ft, each of them being 174ft long; and their several breadths as follows, namely, two of 13 in in the middle, one of 144in in the middle, and the two remaining ones, each 18in at the broader end, and 114in at the narrower ? Ans. 11 5s 9 d. PROBLEM II. To find the solid content of squared or four-sided timber. MULTIPLY the mean breadth by the mean thickness, and the product again by the length, for the content nearly. That is, as the length in feet on C, is to 12 on D, when the quarter girt is in inches, or to 10 on D, when it is in tenths of feet; so is the quarter girt on D, to the content on C. If the tree taper regularly from the one end to the other; either take the mean breadth and thickness in the middle, or take the dimensions at the two ends, and half their sum will be the mean dimensions: which multiplied as above, will give the content nearly. If the piece do not taper regularly, but be unequally thick in some parts and small in others; take several different dimensions, add them all together, and divide their sum by the number of them, for the mean dimensions. EXAMPLES. 1. The length of a piece of timber is 18ft 6in, the breadths at the greater and less end 1ft 6in and 1ft 3in, and the thickness at the greater and less end 1ft 3in and 1ft; required the content. Ans. 28ft 7in. On the one part of the other face are four lines, marked A, B, C, D; the two middle ones B and C being on a slider, which runs in a groove made in the stock. The same numbers serve for both these two middle lines, the one being above the numbers, and the other below. These four lines are logarithmic ones, and the three A, B, C, which are all equal to one another, are double lines, as they proceed twice over from 1 to 10. The other or lowest line, D, is a single one, proceeding from 4 to 40. It is also called the girt-line, from its use in computing the contents of trees and timber; and on it are marked WG at 17·15, and AG at 18·95, the wine and ale gage points, to make this instrument serve the purpose of a gaging rule. On the other part of this face there is a table of the value of a load, or 50 cubic feet of timber, at all prices, from 6 pence to 2 shillings a foot. When 1 at the beginning of any line is accounted 1, then the 1 in the middle will be 10, and the 10 at the end 100; but when 1 at the beginning is counted 10, then the 1 in the middle is 100, and the 10 at the end 1000; and so on. And all the smaller divisions are altered proportionally. |