The Board-Measure Table. Lumber is sold by the square foot, and the value of the table lies in its giving the area of a board, or of any surface, in square feet, when its length in feet and its breadth in inches are known.

Fig. 29

The figures that belong to the outside graduations, 1, 2, 3, and so on up to 24; are employed to represent the width of the board to be measured, and all the lengths included in the table are given in a column under the figure 12 belonging to the outside graduations. On this square, Fig. 29, they are 14, 10, and 8. To find the surface of any board, first look in the column under 12 for a number representing its length, and having found it, run the finger along in the same line until it comes under that figure of the outside graduations that corresponds to the board's width. The figure nearest the finger in this line represents the area of the board in feet.

Example 1

How many square feet are there in a board 10' long and 7" wide?

Under 12 of the outside graduations, in Fig. 29, the 10 is in the second line, and the figure in this line most nearly under 7 of the outside graduations, is 6, which represents the area required, in feet.

Example 2

What is the surface of a board whose length is 8' and whose width is 21"?

As in Example 1, look under 12 of the outside graduations for 8; in this line, under 21 of the outside graduations, will be found the 14 which represents the area required.

The reason that the column under 12, forming, as it does, a part of the body of the table, is taken to represent the length, will be clear when it is remembered that any board 12" wide will contain as many surface feet as it contains linear feet; that is, a board 12" wide and 14' long will have an area of 14 square feet. The figures given under 12 correspond to the usual length to which lumber is cut, and on most squares they are 8, 10, 14, 16, and 18; and, since the figure representing the area differs from the figure representing the length only because the width varies, we must go to the right or the left of the column under 12, when the width is greater or less than 12.

21. The Brace-measure Table gives the length of each side of several right-angled triangles. A brace in carpentry is a timber inserted diagonally between two other timbers which usually are at right angles to each other. If it is required to insert a brace C between A and B, Fig. 30, its length may be determined by using the table on the framing-square, which, within certain limits, gives the carpenter the length of C when the lengths A and B are known.

Taking the group of figures nearest the end of the short leg for the illustration, suppose A (length ab) = 57" and B (length ac)= 57", then C (length bc)= 80.61". By the next group, it will be seen that if A and B each equal 54" or 54', C will equal 76.31", or 76.31'. The two figures representing the length of the two short sides of the triangle, are always given one above the other, and the figure representing the length of the third side, to the right of the other two.

22. A Try-Square is shown by Fig. 31. The beam A in this case is of wood, faced by a brass strip C to protect it from wear. The blade B, at right angles to the beam, is of steel. The graduations on the blade, together with its thinness, make this square more convenient for short measurements than the rule.

Try-squares are made from 4" to 12", their size being expressed by the length of the blade.

23. The Bevel, often improperly called "bevel-square," is made up of parts similar to those of the try-square, as will be seen by Fig. 32. The blade is adjustable to any angle with the beam; the thumb-screw C fastens it when set.

Fig. 30

Fig. 31

Fig. 32

The size of a bevel is expressed by the length of its beam in inches.

24. "Miter-Squares" derive their name from the purpose they are intended to serve. A "miter" in construction is one-half of a right angle, or an angle of 45 degrees. In the "miter-square" the blade, as in the try-square, is permanently set, but at an angle of 45 degrees, as shown by Fig. 33.

The bevel, while neither so convenient nor so accurate, is often made to answer the purpose of the "miter-square."

25. A Combination Try-and-"Miter" Square is shown by Fig. 34. This, while perfect as a try-square, is transformed into a "miter-square " when the face of the beam AB is placed against the working-face (119) of the material.

26. Dividers are much used in spacing and in laying off circles and arcs of circles. The form shown by Fig. 35 is known as "arc and set-screw dividers." The two points are held at any desired distance from each other by the action of the set-screw A upon the arc B. In setting, the final adjustment may be made more delicate by use of the thumb-nut C, which, acting in opposition to the spring D, shortens the arc B or allows the spring to lengthen it, as may be required.

Fig. 33

Fig. 34

Fig. 35

27. Scribing with Dividers: Example 1. - The four legs of a table are of unequal length, and prevent it from standing even. Scribe the legs to length.

First, by means of blocks or wedges under the shorter legs, make the top of the table to stand parallel to some plane surface, as a bench top, or even the floor if it is in good condition, either of which may be designated as F, Fig. 36. Set the dividers equal to or greater than the height of the thickest blocking, so that while one point, a, touches the leg, the other, b, will rest upon F in the same vertical line. Move the dividers, keeping b on F, and producing by a a line on the leg, as ca, which, if the dividers are properly handled, will be parallel to the surface F. Without changing the dividers, mark at least two adjoining faces on each leg, and cut the legs to line.

It is evident that lines thus scribed will all be at an equal distance from the surface F; and the table top, having been made parallel to F, it follows that the lines scribed are parallel to the top, or that the length of the four legs, as defined by the lines, is the same.

Example 2

It is required to fit the end of a board B to the outline abed of A, Fig. 37. Place the board in the position shown, and set the dividers at a distance equal to x. With one point at a and the other at e, let them be moved together, one following the outline abed which the other produces on B, as shown. Cut to line, and the board will fit. When sharp angles, as at f, enter into the outline, greater accuracy will be attained if the point f is located by measuring from the base line hi.

Fig. 36

Fig. 37