RF Cascade Workbook

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(Part 2)

This
is a continuation of Part 1. Slide rules were an enigma to most people
even in the days when handheld digital calculators had not entered the scene. The rows of numbers generally look
nothing like a simple, familiar ruler, and the sliding window thingy with the thin line sent kids and adults alike
running for the tall grass for cover. As with most things not too complicated, learning to use the slide rule can
be mastered with a little instruction. You don't necessarily need to understand logarithms and trigonometry functions,
but it certainly helps if you also want to understand how the device works. It is the same thing as not needing
to know how your Casio digital calculator works in order for it to be useful. If you do an Internet search for instructions
on slide rule usage, there is no shortage of documents. This one from Lawrence I believe does a particularly good
job because it is filled with examples of the most common types of mathematical operations, including powers and
roots. It does not address trig functions because, like many beginner's slide rules, it only hade one functional
side, with instructions on the reverse side.

See a large selection of slide rules at the Slide Rule Museum from Lawrence, including specialty types for electrical engineering, music, photography, carpentry, machining, model railroading, printing, water pipe fitting, and much more. Here is the lowly RF Cafe Slide Rule & Calculator Museum.

**The Quick and Easy "Lawrence"
Slide Rule Instruction Book**

By John Poland

Continued from Part 1

**SQUARING A NUMBER BY THE MENTAL
SURVEY METHOD**

When we square a number we mean we are to multiply the number by itself, thus 6^{2}
is 6 x 6. The small number 2 at the upper right of the figure means the number is to be squared.

When squaring a number on the slide rule we use the D and A scales. The hair line of the indicator is set over the number to be squared on the D scale and the answer is read under the hair line on the A scale.

Example 1: (2)^{2}
= 4

Set the hair line of the indicator over 2 on the D scale and read 4 under the hair line on the A scale.

Example 2: (4)^{2} = 16

Set the hair line of the indicator over 4 on the D scale and read 16 under the hair line on A scale.

Example 3: (18)^{2} = 324

Make the setting as has been explained in examples 1 and 2. The number 18 lies between 10 and 20; so 10^{2} = 100 while 20^{2}
= 400, but since 18 is nearest to 20 the answer will be near 400; thus we have 324.

Example 4: (36.2)^{2} = 1310

The number 36.2 lies between 30 and 40; so 30^{2} = 900
while 40^{2} = 1600, but since 36.2 is closer to 40 we will have four numbers in the answer: thus 1310.

Example 5 (18.7)^{2} = 66.7

The number 8.17 lies between 8 and 9; so 8^{2} = 64
while 9^{2} = 81. but 8.17 is closer to 8 than 9 so we have two numbers in the answer; thus 66.8

Problems:

(92.4)^{2} = 8540

(2.61)^{2} = 6.81

(158)^{2} = 24,900

Squaring a Number by Integral Digit Method. (See page 21.)

When we square a number we use the D and A scales. The hair line of the indicator is set over the number to be squared on the D scale and the answer is read under the hair line on the A scale.

Example 1: (2)^{2} = 4

Set the hair line over unit 2 on the D scale and read 4 under the hair line on the left half of the A scale.

Example 2: (3)^{2}
= 9

Set the hair line over 3 on the D scale and read 9 under the hair line on the left half of the A scale.

Example 3: (25)^{2} = 625

In the above examples the answers fall in the left half of the A scale, so a rule for squaring in this case is:

WHEN SQUARING A NUMBER, IF THE ANSWER FALLS IN THE LEFT HALF OF THE A SCALE MULTIPLY THE INTEGRAL DIGITS IN THE NUMBER BY 2, AND THEN SUBTRACT 1. THIS WILL GIVE THE NUMBER OF INTEGRAL DIGITS IN THE ANSWER.

In example 3, the number 25 has two integral digits. Multiplying the number of integral digits by 2 we obtain 4 but the answer falls in the left half so we must subtract one, making 4 - 1 = 3 integral digits in the answer. Therefore. 625 is the, answer containing three integral digits.

Example 4: (167.3)^{2} = 27,900

The number 167.3 has three integral digits; multiplying this by 2 we obtain six integral digits, but it falls in the left half of the A scale so we must subtract 1, leaving five integral digits in the answer. Since we can only read 279 we add the necessary zeros, making 27900.

We will now consider the squaring of a number when it falls in the right half of the A scale.

Example 5: (5)^{2} = 25

Example 6: (6)^{2} = 36

In the above examples the answer was found under the hair line in the right half of the A scale and in each case we had two times as many integral digits in the answer as in the number to be squared. From this we have the following rule: WHEN SQUARING A NUMBER, IF THE ANSWER FALLS IN THE RIGHT HALF OF THE A SCALE MULTIPLY THE INTEGRAL DIGITS IN THE NUMBER BY 2 AND THIS WILL GIVE THE NUMBER OF INTEGRAL DIGITS IN THE ANSWER.

Example 7: (87.3)^{2} = 7620

The number 87.3 has two integral digits. Multiplying by 2 we obtain four which will be the number of integral digits in the answer. As we are only able to read 76 on the A scale we add the two zeros to make the necessary four digits.

Problems

(42.93)^{2}
Ans. 1840

(305.2)^{2}
Ans. 93100

(.753)^{2}
Ans. .567

(613.4)^{2}
Ans. 376,000

**Square Root of a Number by Mental Survey Method **

When we are going to find the square root of a number, we mean that we are to find a number which, when multiplied by itself, will equal the given number.

Whenever the sign**√**() is placed around a number it means
that square root is required.

Before the square root can be found we must mark off the number into groups of two digits each starting from the decimal point. For example, 3148 which is a whole number will be marked off into two groups with 4 and 8 together and 3 and 1 together in this manner:**√**(31|48|). Here
the first group 31 has two digits. Another example 373 will be **√**(3|73) with only one digit
in the first group. Again in the numbers 538.42 and 6.471 they will be grouped as **√**(5|38.42)
and **√**(|6.47|10).

In the answer to the square root of a number there will be as many numbers in the answer as there are groups in the number itself.

To find the square root of a number is the reverse operation of squaring therefore the A and D scales will be used again. If the first group has one number, as shown by 3|73 or 5|38.42|, set the hair line of the indicator over the number on the left half of the A scale and read the answer on the D scale. If the first group has two numbers as in 31|48, set the hair line of the indicator over 3148 on the right half of the A scale and read the answer under the hair line on the D scale.

Example 1:**√**48 = 6.93

Since this group has two numbers, set the scale on 48 in the right half of the A scale and read 694 on the D scale. Here we have only one group, therefore we will have only one whole number in our answer; thus 6.94.

Example 2:**√**(1|44) = 12

Here we have one number in the first group, so we set 144 on the left half of the A scale and read the answer 12 under the hair line on the D scale. The number has two groups so we have two whole numbers in our answer.

