Instruction for Using a Slide Rule | Page 5

) = cuberoot( 34/1000 ) = 1/10 cuberoot( 34 )
The nearest perfect cube to 34 is 27, so our answer must be close to one-tenth of the cube root of 27 or nearly 0.3. Therefore, we must place the decimal point to give 0.324. A group of examples for practice in extraction of cube root follows:
Example 43: cuberoot( 64 ) = 4 44: cuberoot( 8 ) = 2 45: cuberoot( 343 ) = 7 46: cuberoot( .000715 ) = .0894 47: cuberoot( .00715 ) = .193 48: cuberoot( .0715 ) = .415 49: cuberoot( .516 ) = .803 50: cuberoot( 27.8 ) = 3.03 51: cuberoot( 5.49 ) = 1.76 52: cuberoot( 87.1 ) = 4.43
THE 1.5 AND 2/3 POWER
If the indicator is set over a given number on the A scale, the number under the hair-line on the K scale is the 1.5 power of the given number. If the indicator is set over a given number on the K scale, the number under the hair-line on the A scale is the 2/3 power of the given number.
COMBINATIONS OF PROCESSES
A slide rule is especially useful where some combination of processes is necessary, like multiplying 3 numbers together and dividing by a third. Operations of this sort may be performed in such a way that the final answer is obtained immediately without finding intermediate results.
1. Multiplying several numbers together. For example, suppose it is desired to multiply 4 * 8 * 6. Place the right-hand index of the C scale over 4 on the D scale and set the indicator over 8 on the C scale. Now, leaving the indicator where it is, move the slider till the right-hand index is under the hairline. Now, leaving the slider where it is, move the indicator until it is over 6 on the C scale, and read the result, 192, on the D scale. This may be continued indefinitely, and so as many numbers as desired may be multiplied together.
Example 53: 2.32 * 154 * .0375 * .56 = 7.54
2. Multiplication and division. Suppose we wish to do the following example:
Example 54: (4 * 15) / 2.5 = 24
First divide 4 by 2.5. Set indicator over 4 on the D scale and move the slider until 2.5 is under the hair-line. The result of this division, 1.6, appears under the left-hand index of the C scale. We do not need to write it down, however, but we can immediately move the indicator to 15 on the C scale and read the final result 24 on the D scale under the hair-line. Let us consider a more complicated problem of the same type:
Example 55: (30/7.5) * (2/4) * (4.5/5) * (1.5/3) = .9
First set indicator over 30 on the D scale and move slider until 7.5 on the C scale comes under the hairline. The intermediate result, 4, appears under the right-hand index of the C scale. We do not need to write it down but merely note it by moving the indicator until the hair-line is over the right-hand index of the C scale. Now we want to multiply this result by 2, the next factor in the numerator. Since two is out beyond the body of the rule, transfer the slider till the other (left-hand) index of the C scale is under the hair-line, and then move the indicator to 2 on the C scale. Thus, successive division and multiplication is continued until all the factors have been used. The order in which the factors are taken does not affect the result. With a little practice you will learn to take them in the order which will require the fewest settings. The following examples are for practice:
Example 56: (6/3.5) * (4/5) * (3.5/2.4) * (2.8/7) = .8
Example 57: 352 * (273/254) * (760/768) = 374
An alternative method of doing these examples is to proceed exactly as though you were multiplying all the factors together, except that whenever you come to a number in the denominator you use the CI scale instead of the C scale. The reader is advised to practice both methods and use whichever one he likes best.
3. The area of a circle. The area of a circle is found by multiplying 3.1416=PI by the square of the radius or by one-quarter the square of the diameter
Formula: A = PI * square( R ) A = PI * ( square( D ) / 4 )
Example 58: The radius of a circle is 0.25 inches; find its area.
Area = PI * square(0.25) = 0.196 square inches.
Set left-hand index of C scale over 0.25 on D scale. square(0.25) now appears above the left-hand index of the B scale. This can be multiplied by PI by moving the indicator to PI on the B scale and reading the answer .196 on the