The cube of a number may be obtained in one setting by squaring the number and then multiplying the square by the number itself, using the A and B scales.

3. Find the cube of 28.

Square 28 by locating (with the indicator) the point on A which is opposite 28 on D. Multiply the square by 28, thus cubing it, by placing the 1 of scale B opposite the square of 28 and reading the answer on scale A, opposite the 28 on B. Figure 112 illustrates the setting. The reading on the slide rule is 219. The decimal point is determined by comparing it with the cube of 30 which is 27,000. Hence, we must annex two ciphers to the slide rule reading which gives us 21,900 as the answer.

The cube root can be found by reversing the operation. Three possible answers can be found in this manner. The correct one must be selected by

a rough check.

4. Find the cube root of 42,600.

Set the indicator above the point 426 on A. Move the slide back and forth carefully until the reading on B beneath the hair line is exactly the same as the reading on scale D opposite the end, or 1, of scale C. Three such points can be found, and the following method is used to select the right Beginning at the decimal point in the number, divide it up into groups of three digits, in this manner,-42' 600'. If the number had been 4,260,000 it would be divided as follows: 4' 260' 000'. The nearest integral cube root

one.

of the first group of figures at the left of the number will be the first digit of the answer. Thus in the number 42' 600' the first group of digits is 42, and its nearest integral cube root is 3. Thus the first digit of the answer is 3, and the slide rule reading will fall somewhere between the third and fourth divisions on the scale. The reading thus found is 349, as indicated in Fig. 113. The number of groups of digits to the left of the decimal point in the number determines the number of digits to the left of the decimal point in the cube root of the number. In this case there are two groups of digits, so the cube root must be 34.9.

The same method applies to decimals, except that the groups of three digits fall to the right of the decimal point, and the corresponding number of places in the cube root will be at the right of the decimal point.

5. Find the cube root of .0000864.

First divide the number into groups, .'000 '086 '4. The nearest cube root of 86 is 4, which will be the first digit of the slide rule reading. Making the proper setting on the slide rule, we obtain the reading 442. For each group of three ciphers preceding the first significant figure in the number, there is a cipher preceding the first figure in the answer. In this case there is one group of three ciphers so the answer must be .0442.

Other powers and roots of numbers can be obtained by the use of logarithms as explained in the previous chapter. A scale of logarithms is given on the back of the slide by means of which the logarithms of numbers may be obtained without referring to the table. To use this scale, set the 1 of scale C opposite the number on scale D, then turn the slide rule over and read the logarithms on the center scale of the slide, opposite the mark.

4.

5

147. Decimal Points. The determination of the decimal point
provides the greatest source of error and trouble in slide rule
work. The quickest method and the one most generally used
is the simple expedient of estimating the answer by a rough
calculation. In all the preceding examples the decimal point
was determined in this manner. Surprising dexterity can be
acquired in the approximation of answers by this method.
Example:

Calculate the following:

3.6 X 920 X .0013

42 X 640 X .0005

Making a rough cancellation, we see that .0005 goes into .0013 approxi-
mately 2 times, 640 into 920 about 1.5 times, and 3.6 into 42 about 12 times.

Roughly, then, the answer is about .25. Checking with the slide rule we
find the answer as .3205.

PROBLEMS

228. Find the area in square feet of a rectangular roof 31 ft. 6 in. long
and 25 ft. 9 in. wide.

229. A man works 94 hr. per day, 6 days out of a week, and is paid at the
rate of 47 cts. per hour. Calculate his total weekly pay.

230. A power plant burns about 18 tons of coal per day. How many
tons of coal are burned in a year of 365 days?

231. A foundryman receives a pattern made of birch from which he is
to make 20 castings. He weighs the pattern and finds its weight to
be 40 lb. Using the figures given in the table in Chap. XI, he then
calculates the amount of cast iron required to make the castings,
allowing 10% extra for waste. How many pounds of cast iron
must he use?

232. A circular tank is to be built to contain 200 cu. ft. of water when
full, and is to have a depth of 6 ft. What must be its diameter?
233. Calculate the indicated horsepower of a four-cycle, four-cylinder
gas engine from the following data:

Cylinder diameter is 4 in.; stroke is 51⁄2 in.;

R.p.m.

=

1200; m.e.p. = 75 lb. per square inch.

234. A steel wire .192 in. in diameter sustains a load of 500 lb. Deter-
mine the tensile stress per square inch in the wire.

235. The rated full-load capacity of a generator is 60 hp. What power
is required to drive the generator at full load if the generator
efficiency is 87%?