Example 3:**√**(17|64|)
= 42.1

This number has two numbers in the first group so we set the indicator over 1764 on the right half of the A scale. This answer 421 is read under the hair line on the D scale, Our number has two groups, therefore we will have two whole numbers in our answer: thus 42.1. (See Fig. 17.)

Problems:

**√**(13|82) = 37.2

**√**(5|48|17) = 234

**√**(7.38) = 2.72

**Square Root of a Number by the Integral Digit Method.**

When we say we are .going to find the square root of a given number, we mean that we are going to find an unknown number which, when multiplied by itself, will be equal to the given number.

The sign**√**()
when placed around a number signifies that the square root of that number is required.

Before we can take the square root of a number, we must first divide the number into groups of two digits each, beginning at the decimal point and point off to the right and left as the case may be. For example, the whole number 4257, we begin at the decimal and point off to the left in groups of two digits, thus |42|57. When pointing off, we place the marks above the number so that they will not become confused with the decimal points. In this number we then have the first group as 42 and the second group as 57.

In many cases we will have only one digit in the first group, as in the number 5187165. Here the first group is 5, the second group 87 and the third group 65.

In a number containing whole digits and decimals. as 54257.4927, we mark off starting at the decimal point point right and left, thus 5|42|57.49|27|.

Finding the square root is the reverse of squaring on the slide Rule. Therefore, the A and D scales are used again. When squaring a number we had two simple rules to learn, so when finding the square root we will also have two simple rules to learn.

1st. When the first group contains one digit, set the hair line over the number on the left half of the A scale and read the answer under the hair line on the D scale.

2nd. When the first group contains two digits, set the hair line over the number on the right half of the A scale and read the answer under the hair line on the D scale.

In both cases there will be as many integral digits in the answers as there are whole groups in the numbers.

Example 1:**√**(1|44)
= 12

The number 144 marked off into groups, giving us two groups before the decimal point; therefore, in answer we will have two integral digits, thus 12.

Example 2:**√**(31|76.58) = 56.4

This number has two digits in the first group so we use the right half of the A scale and read 564 on the D scale. But, since there are only two groups in the number before the decimal point we will only have two integral digits in the answer, thus 56.4.

Example 3:**√**(0.71|30|) = .844

Again the first group has two digits, but it also follows the decimal point, so our first digit in the answer will follow the decimal point.

Problems:

**√**(367) =
Ans. 19.16

**√**(57.426) =
Ans. 7.58

**√**(1476.83) =
Ans. 38.5

The "K" Scale.

The K scale is divided into three equal sections (See Figure 1) which can be easily separated into a left third, a middle third and a right third. Upon examination of the scale the user will see that the divisions and markings are identical in all three thirds. Therefore an explanation of anyone of these thirds will apply to the other two also. With this in mind let us examine the left third.

The left third is divided into 9 unequal divisions, as has been found in all the other scales. Here again, each main division acts as a unit. Unit 1 has ten major divisions and each major division has five minor divisions just as was the case of Unit 2 of the D scale. Since the remaining units have divisions similar to other units of preceding scales, the user will be able to determine the division values for his or herself.

**CUBING A NUMBER BY MENTAL
SURVEY METHOD **

When we cube a number we mean we are to multiply the number by itself three times, thus (2)^{3} is 2X2X2.

To find the cube we use the D and K scales. Set the hair line of the indicator over the number on the D scale and then read the answer under the hair line on the K scale.

From Figure 1 we see that there are four ones or indexes. When the cube falls in the left third the answer will be between 1 and 10; if the cube falls in the middle third the answer will be between 10 and 100; if the cube falls in the right third the answer will be between 100 and 1000. This is repeated again, increasing each third making the left third read 1000 to 10,000. the middle third 10,000 to 100,000, etc.

Example 1: (2)^{3} = 8

Set the hair line of the indicator over 2 on the D scale and read 8 on the K scale under the hair line. The answer falls in the left third where our numbering is from 1 to 10. therefore our answer is 8.

Example 2: (3)^{3}
= 27

The answer falls in the middle third where the numbering is from 10 to 100, therefore we have 27.

Example 3: (6)^{3} = 216

The answer falls in the right third where the numbering is from 100 and 1000, therefore we have 216. (See Fig. 18.)

Example 4: (28)^{3} = 21,900

The answer falls in the middle third, which ranges from 10-100, or 10,000 to 100,000. Since 28 is close to 30 and the cube of 30 would be in the 10,000 to 100,000 range, therefore 28^{3} will fall in this range, thus,
21,800.

Problems:

(8.45)^{3} = 603

(12)^{3} = 1,730

(63.52)^{3}=
256,000

**Cubing a number by Integral Digit Method.**

When we cube a number we mean we are to multiply the number by itself three times, thus 6^{3} is 6X6X6.

To find the cube of a number on the slide rule we use the D and K scales. The hair line is set over the number to be cubed on the D scale and read the answer under the hair line on the K scale. When any number is to be cubed the answer may fall in the left third, the middle third or the right third. Therefore, rules must be established to determine the number of integral digits in the answer.

Rule No.1.

WHEN THE CUBE OF A NUMBER FALLS IN THE RIGHT THIRD, MULTIPLY THE INTEGRAL DIGITS IN THE NUMBER BY 3 AND THIS WILL GIVE THE NUMBER OF INTEGRAL DIGITS IN THE ANSWER.

Example 1: (6)^{3} =6X6X6 = 216

Set the hair line over the 6 on the D scale, read 216 under the hair line on the K scale. Following the above rule: number 6 has one integral digit, multiplying one by 3 we have three integral digits required for the answer, thus 216. (See Fig. 18.)

Example 2: (81.5)^{3} = 541,000

The number 81.5 has two integral digits, multiplying this by 3 we will have six integral digits required in the answer. Since we can only read 54 on the K scale we add the four necessary zeros to make six integral digits.

Example 3: (.572)^{3} = .187

The number .572 has zero integral digits, multiplying by 3 we get zero. Thus we place the point in front of the number 186.

Example 4: (.092)^{3} = .00078

The number .092 has minus one integral digit, multiplying minus one by 3 we get minus three integral digits required in the answer. As we learned earlier in the instructions that minus three means three zeros, we place them before the number 76 read on the K scale. Therefore. our answer .00076.

Rule No.2.

WHEN THE CUBE OF A NUMBER FALLS IN THE MIDDLE THIRD, MULTIPLY THE INTEGRAL DIGITS IN THE NUMBER BY 3 AND THEN SUBTRACT 1. THIS WILL GIVE THE NUMBER OF INTEGRAL DIGITS IN THE ANSWER.

Example 1: (4)^{3} = 64

The number 4 has one integral digit, multiplying one by 3 we get 3, but the answer falls in the middle third so we subtract one from 3 giving two integral digits in the answer, thus 64.

