PROGRAMMED SLIDE RULE - Archive...6 5 6789 5 6 789 n Ir.rj^ R ST Panel1DiagramofaSlideF^le (showingonlytheprimary scaledivisions) 3Whatistheotherscaleontheslidecalled?C-scale

A PROGRAMMED SEQUENCE ON THE

SLIDE RULEEugene Roberts POLYTECHNIC HIGH SCHOOL • SAN FRANCISCO CALIFORNIA

CHEMICAL EDUCATION MATERIAL STUDY

W. H. FREEMAN AND COMPANY Cooperating Publishers

SAN FRANCISCO AND LONDON

A Programmed Sequence on the

SLIDE RULEby

Eugene RobertsPolytechnic High SchoolSan Francisco, California

The slide rule is an invaluable tool of the scientist and

engineer. Its use in technical courses at the college

level is mandatory. Its use in high school science and

mathematics classes, while not an absolute requirement for

these classes, will certainly help you through the computa-

tions which arise.

This booklet is designed to introduce you to the slide

rule, to help you learn to read its scales, and to explain

its use in multiplication, division, and the extraction of

square roots. There are four parts

Reading the Scales Page 2

Multiplication 28

Division ^^2

Extraction of Square Roots 52

How to Use This Booklet

This coverage of the slide rule is designed to be undertakenby you on a self-Instructional basis. Using a small sheetof paper or cardboard as a mask, you are to conceal theanswers which are listed in the right hand columns of thebooklet until you have actually written down your own responseon a separate sheet of paper. Do not mark this booklet it-self so others will be able to use it again.

This trial material was developed by CHEM Study to facilitatecomputational work in the high school chemistry course.

Copyright 1962 by The Regents of the University of California.Published in cooperation with W.H. Freeman and Company, SanFrancisco.Printed in the United States of America.

5 fi 7 8 9

G H

Panel 1 Diagram of a Slide Rule(showing only the primaryscale divisions)

READING THE SCALES OF A SLIDE RULE

This first section Is concerned only with developing skillIn reading the slide rule scales preparatory to taking upthe operations of multiplication, division, and extractionof roots. This presentation is purely operational. Nobackground nor theory is Included. The how" is thcovered; the "why" is not.

Look at Panel 1 at the top of the page.

This, as you might suspect, is a skeleton diagram of a

thoroughly

You may want to compare this simple diagram with a sliderule of your own. Basically, all slide rules, from thesimplest to the most expensive, are the same.

In the diagram of Panel 1, the middle, elongated partlabeled "V which sticks out the end is the part on yourown rule which slides back and forth, and hence is calledthe "slide".

2 What two letters of the alphabet are shown on the slide atthe left end?

These letters B and C are used to label (or name) thevarious scales. The top scale on the slide is called theB-scale.

slide rule

B and C

^ ^'"^

6

5 6 7 8 9

5 6 7 8 9

In r. rj^R ST

Panel 1 Diagram of a Slide F^le(showing only the primaryscale divisions)

3 What is the other scale on the slide called? C-scale

All our questions are based on Panel 1, but you will wantto compare your own slide rule, if you have one, with thediagrams, too. YOUR rule may have many more scales thanare shown in Panel 1. We will ignore these "extra" scalesin this program.

The part of the rule through which the slide moves ongrooves is called the frame, or base, or body. We'll callit the frame.

4 What two scales are shown on the frame in Panel 1?

Shown over on the left side of the rule between thenumbers 1 and 2 on the A-scale is a glass-faced "runner"which can be moved along to any part of the male. It issometimes called a "cursor", or 'indicator". In the glassface of the runner is a very thin "hairline", which runsperpendicular to the scales of the slide rule.

5 What letter in Panel 1 points to the hairline? J

What number appears at the left edge of the A-scale and6 the D-scale? 1

A-scale andD-scale

What number appears at the left edge of the B-scale and7 the C-scale?

G H I

6 7 8 9 1

7 8 9 1

Panel 1 Diagram of a Slide Rule(showing only the primaryscale divisions)

Now look over to the right hand end of these scales. Whatnumber Is found at the end of each of the four scales?

