solidity be determined: but in practice a few sections will be found sufficient to answer the purpose. This is the best method that possibly can be devised for the practice of guaging, or for measuring curved timber trees, or the like unequally thick; or any kind of curved solids whatever, generated about an axis; for when all other methods fail, this is the only one that can be depended upon for its

accuracy.

OF

MEASURING TIMBER.

PROBLEM I.

To measure timber scantling.

Find the area at either end, and multiply it by the length, will give the solidity.

EXAMPLE I.

Suppose a joist is 4in. by 9in. and Sft. long, what is the

solidity?

in.

4

9

31 Oii

8

20 feet, the solidity.

EXAMPLE II.

What is the solidity of a joist 3in. by 9in. and 10f. long?

To measure timber trees, or unsquared timber, equally thick.

METHOD I.

Multiply the square of of the trees compass for the side of a square equal in area to the end of the tree, by the length of the tree, and the product will give the solidity.

This method, though easy in practice, is very erroneous in principle, as the content by this rule is too small by above one fourth of itself.

The true rules for measuring round timber, have been already given for measuring a cylinder: but if this rule. should be thought troublesome, the following is a method which will come very near the truth, and nearly as expeditious in practice as the above method, and therefore may be esteemed true.

METHOD 11.

Multiply the square of of the trees compass by the length of the tree, and double the product will be the

content.

MENSURATION

OF

ARTIFICERS WORKS,

CONCERNED IN

BUILDING.

The Artificers' Works which are treated on here, are Bricklayers, Carpenters, Joiners, Masons, Glaziers, Painters, Paviors, Plasterers, Plumbers, and Slaters.

Artificers compute the quantity, or contents of their work, by several different measures, as Glazing and Masonry, by the foot; Painting, Plastering, Paving, &c. by the yard, of 3 feet square, or 9 square feet.

Bricklayers compute the quantity of their work by a rod of 16 feet square, or 2724 square feet, at one brick and a half thick, which Bricklayers call the standard thickness; a rod of 5 yards square, that is, 30 square yards, at 1 brick thick; but although 2724 is a rod of brick work, yet the is always omitted by measurers, and therefore 272 square feet is commonly called a rod of brick work.

All works, whether superficial or solid, are computed by the rules proper for the figure of them.

VOL. I.

нһ

The

The most common instruments for taking the measures are, a five feet rod, divided into feet, and quarters of a foot; and a rule, either divided into inches, or 12 parts, and each 12th part into 12 others: a fractional part beyond this division, Measurers seldom, or never, take any account of.

When the dimensions are taken, by a rule divided in this manner, the best methods to square the dimensions will then be by duodecimals, by the rule of practice, or by the multiplication of vulgar fractions: but, in my opinion, the best method of taking dimensions is with a rule, when each foot is divided into ten parts, and each part into ten other parts, or seconds, because the dimensions may be then squared by the rules of multiplication of decimals, which is by far the shortest and readiest method. Those who contend that duodecimals, or cross multiplication, is the easiest method of squaring dimensions, as well as the most exact, are very much mistaken in their assertion; for if the dimensions are taken in duodecimals, and reduced to decimals, and then squared, the operation, in this case, will be much longer than if it had been done by decimals, and sometimes not so exact but if the dimensions are taken in feet, 10ths, &c. the operation will not only be easier and shorter, but in many cases will be much more exact than duodecimals. The reason is obvious to those who consider, that there are many cases in which it will be impossible to express, truly, a decimal scale equal to a duodecimal one; neither will it, in many cases, be possible to express accurately a duodecimal scale equal to a decimal one; duodecimals have the same property with regard to 12th parts, as decimals have to 10th parts; therefore, in many cases, duodecimals will sometimes circulate and run on, ad infinitum, when reduced from decimals, as decimals will, when reduced from duodecimals and farther, since duodecimals are expressed by a