Example 2: (28.3)^{3} = 22,600

The number 28.3 has two integral digits, multiplying by 3 we get 6, but we must subtract one making five integral digits for the answer. thus 22,400.

Example 3: (.035)^{3} = .0000429

The number has minus one integral digit, multiplying by 3 we get minus three, but we must subtract one making minus four integral digits, thus, .0000428.

Rule No. 3.

WHEN THE CUBE OF A NUMBER FALLS IN THE LEFT THIRD, MULTIPLY THE NUMBER OF INTEGRAL DIGITS BY THREE AND THEN SUBTRACT TWO. THIS WILL GIVE THE NUMBER OF INTEGRAL DIGITS IN THE ANSWER.

Example 1: (2)^{8} = 8

Number 2 has one integral digit, multiplying by 3 we get 3 but we must subtract two, leaving one integral digit in the answer, thus 8.

Example 2: (11)^{3} = 1330

Number 11 has two integral digits, multiplying by 3 we get 6 but we must subtract two, leaving four integral digits in the answer, thus 1330.

Cube Root of a Number

The cube root of a number is the reverse of cubing, therefore, we use the K and D scales.

When finding the cube root we set the hair line of the indicator over the number on the K scale and then read the answer under the hair line in the right third over 125 and read 5 on the D scale. (See Fig. 19.)

The sign**√**() when placed around a number signifies
that the cube root is required.

Before we take the cube root of a number, it must be divided into groups of three numbers each, beginning at the decimal point and point off to the right and left just as we did upon taking the square root. In many cases we will have only one number in the first group, others will be two numbers in the first group and others will be three numbers in the first group.

Examples 1|547.632| has one number in the first group: 38|527, has two numbers in the first group: |157.38 has three numbers in the first group.

After the number has been divided into groups and the first group has only one number, set the hair line of the indicator over the number in the LEFT THIRD of the K scale and read the answer on the D scale.

Example:**√**(2|450)
= 13.5. Here the first group has only one number, therefore we use the left third of the K scale.

If the first group contains two numbers, as**√**(64) we set the hair line in the middle third of the K scale
over 64 and read 4 on the D side.

If the first group contains three numbers as**√**(125),
we set the hair line in the right third over 125 and read 5 on the D scale. (See Fig. 19.)

Problems:

**√**(84.7)
Ans.·= 4.39

**√**(3.76)
Ans. = 1.554

**√**(0.106)
Ans. = .474

**THE C I OR RECIPROCAL SCALE **

The C I scale is the same as the C scale except that it is numbered from right to left instead of left to right.

H we divide one (1) by any number the answer will be the reciprocal of the number. Thus. one-third is the reciprocal of three, one-sixth the reciprocal of six. The reciprocal of four is one-fourth (1/4) or (.25). The number 25 will be found on the C I scale directly above 4 on C scale. For 1/3 or (.333) the number 333 will be found on the C I scale directly above 3 on the D scale. The decimal point is obvious.

Suppose we wished to multiply 25 by the reciprocal of 5 which would be 25 times one-fifth. Set the left index of C on 25 on D as in multiplication, move the hair line to 5 on the C I. scale and read the answer 5 under the hair line on the D scale. (See Fig. 20.) Again let us multiply 89.37 by one-sixth. Set the right index of C over 8937 on the D scale, move hair line to 6 on C I scale; read the answer 14.9 under the hair line on the D scale.

In addition, the C I scale can be used when three factors are to be multiplied to an advantage.

Example: 1.62 x .7 x 5.63 = 6.38

Set the hair line of the indicator over 162 on the D scale, move 7 on the C I scale under the hair line, then slide the indicator so the hair line is over 563 on the C scale; read the answer 6.38 under the hair line on the D scale.

The 3/2 and 2/3 Power

In addition to finding the second power (square) and the third power (cube) of a number on the slide rule, we have also the scales to find the 3/2 power and the 2/3 power of a number.

To find the 3/2 power of a number set the hair line of the indicator over the number on the A scale and read the answer on the K scale.

Example:**√**(4^{3})
= 8

(4) 3/2 is read four raised to the three halves power.

Set the hair line over 4 in the left half of the A scale, read 8 under the hair line on the K scale. (4) 3/2 is the same as the**√**(4^{3})
,square root of 4 cubed. The square root of 4 is 2, then 2 cubed is 8, which proves our answer in the above example.

Problems:

**√**(28^{3}) =148

**√**(6.73^{3}) = 17.5

**√**(11.84^{3}) = 40.7

To find the 2/3 power of a number set the hair line of the indicator over the number on the K scale and read the answer on the A scale.

Example 1:**
**^{3}√(27^{2}) = 9

The number (27)^{2/3} is read 27 raised to the two-thirds
power.

This is the same as the cube root of 27 squared. Set the hair line over 27 on the middle third of the K scale, read the answer under the hair line on the A scale. We know the cube root of 27 is 3 and then squaring 3 we obtain our answer 9.

Problems:

^{3}√(125^{2}) = 25

^{3}√(5.84^{2}) = 3.24

^{3}√(64^{2}) = 16

**What Are Digits and Integral Digits? **

All our numbering system is made by using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0 either singly or by combining them into groups as 7, 8, 5, or 16, 35, 856, etc. Numbers may be integral digits (whole number as 75) or they may take the form of a fraction as .685. To illustrate: the numbers 684, 17, 37850 are composed of digits called integral digits as each one is a whole number while the number 68.4 is composed of three digits, with numbers 6 and 8 being integral digits and the number .4 a decimal or fractional portion of an integral digit. The number 3.785 contains four digits but only one integral digit which is the number 3, as it is the only whole number of the group; the number .785 again being a decimal or fractional portion of an integral digit. The number .568 is composed of three digits but here we have no integral digit as none of them are whole numbers.

IS 75) or they may take the form of a fraction as .685. To illustrate: the numbers 684. 17. 37850 are composed of digits called integral digits as each one is a whole number while the number 68.4 is composed of three digits. with numbers 6 and 8 being integral digits and the number .4 a decimal or fractional portion of an integral digit. The number 3.785 contains four digits but only one integral digit which is the number 3. as it is the only whole number of the group; the number .785 again being a decimal or fractional portion of an integral digit. The number .568 is composed of three digits but here we have no integral digit as none of them are whole numbers.

Now in the number .0568 we again have three digits but because a zero follows the decimal point we must consider this number as having a minus 1 (-1) integral digit. (It must be remembered that zero is not considered a digit unless it is preceded by one of the digits. 1, 2, to 9.) The fractional portion of the number is evident. Again. in the number .00568 we have three digits with two zeros following the decimal point which would mean that this number would have minus 2 (-2) integral digits along with the fractional portion. Therefore. we may say that there are as many integral digits in a number as there are digits before the decimal point and as many minus (-) integral digits as there are zeros following the decimal point. This information will be valuable in performing the different operations.