These I's mark two important parts of the rule, namely theIndexes of the slide rule. The left index of the D-scale Is

shown In the panel by the letter "H" .

The right index of the D-scale is shown on the diagram bythe letter9

10 The letter I points to the left

11 The letter S points to the index of the

12 The letter E points to:

of the C-scale.

13 What letter points to the left index of the D-scale?

Look at the C and D scales in the panel.

Are the lengths of the spaces between the numbers equal or

14 unequal?

15 Are the C and D scales uniform scales or non-uniform scales?

These scales are non-unifonn because they are logarithmicscales. In our diagram we have shown only the marks of

the numbers, and not the detailed divisions you can seeon your own slide rule.

On the C and D scales, for instance, the number 3 Is locatedat the point marked with the letter K.

T

Index

rightC-scale_"left indexof theA-scaleH

unequal

non-uniform

\ I L

itlF 6

H-h^HI J K

Panel 2 A Rough Diagram of the C-Scale(showing only the primary andsecondary divisions)

Now look at Panel 2.

28 This is a rough diagram of

29 This is the scale you would see if you slipped theout of your own slide rule and looked at its bottom scale.

The left index of the C-scale in Panel 2 is indicated by30 the letter .

31 The right index is indicated by the letter .

According to caption. Panel 2 does not show all thedivisions of the C-scale, but only the so-called primary

32 and divisions.

Locate the number 3 indicated by the letter L.

33 The number 4 is indicated by the letters .

How many spaces are there made by the secondary divisions34 between 3 and 4?

35 How many divisions (spaces) are there between 6 and 7?

Remember, we're dealing with Panel 2 at the top of thepage.

36 How many divisions are there between 2 and 3?

From this investigation, or even more investigations, ifyou'd care to make them, we can see that the secondary

37 divisions divide the primary divisions into parts.

Since the 10 smaller secondary divisions divide each ofthe larger primary divisions into 10 parts, each secondary

38 division is just one tenth, or l/lO, or of a major(primary) division.

So, if we want to locate the number 3.1> we need to goJust one secondary division beyond 3, as shown by theletter M.

If we want to locate 4.1, we need to go just one secondary39 division beyond 4, as shown by the letter .

Between the numbers 1 and 2 (shown by letters E and J) thesecondary divisions are so wide that on some slide ruleseach one can be numbered. The number 1.3 has the letter G.

40 The number 1.8 has the letter .

41 The number 2.2 has the letter

the C-scale

slide

E

Z

secondary

NN

10

10

10

10

0.1

a a i

*

ail 1 nkiiliii iU\

M

NN W X Z

Y

Panel 2 A Rough Diagram of the C-Scale(showing only the primary andsecondary divisions)

42 What number is Indicated by the letter N?

43 What number Is indicated by the letter U?

44 What letter indicates the number 8.3?

45 What number is indicated by F?

46 What number is indicated by X?

47 What number is indicated by Y?

48 What number is indicated by Z?

49 What letter indicates the number 1?

50 What letter indicates the right index of the C-scale?

51 What letter indicates the number I.7?

Are you bored doing all these "number exercises"?Don't be!! If you're like most students starting to usea slide rule, you need this practice, even though itseems to be soo-o-o easy to do. Let's continue, then,

52 with locating the letter which indicates the number 2.0.


54 What number does the letter S indicate?

55 What letter indicates the number 5?

56 What letter indicates the number 5.O?

57 What letter indicates the number 5. 00?





62 What number is indicated by the letter R?


3.4

7.5

V

1.2

9.4

9.8

10 (not 1!

)

E

Z

H

J

T

6.4

S

S

F

M

5.5

P

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Panel 3 Diagram Showing Primary, Secondaryand Tertiary Divisions

Now we'll be working with Panel 3.

64 How many scales are shown in Panel 3?

We will completely Ignore the B-scale and the Cl-scale.All our readings will be on the C-scale.

65 In Panel 3, what letter indicates the left index of theC-scale?

You'll notice that our primary and secondary divisionsof Panel 2 are on this C-scale as slightly longer lines.

