It is sometimes necessary to reduce a drawing to a smaller scale, or to find a minute fraction of a given dimension, such fraction not being marked on the lineal measuring rules at hand. Figure 224 represents a scale for finding minute fractions. Draw seven lines parallel to each other, and equidistant draw vertical lines dividing the scale into half-inches, as at a, b, c, etc. Divide the first space e d into equal halves, draw diagonal lines, and number them as in the figure. The distance of point 1, which is at the intersection of diagonal with the second horizontal line, will be 1/24 inch from vertical line e. Point 2 will be 2/24 inch from line e, and so on. For tenths of inches there would require to be but six horizontal lines, the diagonals being drawn as before. A similar scale is shown in Figure 225. Draw the lines A B, B D, D C, C A, enclosing a square inch. Divide each of these lines into ten equal divisions, and number and letter them as shown. Draw also the diagonal lines A 1, a 2, B 3, and so on; then the distances from the line A C to the points of intersection of the diagonals with the horizontal lines represent hundredths of an inch.
Suppose, for example, we trace one diagonal line in its path across the figure, taking that which starts from A and ends at 1 on the top horizontal line; then where the diagonal intersects horizontal line 1, is 99/100 from the line B D, and 1/100 from the line A C, while where it intersects horizontal line 2, is 98/100 from line B D, and 2/100 from line A C, and so on. If we require to set the compasses to 67/100 inch, we set them to the radius of n, and the figure 3 on line B D, because from that 3 to the vertical line d 4 is 6/10 or 60/100 inch, and from that vertical line to the diagonal at n is seven divisions from the line C D of the figure.
In making a drawing to scale, however, it is an excellent plan to draw a line and divide it off to suit the required scale. Suppose, for example, that the given scale is one-quarter size, or three inches per foot; then a line three inches long may be divided into twelve equal divisions, representing twelve inches, and these may be subdivided into half or quarter inches and so on. It is recommended to the beginner, however, to spend all his time making simple drawings, without making them to scale, in order to become so familiar with the use of the instruments as to feel at home with them, avoiding the complication of early studies that would accompany drawing to scale.
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