**The Addition of Integral Digits**

As explained above, numbers having zeros following the decimal point have minus (negative) integral digits, while whole numbers or numbers having digits before the decimal point have plus (positive) integral digits.

In order to determine the number of integral digits quickly and accurately in the answers of multiplication problems of all kinds (as we do not always deal in simple whole numbers) the addition of minus and plus integral digits must be understood.

Adding plus integral digits: Examples. (436 x 24.72): 436 has plus 3 and 24.72 has plus integral digits; adding 3 and 2 we have five integral digits (8367 x .1776): 8567 has plus 4 and .1776 has zero integral digits; adding plus 4 and 0 we have 4 integral digits.

Adding minus integral digits: Examples. (.476 x .00153): .476 has zero and .00153 has minus 2 integral digits, adding 0 and minus 2 we have minus 2 (-2) integral digits.

(.0276 x .000348): .0276 has minus 1 and .000348 has minus 3 integral digits, adding minus 1 and minus 3 we have minus 4 (-4) integral digits.

Adding plus integral digits to minus integral digits or minus integral digits to plus integral digits:

Examples:

(74.3. x .0672); 74.3 has plus 2 and .0672 has minus one integral digit, adding plus 2 and minus 1 we have plus 1 (+ 1) integral digit.

(.00566 x 1873); .00566 has minus 2 and 1873 has plus 4 integral digits, adding minus 2 and plus 4 we have plus 2 (+2) integral digits.

(.000857 x 11.36); .000857 has minus 3 and 11.36 has plus 2 integral digits, adding minus 3 and plus 2 we have minus 1 (-1) integral digits.

From. the above explanation we can establish this rule for adding integral digits: when the integral digits are plus or positive we add them and use the plus sign; when the integral digits are minus or negative we add them and use the minus sign; but when we add plus and minus integral digits we subtract the smaller number from the larger and use the sign of the larger number.

Other Examples:

+6 +3 = 9 -2 + (-4) =-6 +3 + (-2) = +1 -1 + 4 = +3 +4 +2 = +6

+3 + (-5) =-2 -6 +1 =-5 -7 + (-2) = -9 -3 + 0 = -3 +2 +0 = +2

Note:- A thorough explanation in regard to the terms "digits" and integral digit has been mentioned previously on this page.

**The Subtraction of Integral Digits. **

In order to perform division correctly and easily it will be necessary to understand the subtraction of plus and minus integral digits.

In the subtraction of plus and minus integral digits the sign of the subtrahend is changed and the two numbers are added as explained under section, "The Addition of Integral Digits."

Example 1: +6 - (+2) = +4

Here the +2 is the subtrahend, changing its sign to a minus we then add it to +6 giving + (-2) or +4.

Example 2: -1 - (+2) = -3

Here again the (+2) is the subtrahend, changing its sign to a minus; we then add it to (-1) giving -1 + (-2) or -3.

Example 3: +3 - (-2) = 5

Here the (-2) is the subtrahend, changing its sign to a plus; we then add it to +3 giving +3 + (+2) or +5.

Other examples of subtraction:

The signs inside the parenthesis show what the signs become after they are changed.

Note: - Explanation of the digits and integral digits will be found on the preceding page.

Practice Problems:

21. The diameter of a circle is 1.54 inches, what is its circumference?

Answer: 3.1416 x 1.54 =

22. A voltage of 110 volts is impressed across a lamp and a current of .52 amperes flows.

What is the power.

Answer: 110 x .52 =

23. What is the area of a triangle whose base is 6.25 and whose altitude is 8.33?

Area = (6.25 x 8.33)/2

24. There are 24 children in a class room and the sum of all their ages is 384. What is the average age?

Answer: 381 + 24 =

25. A lot is 227 by 96 feet. How many acres does it contain if there are 43560 sq ft. in an acre?

Answer: (227 x 96) ÷ 43560 =

26. An automobile makes a trip of 280 miles on 16 gallons of gasoline. What was the number of miles per gallon?

Answer: 280 ÷ 16 =

27. If a room is 12' x 15' x 8' how many square feet of wall paper would be required to cover the walls and ceiling? Answer: (12 x 15) +2 (8 x 12) +2 (8 x 15) =

28. If the distance between the first floor and the second floor is 8'-9" and there are to be 15 steps, what will be the height of each riser?

Answer (8'-9") ÷ 15 =

29. In a certain production job the allowable cutting speed is 3.75 feet per second. When turning a shaft 4 inches in diameter, how fast should the lathe be run?

Answer: (3.75 x 12 x 60) ÷ 4π =

30. If the average hiking speed of boy scouts is 3.25 miles per hour, how long will it take to hike 15 miles? Answer: 15 ÷ 3.25 =

31. A right triangle has sides 8.8 and 4.21 inches respectively. What is the length of the hypotenuse?

Answer: √(8.8^{2} / 4.21^{2})

32. A motorist makes a trip of 265 miles in 8.75 hours. What is his average speed?

Answer: 265 ÷ 8.75 =

33. A water tank is 15.6 x 8.6 x 3.3 feet. How many gallons of water will it hold? There are 7.48 gallons in a cubic foot.

Answer: 15.6 x 8.6 x 3.3 x 7.48 =

34. How much is the cost of 3 3/4 tons of coal at $9.75 per ton?

Answer: 3.75 x 9.75 =

Answers to Practice Problems:

A careful reading of the foregoing pages will equip the average person with a command of slide rule operations. These are thousands of applications of the slide rule to useful, everyday problems.

A few of these practical everyday tasks are illustrated on the back cover of this book. These sketches illustrate typical problems that can be worked out quickly and accurately by the STUDENT, the HOUSEWIFE, etc. Let us take them up one by one.

1. The Student. Example.

How many feet per minute does a 22" wheel cover when making 166 revolutions every minute?

Solution. Number of teeth = (3.14 x 22 x 166)/12 = 956

2. The Housewife. Example.

How much does the housewife realize, if in a week's time she sold 18 1/2 dozen of eggs at 22 1/2 cents per dozen.

Profit = 18.5 x 225 = $4.17

3. The Salesman. Example.

If an air conditioning system cost $1,210.50 installed, what would be the saving to the customer if a discount of 16% were allowed, if paid for in full within three months.

Solution. Saving = 1210.50 x .16 = $193.70

4. The Draftsman. Example.

A gear 18" in diameter has a circular pitch of 1 1/4". How many teeth does the gear have on it?

Solution.

Number of teeth = (3.14 x 180/1.25

5. The Machinist. Example.

At what R.P.M. should a 1 1/4" high speed drill be run to give a cutting speed of 80 ft. per minute.?