Now, however, additional lines (or divisions) have beenfilled-in so that we can now make closer readings of our

numbers in Panel 3^

66 What number is indicated by the letter R?

All of these answers apply since R is right on the line.

So that we'll both usually get the same answers, let's

give all the answers to two decimal places (three signi-ficant figures ).

67 What number is indicated by the letter X?

68 What number is indicated by the letter Z?

69 What number is indicated by the letters GG?

70 What number is Indicated by the letter U?

3, or 3.0,or 3.00

5.00

6.50

8.70

4.40

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71 What number is Indicated by the letters HH?

If you were correct on these last four items and feelyou can read numbers of this type easily, go to ItemNo. 91.

If you missed any of these last four items, or if youfeel you need more practice, go on to Item No. 72.

72 What number is indicated by E?

73 What number is indicated by K?

Notice that there are 10 secondary divisions between1 and 2, each marked by a little longer line to setthem apart. In Panel 3, letters H, I, and J pointto three of these secondary divisions.

If there were 2 divisions, each would be equal to l/2.If there were 5 divisions, each would be equal to l/5'

7^ Since we have 10 divisions, each would be equal to

75 Look at the letter Ic It Indicates the point which issecondary divisions beyond the number 1.00.

Since each division is l/lO of the way from 1.00 to 2.00,76 five of these divisions would be 5/lO> o^ 0. of the

way from 1.00 to 2.00.

77 Therefore, the letter I indicates the number 1.

9.80

1.00

2.00

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5

0.5 (or,0.50)

1.50

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78 What number Is Indicated by the letter J?

Notice that J Is 8/10' s of the way from 1.00 to

_, and the number79 The number Indicated by K IsIndicated by R Is .

80 You will notice that there are secondary divisionsbetween these numbers.

81 Since there are ten divisions, each division will beequal to one- of the way from 2.00 to 3.00.

82 How m.any secondary divisions are there between thenumber 2.00 Indicated by the letter K and the numberindicated by the letter M.

83 Since there are 4 divisions, and each division is one-tenth, M must be -tenths beyond 2.00.

84 Thus the number indicated by the letter M is 2. ? .

Look at the number indicated by the letter S.

85 How many secondary divisions is it past the number 3. 00?

86 Each of these divisions is one-tenth, so the number willbe tenths past 3.00.

87 The reading at the letter S is

1.80

2.00

2.003.00

10

tenth(1/10)

There arefour.

four-tenths

2.40

7

seven- tenths

3.70

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88 How many secondary divisions is it from S-OO?

89 What number, then is indicated by the letter Y?

90 How many secondary divisions is the mark indicatedby EE from 7-00?

91 What is the number indicated by the letters EE?

92 What number is indicated by the letter FP?

93 What letter is used to indicate the number 2.80?

94 What letter indicates 4.60?

95 What letter indicates 1.20 (on Panel 3)?

If your answer was F, the reading would be 1.02.If your answer was G, the reading would be 1.12.If your answer was K, the reading will be 2.00.



98 What letter indicates I.50?

99 What letter indicates 7. 10?

9

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one

7.10

7.70

P

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M

T

I

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103

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Panel ^

Now shift your attention to Panel 4. How many scalesare shown on this panel?

Once again we will ignore the two top scales andconcentrate on the bottom, or -scale.

Thus far we've done pretty well at reading numbers to thefirst decimal place, for example, 4.50 and 9.30, and so on.Now we want to get on to reading that second decimalplace. We've given our divisions on the C-scale twodifferent names, thus far. The primary divisions andsecondary divisions.

For example, in Panel 4, the letters S-, , Y, and II,indicate the numbers 2.00 , , and .

These are primary divisions. Look at Panel 4.

(always, sometimes) are

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105

106

107

108

109

110

The primary divisionsmarked with a number along the C-scale.

The primary divisions, which are always marked on theC-scale with the number they represent, give us the

(first, second, third) figure of our number.

The secondary divisions are those we first met inPanel 2. For a moment turn back to Item 42 and lookat Panel 2.

How many secondary divisions are there between primarydivisions which are labeled 2 and 3 in Panel 2?

How many secondary divisions are there between theprimary divisions for 7 and 8 in Panel 2.

