Page:Machinery's Handbook, (6th Edition, 1924, machineryshandbo00indu).pdf/125

Rh

By means of the slide-rule, various calculations may be made mechanically with greater ease and rapidity than by ordinary arithmetical methods, and usually with sufficient accuracy for all practical requirements. Slide-rules are used principally for performing multiplication and division, but they may also be used for finding powers, roots, logarithms, and trigonometrical functions, and for various other purposes. The slide-rule in its most common form consists of three main parts. There is a main body or rule, a slide, and a runner or "cursor." Scales A and D (see Fig. 1) are on the rule, and scales B and C on the slide. Fig. 1 shows the right-hand half of the rule and the left-hand half of the slide, this sectional view being shown in order to secure a larger reproduction. The runner, which is in the form of a light metal frame that is free to slide endwise along the rule, is also shown in Fig. 1. Scales A and B are alike, as are scales C and D. All four scales are of the same length, but the graduations on scales A and B are different from those on scales C and D. The graduation 1 (seen at the extreme left in Fig. 1) is in the center of the rule, and scale A has two parts on opposite sides of this middle point 1 that are graduated exactly alike. The left-hand half from 1 to 1 is called the left-hand A scale, and the right-hand half from 1 to 1, the right-hand B scale and the right-hand B scale. Each end of each scale is marked by the figure 1 which is known as the index. Thus, the figure 1 at the left-hand end of a scale is called the left-hand index, and figure 1 at the right-hand end is called the right-hand index.

As will be seen, the divisions on a slide-rule are not uniform. For example, that part of the left-hand D scale between divisions 1 and 2 (see enlarged detailed view, Fig. 2) is divided into ten main parts, no two of which are equal. Nevertheless, each of these main spaces represents 0.1. Each main space is subdivided into ten unequal parts, each of which represents one-tenth of 0.1, or 0.01. On the scales A and B, each of the ten main spaces between 1 and 2 is divided into only five parts; therefore, each subdivision represents 0.02. It is not possible to divide the spaces between graduations 4 and 5, 6 and 7, 8 and 9, etc., into as many parts as between 1 and 2, or 2 and 3, because the graduation lines would be too close together; therefore, the subdivisions near the right-hand end of any of the scales represent greater values than those near the left-hand end of any of the scales represent greater values than those near the left-hand end. This fact must be kept in mind or errors will result in the use of the slide-rule.

Reading the Slide-rule Graduations. — The method of reading the graduations in indicated in Fig. 2. A small figure 1 to the right of the left-hand index 1, represents the value 1.1, the small figure 2 marks the line that represents 1.2, and so on, to the small figure 9, which denotes 1.9. The second line to the right of the left-hand index denotes 1.02, as it is the second of the ten marks between 1 and 1.1. Several other lines at different points of the scale have the values indicated. It will be noticed that in each case the reading is accurate to at least three figures, and in some cases to four. The divisions on all four of the scales on the slide-rule are such that values can be read correctly to three figures; but beyond this it is not possible to proceed accurately, although the fourth figure may be obtained by estimating with the eye the fractional part of the subdivision. For instance, the fourth figure of the reading 1.535 is possible because the point is halfway between 1.53 and 1.54.

The values of these readings are based on the assumption that the left-hand index represents 1. The value of the left-hand index of any scale may be taken as any power of 0.1 or of 10; that is, it may be taken to represent 0.1, 0.01, 0.001, etc., or 10, 100, 1000, etc. If the left-hand index of the D scale represents 0.01, the readings in Fig. 2 must be multiplied by 0.01, so that they become 0.0102,