R.P.M. = (80 x 12)/(3.1416 x 1.25) = 244

6. The Teacher. Example.

How many pounds of air are in a room 15' x 22' x 12', if 0.5 cubic feet weigh a pound?

Pounds of air = (16 x 22 x 12)/13.5 = 312

7. The Timekeeper. Example.

What is the total expenses of a company for the following labor: Bricklayer 42 hours at $1.10; Carpenter 38 hours at $0.98; and Lather 26 hours at $0.851

Cost = 42 x 1.10 + 38 x .98 + 26 x .85 = $105.50

8. The Farmer. Example.

How many tons of silage will a silo 16 feet in diameter and 30 feet high hold if silage weighs 38 lbs. per cubic foot?

Tons = (3.14 x 16^{2} x 30 38)/(4 x 2000) = 11.460

9. The Printer. Example.

How many pictures 2 1/4" x 3 1/2" can be placed on a sheet 12" x 18"

Number = (12/2.25 = 5+)(18/3.5 = 5+) 5 x 5 = 25

10.The Office Worker. Example.

What would be the cost to ship a box weighing 125 lbs. a distance of 176 miles at 4 1/2 cents per pound?

Cost = 125 x .045 = $5.63

11. The Carpenter. Example.

How many feet B.M. are there in 16 pieces 1 1/2" x 10" x 26' long?

Ft. B.M. = (3 x 10 x 26 x 16)/(2 x 12) = 520

**A LAWRENCE SLIDE RULE makes a PERFECT GIFT!**

As the owner of a Lawrence Slide Rule and this new Lawrence Slide Rule Instruction Book, you have no doubt found the operation of a slide rule a fascinating and worthwhile activity.

There's no pleasure EQUAL to the satisfaction of knowing you have mastered this "most useful of man's tools," SUGGESTION: Share your pleasure with a friend. Give him a Lawrence Slide Rule and Book as a GIFT. He will treasure it for years to come - and think of you every time he uses it. The cost is so very small, and the value so great, you'll do your friends a lasting favor by presenting them with something useful, educational and interesting.

Please patronize the store where you bought this book. If you your local merchant cannot supply you, write us at once.

ENGINEERING INSTRUMENTS, Inc.

PERU, INDIANA, U. S. A.

Posted 5/20/2013

See a large selection of slide rules at the Slide Rule Museum from Lawrence, including specialty types for electrical engineering, music, photography, carpentry, machining, model railroading, printing, water pipe fitting, and much more. Here is the lowly RF Cafe Slide Rule & Calculator Museum.

By John Poland

Continued from Part 1

When we square a number we mean we are to multiply the number by itself, thus 6

When squaring a number on the slide rule we use the D and A scales. The hair line of the indicator is set over the number to be squared on the D scale and the answer is read under the hair line on the A scale.

Example 1: (2)

Set the hair line of the indicator over 2 on the D scale and read 4 under the hair line on the A scale.

Example 2: (4)

Set the hair line of the indicator over 4 on the D scale and read 16 under the hair line on A scale.

Example 3: (18)

Make the setting as has been explained in examples 1 and 2. The number 18 lies between 10 and 20; so 10

Squaring 18 **FIG. 16**

Example 4: (36.2)

The number 36.2 lies between 30 and 40; so 30

Example 5 (18.7)

The number 8.17 lies between 8 and 9; so 8

Problems:

(92.4)

(2.61)

(158)

Squaring a Number by Integral Digit Method. (See page 21.)

When we square a number we use the D and A scales. The hair line of the indicator is set over the number to be squared on the D scale and the answer is read under the hair line on the A scale.

Example 1: (2)

Set the hair line over unit 2 on the D scale and read 4 under the hair line on the left half of the A scale.

Example 2: (3)

Set the hair line over 3 on the D scale and read 9 under the hair line on the left half of the A scale.

Example 3: (25)

In the above examples the answers fall in the left half of the A scale, so a rule for squaring in this case is:

WHEN SQUARING A NUMBER, IF THE ANSWER FALLS IN THE LEFT HALF OF THE A SCALE MULTIPLY THE INTEGRAL DIGITS IN THE NUMBER BY 2, AND THEN SUBTRACT 1. THIS WILL GIVE THE NUMBER OF INTEGRAL DIGITS IN THE ANSWER.

In example 3, the number 25 has two integral digits. Multiplying the number of integral digits by 2 we obtain 4 but the answer falls in the left half so we must subtract one, making 4 - 1 = 3 integral digits in the answer. Therefore. 625 is the, answer containing three integral digits.

Example 4: (167.3)

The number 167.3 has three integral digits; multiplying this by 2 we obtain six integral digits, but it falls in the left half of the A scale so we must subtract 1, leaving five integral digits in the answer. Since we can only read 279 we add the necessary zeros, making 27900.

We will now consider the squaring of a number when it falls in the right half of the A scale.

Example 5: (5)

Example 6: (6)

In the above examples the answer was found under the hair line in the right half of the A scale and in each case we had two times as many integral digits in the answer as in the number to be squared. From this we have the following rule: WHEN SQUARING A NUMBER, IF THE ANSWER FALLS IN THE RIGHT HALF OF THE A SCALE MULTIPLY THE INTEGRAL DIGITS IN THE NUMBER BY 2 AND THIS WILL GIVE THE NUMBER OF INTEGRAL DIGITS IN THE ANSWER.

Example 7: (87.3)

The number 87.3 has two integral digits. Multiplying by 2 we obtain four which will be the number of integral digits in the answer. As we are only able to read 76 on the A scale we add the two zeros to make the necessary four digits.

Problems

(42.93)

(305.2)

(.753)

(613.4)

When we are going to find the square root of a number, we mean that we are to find a number which, when multiplied by itself, will equal the given number.

Whenever the sign

Before the square root can be found we must mark off the number into groups of two digits each starting from the decimal point. For example, 3148 which is a whole number will be marked off into two groups with 4 and 8 together and 3 and 1 together in this manner:

In the answer to the square root of a number there will be as many numbers in the answer as there are groups in the number itself.

To find the square root of a number is the reverse operation of squaring therefore the A and D scales will be used again. If the first group has one number, as shown by 3|73 or 5|38.42|, set the hair line of the indicator over the number on the left half of the A scale and read the answer on the D scale. If the first group has two numbers as in 31|48, set the hair line of the indicator over 3148 on the right half of the A scale and read the answer under the hair line on the D scale.

Example 1:

Since this group has two numbers, set the scale on 48 in the right half of the A scale and read 694 on the D scale. Here we have only one group, therefore we will have only one whole number in our answer; thus 6.94.

Example 2:

Here we have one number in the first group, so we set 144 on the left half of the A scale and read the answer 12 under the hair line on the D scale. The number has two groups so we have two whole numbers in our answer.