How many secondary divisions are there between any twosuccessive primary divisions in Panel 2?

Going back to Panel 4 now, the letters T, HH, and JJindicate the secondary divisions which stand for thenumbers 2.40 , , and .

(first,These secondary divisions give us thesecond, third) figure of our number.

Are the secondary divisions always marked with a number?

(The secondary divisions are un-marked except between 1and 2 on some slide rulers. Maybe your slide rule isone which has them marked between 1 and 2.

)

3

C-scale

3.00 and5.00

always

first

10

10

10

4.10 and6.40

second

No

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Panel ^

Now we are ready for the divisions which appear betweenthe various secondary divisions. These are called thetertiary divisions. If we learn this term it will makeit easy for us to refer to these "smallest" divisionson the C-scale. "Tertiary" is pronounced ter-she-airy ,

with the accent on the first syllable.

Name of the division

PrimarySecondaryTertiary

Figure represented in Number

FirstSecond

9

111 What should be in the blank space in this chart?

112 The tertiary divisions, then, are used to give usthe figure of our number.

113 What numbers are indicated by the letters I and Kin Panel 4.

114 How many tertiary divisions are there between these twonumbers?

115 Since there are 10 divisions, each tertiary division hasa value of -tenth of a secondary division.

116 Now locate J and note the mark it points to. I is 1.20.How many of the tertiary divisions are there betweenI and J?

In going from 1.20 to 1.30 there are ten divisions, butJ is only five divisions beyond 1.20, or just half-way.So J Indicates the number 1.25 on our C-scale.

117 Select the number which is indicated by the letter L:a)l.40, b) 1.45, c) 1.50, d) 1.55-

Now look at the number indicated by the letter M.

118 Is it 1.60?

M is one small division beyond I.60.

119 If it is one small division beyond I.60, is Ma) 1.61, b) 1.70, c) 1.50 or d) 1.66?

121 If the number Indicated by N is four small divisionsfrom 1.60, what number is It?

third

third

1.20 and1.30

10

one - tenth

five

b) 1.45

No

a)l.6l

1.64

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122 Is the number indicated by the letter P equal to I.70?

123 How many divisions are there between the number indicatedby P and I.60?

124 The number indicated by P, then, is 1.6?

125 What reading would you assign to the letter 0?





130 What letter indicates the right index of the C-scale

131 What number is indicated by the letter H?

132 What number is indicated by K?

133 What number is indicated by the letter F?

134 What letter indicates the left index of the C-scale?

135 What number is indicated by T?

136 What number is indicated by V?

137 In between these last two numbers, T and V, how manytertiary divisions do you count?

138 In going from 2.40 to 2.5O in five divisions, eachdivision must have a value equal to a ) 1, b) 2, c) 3,d) 4?

This means that each division has a value of 2.

Since V has the value 2.5O the number indicated by thenext small division would have the value of 2.52.

139 The number indicated by the letter U, which is Just onesmall division above 2.40, has the value 2.42.

140 What Is the number indicated by the letter W?

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9

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1.66

Q

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E

KK

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1.30

1.01

E

2.40

2.50

5

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2.42

2.72

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141 Locate the numbers 3.6O and 3.70 In Panel 4. These areIndicated by the letters and .

142 How many tertiary divisions are there between these twoniimbers?

1^3 This means that, as before, each division will have avalue of (1, 2, 3, ^).

l44 If each division has a value of 2, what is the numberindicated by the next small division above (to the rightof) 3.70?

1^5 What number is indicated by the letter Z?

Since, in this part of the C-scale (between 2.00 and5.00), each of the tertiary divisions has a value of 2,we can set-up the following chart:

No. of Divisions

12

34

Value

24

146

147

Plll-in the two blank spaces.

Locate the point indicated by the letter S on the C-scale,

This number lies between 2.10 and 2.20.

How many tertiary divisions is it from 2.10?

148 In this part of the C-scale, each of the tertiary divisionshas a value of .

149 Since we have 4 divisions, with a value of 2 for eachdivision, our total value for the 4 divisions is4x2, or .

150 So, our number indicated by S is 2.1?_.

151 What nximber is indicated by the letters EE?

If you did not get this answer correct, you may wantto go back to Item No. 137 and follow this developmentthrough again.

