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9. Use of the scales DF and CF (folded scales). The DF and the CF scales are the same as the D and the C scales respectively except in the position of their indices. The fundamental fact concerning the folded scales may be stated as follows: if for any setting of the slide, a number M of the C scale is opposite a number N on the D scale, then the number M of the CF scale is opposite the number N on the DF scale. Thus, if the learner will draw 1 of the CF scale opposite 1.5 on the DF scale, he will find the following opposites on the CF and DF scales |
| CF | 1 | 2 | 4 | 5 | 6 | 6.67 | x |
| DF | 1.5 | 3 | 6 | 7.5 | 9 | 1 | 1.5 × x |
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and the same opposites will appear on the C and D scales. The following statement relating to the folded scales is basic. The process of setting the hairline to a number N on scale C to find its opposite M on scale D may be replaced by setting the hairline to n on scale CF to find its opposite m on scale DF. The statement holds true if letters C and D are interchanged. In accordance with the principle stated above, if the operator wishes to read a number on the D scale opposite a number N on the C scale but cannot do so, he can generally read the required number on the DF scale opposite N on the CF scale. For example to find 2 × 6, to 2 on D set left index of C, push hairline to 6 on CF, at the hairline read 12 on DF. By using the CF and DF scales we saved the trouble of moving the slide as well as the attendant source of error. This saving, entering as it does in many ways, is a main reason for using the folded scales. The folded scales may be used to perform multiplications and divisions just as the C and D scales are used. Thus to find 6.17 × 7.34, to 617 on DF set index of CF, push hairline to 734 on CF, at the hairline read 45.3 on DF; or to 617 on DF set index of CF, push hairline to 734 on C, at the hairline read 45.3 on D. Again to find the quotient 7.68/8.43, push hairline to 768 on DF, draw 843 of CF under the hairline, opposite the index of CF read 0.911 on DF; or push hairline to 768 on DF, draw 843 of CF under the hairline, opposite the index of C read 0.911 on D. It now appears that we may perform a multiplication or a division in several ways by using two or more of the scales C, D, CF, and DF. The sentence written in italics near the beginning of the article sets forth the guiding principle. A convenient method of multiplying or dividing a number by π (= 3.14 approx.) is based on the statement: any number on DF is π times its opposite on D, and any number on D is 1/π times its opposite on DF. For example, to find the value of 4π, push hairline to 4 on D, at hairline read on DF, 12.57 = 4π, to find the value of 3/π push hairline to 3 on DF, at hairline read on D, 0.955 = 3/π. Perform each of the operations indicated in the following exercises. Whenever possible without resetting, read the answer on D and also on DF. |
1.  5.78 × 6.35.2. 7.84 × 1.065.3. 0.00465 ÷ 73.6.4. 0.0634 × 53,600.5. 1.769 ÷ 496.6. 946 ÷ 0.0677.7. 813 7 × 1.951.8. 0.00755 ÷ 0.338. |
9. 0.0948 ÷ 7.23. 10. 149.0 ÷ 63.3.11. 2.718 ÷ 65.7.12. 783 π.13. 783 ÷ π.14. 0.0876 π.15. 0.504 ÷ π.16. 1.072 ÷ 10.97. |
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17. The circumference of a circle measures 8.43 inches. Find its diameter. 18. A cylindrical tube is 13 inches long and has an outside diameter of 2 and (1/8)
inches. Find its outside surface area. |
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