Circles & Squares

from The Carpenters’ Steel Square and Its Uses
by Fred T. Hodgson

In the hand of the intelligent mechanic the square becomes a simple calculating machine of the most wonderful capacity, and by it they solve problems of the kinds continually arising in mechanical work.

The blade of the square should be 24 inches long and two inches wide, and the tongue from 14 to 18 inches long and 1-½ inches wide. The tongue should be at right angles with the blade, or in other words the “square” should be perfectly square.

In Fig. 28 we show how the centre of a circle may be determined without the use of compasses; this is based on the principle that a circle can be drawn through any three points that are not actually in a straight line. Suppose we take A B C D for four given points, then draw a line from A to D, and from B to C; get the centre of these lines, and square from these centres as shown, and when the square crosses the line, or where the lines intersect, as at X, there will be the centre of the circle. This is a very useful rule, and by keeping it in mind the mechanic may very frequently save themself much trouble, as it often happens that it is necessary to find the centre of the circle, when the compasses are not at hand.

On Fig. 33 we show a quick method of finding the centre of a circle: Let N N, the corner of the square, touch the circumference, and where the blade and tongue cross it will be divided equally; then move the square to any other place and mark in the same way and straight edge across, and where the line crosses A, B, as at O, there will be the centre of the circle.