FF andGG

5

2

3.72

3.22

6, 8

2.18

3.34

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Panel 5

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HI J K L M N

Now refer to Panel 5«

152 This Panel 5 shows the same three scales that wereshown on the previous panel, namely the , ,

and scales.

153 On Panel 5? what values are indicated by the lettersI and J?

15^ Looking at these two numbers (2.12 and 2.14) whereshould the number 2.13 lie in relation to them?

155 Looking at Panel 5^ is there a division mark on thescale between letters I and J?

156 Even though there is no mark between 2.12 and 2.14,it is easy to locate 2.13 because 2.13 is just(how far) between 2.12 and 2.l4.

157 Let's take the number 3.25. This number is located Justhalf-way between 3.24 and .

158 Are the numbers 3.24 and 3.26 marked by divisions onthe C-scale?

159 Is the number 3.25 marked by a division on the C-scalebetween 3-24 and 3.26?

160 Even though it is not marked, we know that the number 3.25is located Just ^between 3 » 24 and 3.26.

161 Look at the number indicated by the letter K. Is it onone of the marked divisions?

162 What is the number of the next division to the right ofthe letter K?

B, CI,andC-scales

I: 2.12J: 2.14

half-waybetween

Kg

half-way

3.26

Yes

No

half-way

No

2.40

16

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163

164

165

166

167

168

169

170

What Is the number of the next division to the left ofthe letter K?

If the letter K Is just half-way between the divisions for2.38 and 2.'4-0, what number does it indicate?

What number does the letter P indicate?

What number does the letter N indicate?

What number is indicated by the letter 07

You' 11 remember that we have three kinds of markingson our C-scale, primary, secondary, and tertiary.In the range of numbers between 1.00 and 2.00 on theC-scale of Panel 5^ there are (how many) tertiarymarkings between each secondary mark.

(how many)Between 2.00 and 5.00, there aretertiary markings between each secondary mark?

Now we are down to the tertiary markings between5.00 and the end of the scale at 10.00. This lastnumber is Indicated by the letter in Panel 5«

171 The right index of the C-scale is indicated by the letter

172 Locate the number 4.60. It is indicated by the letter.

173 Locate the number 4.70. It is indicated by theletter .

174 Now we have the numbers 4.60 and 4.70. The number4.65 would be located just -way between thesetwo numbers

.

X Y Z EE

Panel 5

2.38

2.39

3.79

2.84

3.51

10

EE

EE

S

T

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Panel 5

175

176

177

178

179

180

l8l

182

183

184

185

186

Locate the point on the C-scale which is half-waybetween 4.60 and 4.70. This is the number 4.65- Is itmarked by a division?

The number 4.25 lies Just half-way between 4.20and .

Locate 4.20 and 4.30 on the C-scale. Half-way betweenthese two numbers you will locate 4.25 , which isindicated by the letter .

Does 4.25 lie exactly on a line division?

The number 5*35 lies half-way between the numbers 5 '30and

On the C-scale, 5-35 is indicated by the letter

Does it lie exactly on a line division?

The number 6.45 is indicated by the letter V. It liesJust half-way between and .

What number is indicated by the letter W?

What number is indicated by the letter X?

What number is indicated by the letter Y?

What number is indicated by the letter Z?

What letter indicates the number 2.58?

What letter indicates the number 1.02?

If you selected F for this last one you were at thenumber 1.20.

iliiiili

No

4.30

No

5.40

U

Yes

6.40 and6.50

7.15

8.05

8.50

9.55

M

E

H I J K L M N

18

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Panel 5

187

188

189

190

191

192

193

194

195

196

197

198

199

If you missed this answer, and are confused by It, youmay want to try Item No. 95 and Items No. 127-133 againbefore coming back to Item No. l87.

Is the number 2.22 marked by a division?

Is the number 3-33 marked by a division?


What letter Is closest to Indicating the number 3-95?


The next division to the right of 5 '95 marks thenumber .

The next division to the right of 6.00 marks thenumber .

What n\imber is indicated by the letter V/?

