In like manner, may any other proportion be worked.

To find the superficial content of a board, plank, &c.

Extend from 1 to the breadth; that extent will reach from the length to the superficial content.

EXAMPLE.

Suppose a board or plank 15 inches broad, and 27 feet long; required the content?

Extend from 1 to 1 foot 3 inches; that extent will reach from 27 feet to 33.75 feet, the superficial content.

Or, Extend from 12 inches to 15 inches, &c.

The solid content is found by extending from 1 to the breadth; that extent will reach from 1 to a 4th number; and from 1 to that 4th number, will reach from the length to the solid content.

EXAMPLE I.

What is the content of a square pillar, 21 feet 9 inches long, 1 foot 3 inches broad on each side?

The extent from 1 to 1.25, will reach from 1.25 to

from 1 to 1.56, will reach from the length 21.75 to $3.98, or 34 feet solid.

EXAMPLE II.

Suppose a piece of timber 1.25 feet broad, .56 feet deep, and 36 feet long; required the content.

Extend from 1 to 1.25, that extent will reach from .56 to .7; then extend from 1 to .7, that extent will reach from 36 to 25.2 feet, the solid content.

The line of Sines, marked Sin. begins at the left hand, and is figured thus: 1, 2, 3, 4, 5, &c. to 10; then 20, 30, 40, &c. to 90, ending at the right hand, where is a brass pin, here, and in all lines under it: these figures are called Degrees.

The line of versed sines, marked V. S. begins at the right hand, against 90 on the sines, and from thence figured towards the left hand, thus: 10, 20, 30, 40, &c. ending at the left hand, about 169; each of the subdivisions, from 10 to 30, are 2 degrees, and from thence to 90, it is single degrees; and from thence to the end, each degree is divided into 15 minutes.

The line of Tangents, marked Tan. begins at the left hand, and figured to the right, thus: 1, 2, 3, &c. to 10, and so on to 20, 30, 40, and 45, where is a brass pin, just

H

under and even with 90, in the line of sines; from thenee back, it is figured 50, 60, 70, 80, &c. to 89, ending at the left hand. Where it began, at one degree, the subdivisions are as the sines.

The line of Meridional Parts, marked Mer. begins at the right hand, and numbered 10, 20, 30, to the left hand, where it ends at 87 degrees. This line, with the line of equal parts, marked E. P. under it, are used together, and only in Mercator's sailing. The upper line contains the degrees of the meridian, or latitude, in Mercator's chart; and the lower, the equator, and contains the degrees of longitude.

OF

LOGARITHMS.

LOGARITHMS are a series of numbers, by which the work of multiplication may be performed by addition, and division may be done by subtraction; for, if the logarithm of any two numbers be added together, the sum will be the logarithm of the product: and if the logarithm of the divisor be subtracted from the logarithm of the dividend, the remainder will be the logarithm of the quotient and if the logarithm of any number be divided by 2, the quotient will be the logarithm of the square root of that number. And if the logarithm of any number be divided by 3, the quotient will be the logarithm of the cube-root of that number.

To find the logarithm of any number less than 5 figures.

EXAMPLES.

To find the logarithm of 7.

Look in the table for the number 7, in the side column, and against it is .84510: this number being but one figure, the index to the logarithm is 0.

To find the logarithm of 79.

Look in the table for the number 79, in the side column, and against it is .89763; 1 being the index, because the given number has two figures.

To find the logarithm of 763.

Look for 763 as before, against which is .88252, the index being 2, because the given number has three figures.

To find the logarithm of 7634.

Find the three first figures, viz. 763, in the side column as before, and the fourth figure 4, at the top of the page; then opposite 763, and under is .88275, to which prefix the index 3, because the given number has four figures.

To find the logarithm of five figures, or more.

Suppose 76345.

Find the logarithm of the four first figures, as before, which will be 88275; take the difference between this logarithm, and the next greater, which is 6; then say, if 10 give 6, what will the remaining figure, viz. 5, give? thus, If 10 6 :: 5 3, the fourth number is 3, which, added to the former logarithm 88275, gives 88278, to which prefix the index 4, because there are five figures, and it gives the logarithm of 76545, viz. 4.88278.

To find the logarithm of 763458.

Find the logarithm of the four first figures, as before,