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By Cross Multiplication.
521 4 6
2 0 0
1042 9 0
2. Required the solid content of a wall whose length is 53 feet 6 inches, its height 12 feet 3 inches, and its thickness 2 feet.
Ans. 1310 feet 9 in. 3. What is a marble slab worth, whose length is 5 feet 7 inches, and breadth 1 foot 10 inches, at 80 cents per foot ?
dolls. cts. m.
Ans. 8 18 8 4. What is the solid content of a wall, whose length is 60 feet 9 inches, its height 10 feet 3 inches, and its thickness 21 feet?
Ans. 1556.71875 feet. 5. In a chimney-piece, suppose the Length of the mantel and slab, each
4 6 Breadth of both together,
3 2 Length of each jamb,
4 4 Breadth of both together,
1 9 What will be the content of the chimney-piece ?
Ans. 21 feet 10 in. 6. The dimensions of a certain building are as follow : viz. 58 feet by 26 on the outside; height of the building 22 feet, height of the gable at each end 12 feet, thickness of the wall 15 inches. Two doors 41 by 8 feet each, 28 windows each 31 by 6 feet: what will the mason work amount to at 56 cents a perch, and what must be paid for the stone at 44 cents a perch?
Ans. For the work, $136 03; For the stone, $71 95}.
CARPENTERS' AND JOINERS' WORK*
CARPENTERS' and JOINERS' work is that of flooring, partitioning, roofing, &c., and is measured by the square of 100 feet.
* Note.-Large and plain articles are usually measured by the foot, or yard, &c. square; but enriched mouldings, and some other articles, are often estimated by running or lineal measure, and some things are rated by the piece.
In measuring of joists it is to be observed, that only one of their dimensions is the same with that of the floor, and the other will exceed the length of the room by the thickness of the wall, and one-third of the same, because each end is let into the wall about two-thirds of its thickness.
No deductions are made for hearths, on account of the additional trouble and waste of materials.
Partitions are measured from wall to wall for one dimension, and from floor to floor, as far as they extend, for the other.
„No deduction is made for door-ways, on account of the trouble of framing them.
In measuring of Joiners' work, the string is made to ply close to every part of the work over which it passes.
In roofing, the length of the house in the inside, together with two-thirds of the thickness of one gable, is to be considered as the length, and the breadth is equal to double the length of a string, which is stretched from the ridge down to the rafter, along the eaves-board, till it meets with the top of the wall.
For stair-cases, take the breadth of all the steps, and make 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 wbole 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 girth of its two upper surfaces, or the tread and riser.
CARPENTERS' AND JOINERS' WORK.
1. If a floor be 57 feet 3 inches long, and 28 feet 6 inches broad, how many squares will it contain ?
By Decimals. 57.25 x 28.5 x 1631.625 sq. ft.=16 sq. 31 ft. 7 in. 6". Ans.
By Cross Multiplication.
28 7 6
1631 7 6
For the balustrade, take the whole length of the upper. part of the hand-rail, and girth over its end till it meet the top of the newel-post, for the length; and twice the length of the baluster upon the landing, with the girth of the hand-rail, for the breadth.
For wainscotting, take the compass of the room for the length, and the height from the floor to the ceiling, making the string ply close into all the mouldings, for the breadth. Out of this must be made deductions for windows, doors, chimneys, &c., but workmanship is counted for the whole, on account of the extraordinary trouble.
For doors, it is usual to allow for their thickness, by adding it into both the dimensions of length and breadth, and then multiplying them together for the area. If the door be panelled on both sides, take double its measure for the workmanship ; but if one side only be panelled, take the area and its half for the workmanship.
For the surrounding architrave, gird it about the outermost 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, &c., are measured in the same manner.
In the measuring of roofing for workmanship alone, all holes for chimneys-shafts and sky-lights are generally deducted.
But in measuring for work and materials, they commonly measure in all sky-lights, luthern-lights, and holes for the chimneyshafts, on account of their trouble and waste of materials.
2. A floor is 53 feet 6 inches long, and 47 feet 9 inches broad : how many squares does it contain ?
Ans. 25 sq. and 54 feet 74 in. 3. A partition is 91 feet 9 inches long, and 11 feet 3 inches broad: how many squares does it contain ?
Ans. 10 sq. and 32 feet. 4. *If a house within the walls be 44 feet 6 inches long, and 18 feet 3 inches broad; how many squares of roofing will cover it, allowing the roof to be of a true pitch ?
Ans. 12 sq. and 18 feet. 5. If a house measure 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 cost roofing, at 1 dollar 40 cts. per square ?
Ans. 33 dolls. 73 cts. 3 m.
* It is customary to reckon the flat and half of any building within the walls, for the measure of the roof of that building, when the roof is of a true pitch, or so that the length of the rafters is of the breadth of the building.
SLATERS AND TILERS' WORK.
In these works the content of a roof is found by multiplying the length of a ridge by the girth from eave to eave; and, in slating, allowance must be made for the double row at the bottom.
In taking the girth, the line is made to ply over the lowest row of slates, and returned up the under side till it meet with the wall or eaves-board; but in tiling, the line is stretched down only to the lowest part, without returning it up again.
Double measure is generally allowed for hips, valleys, gutters, &c. but no deductions are made for chimneys.*
* In angles formed in a roof, running from the ridge to the eaves, that angle of the roof which bends inwards, is called a valley; and the angle bending outwards is called a hip. And in tiling and slating, it is common to add the length of the valleys to the content in feet; and sometimes also the hips are added.
In slating it is common to reckon the breadth of the roof 2 or 3 inches broader than what it measures, because the first row is almost covered by the second; and this is done sometimes when a roof is tiled.
Note.-Sky-lights and chimney-shafts are always deducted; but they seldom deduct luthern-lights, or garret-windows on the roof; for the covering them is reckoned equal to the hole in the roof.
In all works of this kind the content is computed, either in yards of 9 square feet, or in squares of a hundred feet, and the same allowance of hips and valleys is to be made as in roofing.