What number is indicated by the letter VY?

What number is Indicated by the letter G?

The number 2.05 is indicated by the letter .

If your answer was L, you selected the number2. 50 1 This Is an easy error to make, so youmust be alert to avoid it.

Is the number 3-^5 indicated by a division mark?

Is the number 6.I5 Indicated by a division mark?

5 6

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Panel 6 A Section of the C-Scale EnlargedThree Times for Instructional Purposes

200

201

202

203

204

205

206

207

208

209

Now look at Panel 6.

This panel shows a section of thea slide rule which has been enlarged

_-scale oftimes.

We've enlarged this section of the scale In Panel6 to make it easier to illustrate some of thepoints of reading the tertiary scale in this partof the slide rule. If you have a slide rule ofyour own you can compare its C- scale with thisenlargement and see that they are essentiallythe same.

In Panel 6, the letter J indicates the niimberwhich is marked by a primary division.

The letter L indicates the numbermarked by a secondary division.

which is

In between this primary division of J and thesecondary division of L there is another division,a tertiary division which is marked by theletter

This letter K indicates the numberis just half-way between 5-00 and 5. 10,

which

Since the number 5-02 falls between 5. 00 and 5 '05,it (5.02) should be located somewhere between theletters J and .

In considering the location of the number 5 '02between 5-00 and 5.05:

exactly half-way betweena little less than half-way betweena little more than half-way betweenoo _

210

211

212

215

218

219

Now divide your line into five equal spaces by puttingfour marks in between 6.00 and 6.O5. Don't use a rulerto do this. Just Judge it "by eye."

The left hand division is labeled 6.00 and the righthand one is labeled 6.O5. Number each of thein-between divisions with its proper number between6.00 and 6.O5.

Look at the line segment below and estimate the numberwhich is Indicated by the long, perpendicular line?

Which number does the long,vertical line indicate?

6.006.106.016.206.02

213 On this same segment, which number does the long,vertical line indicate?

\ \ \ \

_ _ (vj <*) •X o o q o2| «b «> <«» to

c) 6.01

a) 6.02b) 6.03c) 6.04d) 6.30

214 On the segment which is shown, which number does thelong, vertical line indicate?

a) 6.02g b 6.031*0 c) 6.04' d) 6.20

Now draw a line which is only about half an inch long,mark a division at each end, label the left division4.05 and the right one 4.10.

216 Once again, divide this line into five equal spaces byinserting four division marks between 4.05 and 4.10.

217 Label each of the divisions with its proper number.

c) 6.04

a) 6.02

o

oI M I I

^•

o

What number does the long,vertical line indicate?

//hat number does the long,vertical line indicate?

a) 8.76bj 8.77c 8.78d) 8.79

4.054.014.904.104.09

o00

You might have selected a 8.76 but notice that thevertical line is closer to the center than it is tothe left mark.

(o rôot0000 o

1

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e) 4.09

b) 8.77

21

T

7.

Ti'F G H

7.20 7.30 7A0 7.50

t' t'

t' t'

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t ItP Q

7.60

Panel 7

220

221

222

223

224

225

Look at Panel 7.

The letter F indicates the number

The letter J indicates the number

The letter H indicates the number

Remembering how you judged the distances on the linesegments on the last couple of pages, what letterwould you select as indicating 7-l6?

What letter indicates the number 7-12?

The letter indicates the number

226 The letter N Indicates the number;

a

5 6\^

I I I . I . I I I I I .

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Panel 6 A Section of the C-Scale EnlargedThree Times for Instructional Purposes

236

237

238

239

240

241

242

243

244

245

Using this same method, what Is the number Indicatedby the letter E in Panel 6?

In Panel 6, what number is Indicated by the letter L?

Using our method of dividing the space into 5 equalparts as we did before, what is the number indicatedby the letter F (on Panel 6)?

What number is indicated by the letter N?

The letter I indicates the niomber.

Often the third figure in a number is a matter ofIndividual interpretation--what looks like 4.73to one person is closer to 4.74 for another. Ifyou are only one nximber away from the answergiven in this program don't be concerned thatyou are wrong.

The niunber is indicated by the letter G.

