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2. Multiply the product thus found by the fquare of the height of the fegment, and this product again by ,5236, and it will give the folidity required. ́

EXAMPLE. The axes of a fpheroid are 50, and 30; what is the folidity of that fegment, whofe height is 5, and its bafe perpendicular to the fixed axe ?

30
30

of fixed axe = 2500)900 of the revolving axe

,36

D

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PROB. 22. To find the furface or folidity of the five regular bodies. RULE 1, To find the furface, multiply the fquare of the fide of the given body by the tabular fuperficial multiplier against the given name, and the product will be the fuperficies.

2.

To find the folid content, multiply the tabular number againft the given name by the cube of the fide, and the product will be the folidity.

A TABLE of the Superficies and Solidity of each Body,

whofe Side is 1.

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Note. The folidity of any irregular body may be determined by immerfing the fame in a veffel of water; for the folid content of the additional fpace, occupied by the fluid on account of the immersed body, will be equal to the folidity of that body.

2 U 2

PROB. 23.

PROB. 23. To find the folidity of timber.

The menfuration of timber (fuch as cylinders, pyramids, cones, &c. and their fruftums (being very troublesome by the exact rules given in this fection, an approximation has taken place, and the contents of fuch trees, or pieces of timber, are generally computed by the following

RULES 1. Multiply the fquare of the quarter girt (or of the circumference) in inches by the length in feet, and divide that product by 144; the quotient will be the content in feet.

2. Multiply the fquare of of the girt, or circumference, by twice the length; the product will be the content.

E. I,

What is the content of a tree, whofe girt is 40 inches, and length 6 feet?

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Note. By the above example it appears, that the first rule is erroneous, by above part of the true content. The fecond rule differs from the truth only I foot in 190, and is full as eafy in practice; therefore I think it ought to be brought into general ufe among the practitioners in this art, fince the cafe of the other method is the only argument alledged for employing it.

E. 2.

How many feet of timber are there in a tree, whofe girt is 48 inches, and length 9 feet?

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144)1658,88(11,52 feet Answ.

LXIX. ARTIFICERS WORK.

I. OF BRICKLAYERS WORK.

BRICKLAYERS compute, or value their work, at the rate of a

brick and a half thick; and, if a wall be more or less than this

ftandard, it must be reduced to it by the following

RULE. Multiply the fuperficial content of the wall in feet, by the number of half bricks in the thickness, aud of the product will be the content required.

E. I. How many fquare rods are there in a wall 52 feet long, 12 feet high, and 2 bricks thick?

52 Length

12 = Height

272)624,00 (2,29

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In practice it is ufual to divide the fquare feet by 272, omit144

ting the in favour of the workmen.

The ufual way to take the dimenfions of a building, is to measure half round its middle, on the outfide, and half round on the infide; and this will give the true compass, in which the thickness of the wall is included.

When the height of the building is unequal, take several different altitudes, and their fum being divided by the number you have taken, may be confidered as the mean height.

To meafure a chimney ftanding by itfelf, without any party wall adjoining, girt it about for the length, and reckon the height of the ftory for the breadth; but if it ftands against a wall, you must measure it round to the wall for the girt, and take the height as before.

When the chimney is wrought upright from the mantle-tree to the ceiling, the thicknefs muft always be the fame with the jambs; and nothing is deducted for the vacancy between the floor and the mantle-tree, because of the gathering of the breast and wings, to make room for the hearth in the next ftory.

To measure chimney fhafts, or that part which appears above the roof, girt them with a line, about the leaft place for the length, and take the height for the breadth; and if they be 4 inches thick, fet down the thickness at one brick-work; but if they be 9 inches thick, reckon it at a brick and a half, in confideration of the plaftering and fcaffolding.

All

All windows, doors, &c. are to be deducted out of the contents of the walls in which they are placed. But this deduction is made only with regard to the materials; for the value of their workmanship is added to the bill, at the stated rate agreed on.

E. 2. A gentleman built a wall round his garden, which is 942 feet long, 8 feet high, and 2 bricks thick; how many rods doth it contain? 942 = Length

8 = Height

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E. 3. How many rods are there in a wall 824 feet long, 12 feet high, and 2 bricks thick ?

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To masons work belongs all forts of ftone work, and the measure made ufe of is a foot, either fuperficial or folid.

RULE 1. For folid measure, multiply continually into one fum the length, breadth, and thickness, and the product will be the folidity.

2.

For fuperficial measure, multiply the length and breadth of every part of the projection together, and the product will be the content.

E. 1. What is the folid content of a wall, whofe length is 32 feet 6 inches, its height 5 feet 3 inches, and thickness a feet?

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