Example 3:

This number has two numbers in the first group so we set the indicator over 1764 on the right half of the A scale. This answer 421 is read under the hair line on the D scale, Our number has two groups, therefore we will have two whole numbers in our answer: thus 42.1. (See Fig. 17.)

Square Root of 17.64 **FIG. 17**

Problems:

When we say we are .going to find the square root of a given number, we mean that we are going to find an unknown number which, when multiplied by itself, will be equal to the given number.

The sign

Before we can take the square root of a number, we must first divide the number into groups of two digits each, beginning at the decimal point and point off to the right and left as the case may be. For example, the whole number 4257, we begin at the decimal and point off to the left in groups of two digits, thus |42|57. When pointing off, we place the marks above the number so that they will not become confused with the decimal points. In this number we then have the first group as 42 and the second group as 57.

In many cases we will have only one digit in the first group, as in the number 5187165. Here the first group is 5, the second group 87 and the third group 65.

In a number containing whole digits and decimals. as 54257.4927, we mark off starting at the decimal point point right and left, thus 5|42|57.49|27|.

Finding the square root is the reverse of squaring on the slide Rule. Therefore, the A and D scales are used again. When squaring a number we had two simple rules to learn, so when finding the square root we will also have two simple rules to learn.

1st. When the first group contains one digit, set the hair line over the number on the left half of the A scale and read the answer under the hair line on the D scale.

2nd. When the first group contains two digits, set the hair line over the number on the right half of the A scale and read the answer under the hair line on the D scale.

In both cases there will be as many integral digits in the answers as there are whole groups in the numbers.

Example 1:

The number 144 marked off into groups, giving us two groups before the decimal point; therefore, in answer we will have two integral digits, thus 12.

Example 2:

This number has two digits in the first group so we use the right half of the A scale and read 564 on the D scale. But, since there are only two groups in the number before the decimal point we will only have two integral digits in the answer, thus 56.4.

Example 3:

Again the first group has two digits, but it also follows the decimal point, so our first digit in the answer will follow the decimal point.

Problems:

The "K" Scale.

The K scale is divided into three equal sections (See Figure 1) which can be easily separated into a left third, a middle third and a right third. Upon examination of the scale the user will see that the divisions and markings are identical in all three thirds. Therefore an explanation of anyone of these thirds will apply to the other two also. With this in mind let us examine the left third.

The left third is divided into 9 unequal divisions, as has been found in all the other scales. Here again, each main division acts as a unit. Unit 1 has ten major divisions and each major division has five minor divisions just as was the case of Unit 2 of the D scale. Since the remaining units have divisions similar to other units of preceding scales, the user will be able to determine the division values for his or herself.

When we cube a number we mean we are to multiply the number by itself three times, thus (2)

To find the cube we use the D and K scales. Set the hair line of the indicator over the number on the D scale and then read the answer under the hair line on the K scale.

From Figure 1 we see that there are four ones or indexes. When the cube falls in the left third the answer will be between 1 and 10; if the cube falls in the middle third the answer will be between 10 and 100; if the cube falls in the right third the answer will be between 100 and 1000. This is repeated again, increasing each third making the left third read 1000 to 10,000. the middle third 10,000 to 100,000, etc.

Example 1: (2)

Set the hair line of the indicator over 2 on the D scale and read 8 on the K scale under the hair line. The answer falls in the left third where our numbering is from 1 to 10. therefore our answer is 8.

Example 2: (3)

The answer falls in the middle third where the numbering is from 10 to 100, therefore we have 27.

Example 3: (6)

The answer falls in the right third where the numbering is from 100 and 1000, therefore we have 216. (See Fig. 18.)

Example 4: (28)

Hairline Cubing 6**FIG. 18**

The answer falls in the middle third, which ranges from 10-100, or 10,000 to 100,000. Since 28 is close to 30 and the cube of 30 would be in the 10,000 to 100,000 range, therefore 28

Problems:

(8.45)

(12)

(63.52)

When we cube a number we mean we are to multiply the number by itself three times, thus 6

To find the cube of a number on the slide rule we use the D and K scales. The hair line is set over the number to be cubed on the D scale and read the answer under the hair line on the K scale. When any number is to be cubed the answer may fall in the left third, the middle third or the right third. Therefore, rules must be established to determine the number of integral digits in the answer.

Rule No.1.

WHEN THE CUBE OF A NUMBER FALLS IN THE RIGHT THIRD, MULTIPLY THE INTEGRAL DIGITS IN THE NUMBER BY 3 AND THIS WILL GIVE THE NUMBER OF INTEGRAL DIGITS IN THE ANSWER.

Example 1: (6)

Set the hair line over the 6 on the D scale, read 216 under the hair line on the K scale. Following the above rule: number 6 has one integral digit, multiplying one by 3 we have three integral digits required for the answer, thus 216. (See Fig. 18.)

Example 2: (81.5)

The number 81.5 has two integral digits, multiplying this by 3 we will have six integral digits required in the answer. Since we can only read 54 on the K scale we add the four necessary zeros to make six integral digits.

Example 3: (.572)

The number .572 has zero integral digits, multiplying by 3 we get zero. Thus we place the point in front of the number 186.

Example 4: (.092)

The number .092 has minus one integral digit, multiplying minus one by 3 we get minus three integral digits required in the answer. As we learned earlier in the instructions that minus three means three zeros, we place them before the number 76 read on the K scale. Therefore. our answer .00076.

Rule No.2.

WHEN THE CUBE OF A NUMBER FALLS IN THE MIDDLE THIRD, MULTIPLY THE INTEGRAL DIGITS IN THE NUMBER BY 3 AND THEN SUBTRACT 1. THIS WILL GIVE THE NUMBER OF INTEGRAL DIGITS IN THE ANSWER.

Example 1: (4)

The number 4 has one integral digit, multiplying one by 3 we get 3, but the answer falls in the middle third so we subtract one from 3 giving two integral digits in the answer, thus 64.

Example 2: (28.3)

The number 28.3 has two integral digits, multiplying by 3 we get 6, but we must subtract one making five integral digits for the answer. thus 22,400.

Example 3: (.035)

The number has minus one integral digit, multiplying by 3 we get minus three, but we must subtract one making minus four integral digits, thus, .0000428.

Rule No. 3.

WHEN THE CUBE OF A NUMBER FALLS IN THE LEFT THIRD, MULTIPLY THE NUMBER OF INTEGRAL DIGITS BY THREE AND THEN SUBTRACT TWO. THIS WILL GIVE THE NUMBER OF INTEGRAL DIGITS IN THE ANSWER.

Example 1: (2)

Number 2 has one integral digit, multiplying by 3 we get 3 but we must subtract two, leaving one integral digit in the answer, thus 8.

