2. Reading the scales. (1) Everyone has read a ruler in measuring a length. The number of inches is shown by a number appearing on the ruler, then small divisions are counted to get the number of 16th's of an inch in the fractional part of the inch, and finally in close measurement, a fraction of a 16th of an inch may be estimated. We first read a primary length, then a secondary length, and finally estimate a tertiary length. Exactly the same method is used in reading the slide rule. The divisions on the slide rule are not uniform in length, but the same principle applies.
Figure 1 represents, in skeleton form, the fundamental scale of the slide rule, namely the D scale. An examination of
this actual scale on the slide rule will show that it is divided into 9 parts by primary marks which are numbered 1, 2, 3, . . . , 9, 1. The space between any two primary marks is divided into ten parts by nine secondary marks. These are not numbered on the actual scale except between the primary marks numbered 1 and 2. Fig. 2 shows the secondary marks lying between the primary marks of the D scale. On this scale each small number gives the reading to be associated with its corresponding secondary mark. Thus, the first secondary mark after 2 is numbered 21, the second 22, the
third 23, etc.; the first secondary mark after 3 is numbered 31, the second 32, etc. Between the primary marks numbered 1 and 2 the secondary marks are numbered 1, 2, . . . , 9. Evidently the readings associated with these marks are 11, 12, 13, . . , 19. Finally between the secondary marks, see Fig. 3, appear smaller or tertiary marks which aid in
obtaining the third digit of a reading. Thus between the secondary marks numbered 22 and 23 there are 4 tertiary marks. If we think of the end marks as representing 220 and 230, the four tertiary marks divide the interval into five parts each representing 2 units. Hence with these marks we associate the numbers 222, 224, 226, and 228; similarly the tertiary marks between the secondary marks numbered 32 and 33 are read 322, 324, 326, and 328, and the tertiary marks between the primary marks numbered 3 and the first succeeding secondary mark are read 302, 304, 306, and 308. Between any pair of secondary marks to the right of the primary mark numbered 4, there is only one tertiary mark. Hence, each smallest space represents five units. Thus the primary mark between the secondary marks representing 41 and 42 is read 415, that between the secondary marks representing 55 and 56 is read 555, and the first tertiary mark to the right of the primary mark numbered 4 is read 405.
The reading of any position between a pair of successive tertiary marks must be based on an estimate. Thus a position half way between the tertiary marks associated with 222 and 224 is read 223 and a position two fifths of the way from the tertiary mark numbered 415 to the next mark is read 417. The principle illustrated by these readings applies in all cases.
Consider the process of finding on the D scale the position representing 246. The first figure on the left, namely 2, tells us that the position lies between the primary marks numbered 2 and 3. This region is indicated by the brace in Fig. (a).
The second figure from the left, namely 4, tells us that the position lies between the secondary marks associated with 24 and 25. This region is indicated by the brace in Fig. (b). Now there are 4 marks between the secondary marks
associated with 24 and 25. With these are associated the numbers 242, 244, 246, and 248 respectively. Thus the
position representing 246 is indicated by the arrow in Fig. (c). Fig. (abc) gives a condensed summary of the process.
It is important to note that the decimal point has no bearing upon the position associated with a number on the C and D scales. Consequently, the arrow in Fig. (abc) may represent 246, 2.46, 0.000246, 24,600, or any other number whose principal digits are 2, 4, 6. The placing of the decimal point will be explained later in this chapter.
For a position between the primary marks numbered 1 and 2, four digits should be read; the first three will be exact and the last one estimated. No attempt should be made to read more than three digits for positions to the right of the primary mark numbered 4.(2)
While making a reading, the learner should have definitely in mind the number associated with the smallest space under consideration. Thus between 1 and 2, the smallest division is associated with 10 in the fourth place; between 2 and 3, the smallest division has a value 2 in the third place; while to the right of 4, the smallest division has a value 5 in the third place.
The learner should read from Fig. 4 the numbers associated with the marks lettered A, B, C, . . . and compare his readings with the following numbers: A 365, B 327, C 263, D 1745, E 1347, F 305, G 207, H 1078, I 435, J 427.
