14 feet 6 inches, and height 10 feet 4 inches; how many yards of painting are in it, deducting a fire-place of 4 feet by 4 feet 4 inches, and two windows each 6 feet by 3 feet 2 inches? Ans. 73 yards.

EXAM. 3. What cost the painting of a room, at 6d. per yard; its length being 24 feet 6 inches, its breadth 16 feet 3 inches, and height 12 feet 9 inches; also the door is 7 feet by 3 feet 6, and the window-shutters to two windows each 7 feet 9 by 3 feet 6; but the breaks of the windows themselves are 8 feet 6 inches high, and 1 foot 3 inches deep; including also the window cills or seats, and the soffits above, the dimensions of which are known from the other dimensions: but deducting the fire-place of 5 feet by 5 feet 6? Ans. 31. 3s. 104d.

IX. 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.

In taking the length and breadth of a window, the cross bars between the squares are included. Also windows 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.

EXAMPLES.

EXAM. 1. How many square feet contains the window which is 4.25 feet long, and 2.75 feet broad? Ans. 113.

EXAM. 2. What will the glazing a triangular sky-light come to, at 10d. per foot; the base being 12 feet 6 inches, and the perpendicular height 6 feet 9 inches?

Ans. 11. 15s. 1d.

EXAM. 3. There is a house with three tiers of windows, three windows in each tier, their common breadth 3 feet 11 inches:

now the height of the first tier is 7 feet 10 inches

of the second

of the third

Required the expence of glazing at 14d. per foot?

Ans. 13. 11. 10d.

EXAM. 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 height of the lower tier is 7 feet 9 inches

of the middle

of the upper

and of an oval window over the door 1 101

the common breadth of all the windows being 3 feet 9 inches?

Ans. 121. 5s. 6d.

X. PAVERS' WORK.

PAVERS', work is done. by the square yard. And the content is found by multiplying the length by the breadth.

EXAMPLES.

EXAM. 1. What cost the paving a foot path, at 3s. 4d, a yard; the length being 35 feet 4 inches, and breadth 8 feet 3 inches? Ans. 51. 7s. 11.

EXAM. 2. What cost the paving a court, at 3s. 2d. per yard; the length being 27 feet 10 inches, and the breadth 14 feet 9 inches? Ans. 71. 4s. 54d.

EXAM. 3. What will be the expense of paving a rectangu→ lar court-yard, whose length is 63 feet, and breadth 45 feet; in which there is laid a foot-path of 5 feet 3 inches broad, running the whole length, with broad stones, at 3s. a yard; the rest being paved with pebbles at 2s. 6d. a yard ? Ans. 40%. 5s, 10d.

XI. PLUMBERS' WORK.

PLUMBERS' work is rated at so much a pound, or else by the hundred weight of 112 pounds.

Sheet lead, used in roofing, guttering, &c, is from 6 to 10lb. to the square foot. And a pipe of an inch bore is commonly 13 or 14 lb. to the yard in length.

EXAMPLES.

EXAM. 1. How much weighs the lead which is 39 feet

6 inches

6 inches long, and 3 feet 3 inches broad, at 8lb. to the square foot? Ans. 1091

EXAM. 2. What cost the covering and guttering a roof with lead, at 18s. the cwt; the length of the roof being 43 feet, and breadth or girt over it 32 feet; the guttering 57 feet long, and 2 feet wide; the former 9.831 lb. and the latter 7.373 lb. to the square foot? Ans. 115/. 9s. 1d.

XII. TIMBER MEASURING.

PROBLEM I.

To find the Area, or Superficial Content, of a Beard or Plank, MULTIPLY the length by the mean breadth.

Note. When the board is tapering, add the breadths at the two ends together, and take half the sum for the mean breadth. Or else take the mean breadth in the middle.

By the Sliding Rule.

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.

EXAMPLES.

EXAM. 1. What is the value of a plank, at 11d. per foot, whose length is 12 feet 6 inches, and mean breadth 11 inches? Ans. 1s. 5d. EXAM. 2. Required the content of a board, whose length is 11 feet 2 inches, and breadth 1 foot 10 inches?

Ans. 20 feet 5 inches 8". EXAM. 3. What is the value of a plank, which is 12 feet 9 inches long, and 1 foot 3 inches broad, at 21⁄2d. a foot. Ans. 3s. 33d.

EXAM. 4. Required the value of 5 oaken planks at 3d. per foot, each of them being 172 feet long; and their several breadths as follows, namely, two of 13 inches in the middle, one of 141⁄2 inches in the middle, and the two remaining ones, each 18 inches at the broader end, and 114 at the narrower? Ans. 11. 5s. 94d.

PROBLEM

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.

As length: 12 or 10 :: quarter girt : solidity.

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.

Note 1. 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.

2. 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.

EXAM. 1. The length of a piece of timber is 18 feet 6 inches, the breadths at the greater and less end 1 foot 6 inches and 1 foot 3 inches, and the thickness at the greater and less end 1 foot 3 inches and 1 foot; required the solid content? Ans. 28 feet 7 inches.

EXAM. 2 What is the content of the piece of timber, whose length is 24 feet, and the mean breadth and thickness each 104 feet? Ans. 26 feet.

EXAM. 3. Required the content of a piece of timber, whose length is 20.38 feet, and its ends unequal squares, the sides of the greater being 19 inches, and the side of the less 92 inches? Ans. 29 7562 feet.

EXAM. 4. Required the content of the piece of timber, whose length is 27-36 feet; at the greater end the breadth is 1.78, and thickness 1.23; and at the less end the breadth is 104, and thickness 0.91 feet? Ans. 41.278 feet.

PROBLEM III.

To find the Solidity of Round er Unsquared Timber. MULTIPLY the square of the quarter girt, or of of the mean circumference, by the length, for the content.

By the Sliding Rule.

As the length upon c: 12 or 10 upon D::

quarter girt, in 12ths or 10ths, on D: content on c.

Note 1. When the tree is tapering, take the mean dimensions as in the former problems, either by girting it in the middle, for the mean girt, or at the two ends, and taking half the sum of the two; or by girting it in several places, then adding all the girts together, and dividing the sum by the number of them, for the mean girt. But when the tree is very irregular, divide it into several lengths, and find the content of each part separately.

2. This rule, which is commonly used, gives the answer about less than the true quantity in the tree, or nearly what the quantity would be, after the tree is hewed square in the usual way: so that it seems intended to make an allowance for the squaring of the tree.

EXAMPLES.

EXAM. 1. A piece of round timber being 9 feet 6 inches long, and its mean quarter girt 42 inches; what is the content? Ans. 116 feet.

EXAM. 2. The length of a tree is 24 feet, its girt at the thicker end 14 feet, and at the smaller end 2 feet; required the content? Ans. 96 feet.

EXAM. 3. What is the content of a tree, whose mean girt is 3.15 feet, and length 14 feet 6 inches?

Ans. 8.9922 feet.

EXAM. 4. Required the content of a tree; whose length is 17 feet, which girts in five different places as follows, namely, in the first place 943 feet, in the second 7·92, in the third 6.15, in the fourth 4-74, and in the fifth 3·16?

Ans. 42.519525,