Example 2: (11)

Number 11 has two integral digits, multiplying by 3 we get 6 but we must subtract two, leaving four integral digits in the answer, thus 1330.

Cube Root of a Number

The cube root of a number is the reverse of cubing, therefore, we use the K and D scales.

When finding the cube root we set the hair line of the indicator over the number on the K scale and then read the answer under the hair line in the right third over 125 and read 5 on the D scale. (See Fig. 19.)

The sign

Before we take the cube root of a number, it must be divided into groups of three numbers each, beginning at the decimal point and point off to the right and left just as we did upon taking the square root. In many cases we will have only one number in the first group, others will be two numbers in the first group and others will be three numbers in the first group.

Examples 1|547.632| has one number in the first group: 38|527, has two numbers in the first group: |157.38 has three numbers in the first group.

After the number has been divided into groups and the first group has only one number, set the hair line of the indicator over the number in the LEFT THIRD of the K scale and read the answer on the D scale.

Example:

If the first group contains two numbers, as

If the first group contains three numbers as

Cube Root of 125 **FIG. 19 **

Problems:

The C I scale is the same as the C scale except that it is numbered from right to left instead of left to right.

H we divide one (1) by any number the answer will be the reciprocal of the number. Thus. one-third is the reciprocal of three, one-sixth the reciprocal of six. The reciprocal of four is one-fourth (1/4) or (.25). The number 25 will be found on the C I scale directly above 4 on C scale. For 1/3 or (.333) the number 333 will be found on the C I scale directly above 3 on the D scale. The decimal point is obvious.

Suppose we wished to multiply 25 by the reciprocal of 5 which would be 25 times one-fifth. Set the left index of C on 25 on D as in multiplication, move the hair line to 5 on the C I. scale and read the answer 5 under the hair line on the D scale. (See Fig. 20.) Again let us multiply 89.37 by one-sixth. Set the right index of C over 8937 on the D scale, move hair line to 6 on C I scale; read the answer 14.9 under the hair line on the D scale.

Using C I Scale **FIG. 20**

In addition, the C I scale can be used when three factors are to be multiplied to an advantage.

Example: 1.62 x .7 x 5.63 = 6.38

Set the hair line of the indicator over 162 on the D scale, move 7 on the C I scale under the hair line, then slide the indicator so the hair line is over 563 on the C scale; read the answer 6.38 under the hair line on the D scale.

The 3/2 and 2/3 Power

In addition to finding the second power (square) and the third power (cube) of a number on the slide rule, we have also the scales to find the 3/2 power and the 2/3 power of a number.

To find the 3/2 power of a number set the hair line of the indicator over the number on the A scale and read the answer on the K scale.

Example:

(4) 3/2 is read four raised to the three halves power.

Set the hair line over 4 in the left half of the A scale, read 8 under the hair line on the K scale. (4) 3/2 is the same as the

Problems:

To find the 2/3 power of a number set the hair line of the indicator over the number on the K scale and read the answer on the A scale.

Example 1:

The number (27)

This is the same as the cube root of 27 squared. Set the hair line over 27 on the middle third of the K scale, read the answer under the hair line on the A scale. We know the cube root of 27 is 3 and then squaring 3 we obtain our answer 9.

Problems:

All our numbering system is made by using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0 either singly or by combining them into groups as 7, 8, 5, or 16, 35, 856, etc. Numbers may be integral digits (whole number as 75) or they may take the form of a fraction as .685. To illustrate: the numbers 684, 17, 37850 are composed of digits called integral digits as each one is a whole number while the number 68.4 is composed of three digits, with numbers 6 and 8 being integral digits and the number .4 a decimal or fractional portion of an integral digit. The number 3.785 contains four digits but only one integral digit which is the number 3, as it is the only whole number of the group; the number .785 again being a decimal or fractional portion of an integral digit. The number .568 is composed of three digits but here we have no integral digit as none of them are whole numbers.

IS 75) or they may take the form of a fraction as .685. To illustrate: the numbers 684. 17. 37850 are composed of digits called integral digits as each one is a whole number while the number 68.4 is composed of three digits. with numbers 6 and 8 being integral digits and the number .4 a decimal or fractional portion of an integral digit. The number 3.785 contains four digits but only one integral digit which is the number 3. as it is the only whole number of the group; the number .785 again being a decimal or fractional portion of an integral digit. The number .568 is composed of three digits but here we have no integral digit as none of them are whole numbers.

Now in the number .0568 we again have three digits but because a zero follows the decimal point we must consider this number as having a minus 1 (-1) integral digit. (It must be remembered that zero is not considered a digit unless it is preceded by one of the digits. 1, 2, to 9.) The fractional portion of the number is evident. Again. in the number .00568 we have three digits with two zeros following the decimal point which would mean that this number would have minus 2 (-2) integral digits along with the fractional portion. Therefore. we may say that there are as many integral digits in a number as there are digits before the decimal point and as many minus (-) integral digits as there are zeros following the decimal point. This information will be valuable in performing the different operations.

As explained above, numbers having zeros following the decimal point have minus (negative) integral digits, while whole numbers or numbers having digits before the decimal point have plus (positive) integral digits.

In order to determine the number of integral digits quickly and accurately in the answers of multiplication problems of all kinds (as we do not always deal in simple whole numbers) the addition of minus and plus integral digits must be understood.

Adding plus integral digits: Examples. (436 x 24.72): 436 has plus 3 and 24.72 has plus integral digits; adding 3 and 2 we have five integral digits (8367 x .1776): 8567 has plus 4 and .1776 has zero integral digits; adding plus 4 and 0 we have 4 integral digits.

Adding minus integral digits: Examples. (.476 x .00153): .476 has zero and .00153 has minus 2 integral digits, adding 0 and minus 2 we have minus 2 (-2) integral digits.

(.0276 x .000348): .0276 has minus 1 and .000348 has minus 3 integral digits, adding minus 1 and minus 3 we have minus 4 (-4) integral digits.

Adding plus integral digits to minus integral digits or minus integral digits to plus integral digits:

Examples:

(74.3. x .0672); 74.3 has plus 2 and .0672 has minus one integral digit, adding plus 2 and minus 1 we have plus 1 (+ 1) integral digit.

(.00566 x 1873); .00566 has minus 2 and 1873 has plus 4 integral digits, adding minus 2 and plus 4 we have plus 2 (+2) integral digits.

(.000857 x 11.36); .000857 has minus 3 and 11.36 has plus 2 integral digits, adding minus 3 and plus 2 we have minus 1 (-1) integral digits.

From. the above explanation we can establish this rule for adding integral digits: when the integral digits are plus or positive we add them and use the plus sign; when the integral digits are minus or negative we add them and use the minus sign; but when we add plus and minus integral digits we subtract the smaller number from the larger and use the sign of the larger number.

Other Examples:

+6 +3 = 9 -2 + (-4) =-6 +3 + (-2) = +1 -1 + 4 = +3 +4 +2 = +6

+3 + (-5) =-2 -6 +1 =-5 -7 + (-2) = -9 -3 + 0 = -3 +2 +0 = +2

Note:- A thorough explanation in regard to the terms "digits" and integral digit has been mentioned previously on this page.

In order to perform division correctly and easily it will be necessary to understand the subtraction of plus and minus integral digits.

In the subtraction of plus and minus integral digits the sign of the subtrahend is changed and the two numbers are added as explained under section, "The Addition of Integral Digits."

Example 1: +6 - (+2) = +4

Here the +2 is the subtrahend, changing its sign to a minus we then add it to +6 giving + (-2) or +4.

Example 2: -1 - (+2) = -3

Here again the (+2) is the subtrahend, changing its sign to a minus; we then add it to (-1) giving -1 + (-2) or -3.

Example 3: +3 - (-2) = 5

Here the (-2) is the subtrahend, changing its sign to a plus; we then add it to +3 giving +3 + (+2) or +5.

Other examples of subtraction:

The signs inside the parenthesis show what the signs become after they are changed.

Note: - Explanation of the digits and integral digits will be found on the preceding page.

Practice Problems:

21. The diameter of a circle is 1.54 inches, what is its circumference?

Answer: 3.1416 x 1.54 =

22. A voltage of 110 volts is impressed across a lamp and a current of .52 amperes flows.

What is the power.

Answer: 110 x .52 =

23. What is the area of a triangle whose base is 6.25 and whose altitude is 8.33?

Area = (6.25 x 8.33)/2

24. There are 24 children in a class room and the sum of all their ages is 384. What is the average age?

Answer: 381 + 24 =

25. A lot is 227 by 96 feet. How many acres does it contain if there are 43560 sq ft. in an acre?

Answer: (227 x 96) ÷ 43560 =

26. An automobile makes a trip of 280 miles on 16 gallons of gasoline. What was the number of miles per gallon?

Answer: 280 ÷ 16 =

27. If a room is 12' x 15' x 8' how many square feet of wall paper would be required to cover the walls and ceiling? Answer: (12 x 15) +2 (8 x 12) +2 (8 x 15) =

28. If the distance between the first floor and the second floor is 8'-9" and there are to be 15 steps, what will be the height of each riser?

Answer (8'-9") ÷ 15 =

29. In a certain production job the allowable cutting speed is 3.75 feet per second. When turning a shaft 4 inches in diameter, how fast should the lathe be run?

Answer: (3.75 x 12 x 60) ÷ 4π =

30. If the average hiking speed of boy scouts is 3.25 miles per hour, how long will it take to hike 15 miles? Answer: 15 ÷ 3.25 =

31. A right triangle has sides 8.8 and 4.21 inches respectively. What is the length of the hypotenuse?

Answer: √(8.8

32. A motorist makes a trip of 265 miles in 8.75 hours. What is his average speed?

Answer: 265 ÷ 8.75 =

33. A water tank is 15.6 x 8.6 x 3.3 feet. How many gallons of water will it hold? There are 7.48 gallons in a cubic foot.

Answer: 15.6 x 8.6 x 3.3 x 7.48 =

34. How much is the cost of 3 3/4 tons of coal at $9.75 per ton?

Answer: 3.75 x 9.75 =

Answers to Practice Problems:

A careful reading of the foregoing pages will equip the average person with a command of slide rule operations. These are thousands of applications of the slide rule to useful, everyday problems.

A few of these practical everyday tasks are illustrated on the back cover of this book. These sketches illustrate typical problems that can be worked out quickly and accurately by the STUDENT, the HOUSEWIFE, etc. Let us take them up one by one.

1. The Student. Example.

How many feet per minute does a 22" wheel cover when making 166 revolutions every minute?

Solution. Number of teeth = (3.14 x 22 x 166)/12 = 956

2. The Housewife. Example.

How much does the housewife realize, if in a week's time she sold 18 1/2 dozen of eggs at 22 1/2 cents per dozen.

Profit = 18.5 x 225 = $4.17

3. The Salesman. Example.

If an air conditioning system cost $1,210.50 installed, what would be the saving to the customer if a discount of 16% were allowed, if paid for in full within three months.

Solution. Saving = 1210.50 x .16 = $193.70

4. The Draftsman. Example.

A gear 18" in diameter has a circular pitch of 1 1/4". How many teeth does the gear have on it?

Solution.

Number of teeth = (3.14 x 180/1.25

5. The Machinist. Example.

At what R.P.M. should a 1 1/4" high speed drill be run to give a cutting speed of 80 ft. per minute.?

R.P.M. = (80 x 12)/(3.1416 x 1.25) = 244

6. The Teacher. Example.

How many pounds of air are in a room 15' x 22' x 12', if 0.5 cubic feet weigh a pound?

Pounds of air = (16 x 22 x 12)/13.5 = 312

7. The Timekeeper. Example.

What is the total expenses of a company for the following labor: Bricklayer 42 hours at $1.10; Carpenter 38 hours at $0.98; and Lather 26 hours at $0.851

Cost = 42 x 1.10 + 38 x .98 + 26 x .85 = $105.50

8. The Farmer. Example.

How many tons of silage will a silo 16 feet in diameter and 30 feet high hold if silage weighs 38 lbs. per cubic foot?

Tons = (3.14 x 16

9. The Printer. Example.

How many pictures 2 1/4" x 3 1/2" can be placed on a sheet 12" x 18"

Number = (12/2.25 = 5+)(18/3.5 = 5+) 5 x 5 = 25

10.The Office Worker. Example.

What would be the cost to ship a box weighing 125 lbs. a distance of 176 miles at 4 1/2 cents per pound?

Cost = 125 x .045 = $5.63

11. The Carpenter. Example.

How many feet B.M. are there in 16 pieces 1 1/2" x 10" x 26' long?

Ft. B.M. = (3 x 10 x 26 x 16)/(2 x 12) = 520

As the owner of a Lawrence Slide Rule and this new Lawrence Slide Rule Instruction Book, you have no doubt found the operation of a slide rule a fascinating and worthwhile activity.

There's no pleasure EQUAL to the satisfaction of knowing you have mastered this "most useful of man's tools," SUGGESTION: Share your pleasure with a friend. Give him a Lawrence Slide Rule and Book as a GIFT. He will treasure it for years to come - and think of you every time he uses it. The cost is so very small, and the value so great, you'll do your friends a lasting favor by presenting them with something useful, educational and interesting.

Please patronize the store where you bought this book. If you your local merchant cannot supply you, write us at once.

ENGINEERING INSTRUMENTS, Inc.

PERU, INDIANA, U. S. A.

Posted 5/20/2013