The letter H indicates the number

What number is indicated by the letter 0?

The number is indicated by the letter P

The number indicated by the letter M is

4

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Panel 8

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254

The readings we made In panel 6 were from

an enlarged version of the C- Scale.

In Panel 8 we will use an actual C-scale in

practicing our readings as a ^^J^'^P °^scalesprogram on reading the scales of C and D- scales

of a slide rule.

On Panel 8 a number of "hairlines" have been

Sawn'to gi?e you some practice on reading settings

which have been made on an actual C-scale. in

these readings you ought to get the ^1-t two

fiffures of the numbers correct, but the thira

filSê is sometimes subject to different inter-

pjftat ions by different .people. ^^J-^.^^^ J°ôught to agree with the given answer within one

niimber of the third figure.

What number does hairline H indicate on the

C-scale of Panel 8?

What is the number under hairline L?

What is the number under hairline Q?

What is the number \inder hairline S?

What is the number \inder hairline J?

What is the number under hairline M?

What is the number linder hairline F?

What is the number under hairline G?

What number is under I?

Notice that the hairline I is half-way between

the division marks for 2.l4 and 2.l6.

255 What number is under K?

256 What number is under hairline N?

257 The n\.imber under hairline is _

2.00

3.40

4.60

5.15

2.48

3.74

1.70

1.89

2.15

2.91

3.87

4.21

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Panel 8

258 What niiniber is under hairline P?

259 What nLunber Is under hairline R?

You might have read R as 5-04, but not as 5.O5or 5.02.

260 What number Is Indicated by hairline T?

You might have read T as 6.82, but not as 6.8Oor 6.83.

261 What Is the number of hairline U?

You might have read It as 7-73, but NOT as 7.75.

On your own slide rule you will find that the"hairline" in the glass face of the runner reallyis a hairline , and not nearly as thick as the linedrawn on Panel 8. This thin hairline makes iteasier to read the numbers on the scales.

The reading of numbers on the scales of a slide ruleis the hardest part of using a slide rule--that iswhy we have spent so much time in getting thisfoundation prior to actually using the slide rule.

The numbers we have been reading from the slide rulehave had a figure followed by a decimal point, i.e.,3.48 or 6.94 and so forth. To be of any use, theslide rule must be able to use any numbers. Thisprogram has used this form for numbers (5.67), be-cause it Is easier to learn to read the scaleswith this type of number.

Thus far, using numbers like 3.45. we have used262 numbers with only (how many) figures in them.

From our last exercise in locating numbers onPanel 8 we can appreciate that it is difficult to

263 "read" the slide rule any closer than figures.

Thus any number we want to set on the slide rule264 will have to be changed to a number with only

figures in it.

4.49

5.03

6.81

7.74

three

3

3

25

265

266

267

268

269

270

271

272

273

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Panel 8

There Is an exception here, since on the C-scalethe divisions between 1 and 3 are wide enough sothat you can set, sometimes, four figures. Toshow this, go back to Panel 8 for a moment, andnote the reading of hairline E. What number,using four figures does It Indicate?

If you find you can set four figures, then do so,but we're going to assume that we can only set 3figures In order to keep this presentation to yousimple. Since we will set only three figures,any number we get must then be changed tofigures.

If we change the number 456 to a form that we areused to setting on our C-scale, we would call It4.56.

How would we change 234 In order to have It In"our" form?

This means that, for the time being, we are Ig-noring the true position of the decimal polnt--but don't worry about It now.

The number 13,600 would become 1 . 36 In "our" for-mat. How would we change the number 65 » 700?

Change 116,000 to our format.

Change O.OO987 to our format.

All we are doing here Is to rewrite the number sothat It lies between 1 and and Is In a formthat we are used to locating on the C-scale.

If a number has more than three figures In It, wemerely "round It off" to three figures, and put Itbetween 1 and 10. For example, 2342 becomes 2.34.

4532 would become

0.009874 would become

26

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2.34

6.57

1.16

9.87

10

4.53

9.87

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Panel 8

If the fourth numter which is dropped is a 5 orlarger, then we raise the value of " the third Tiumberby 1. For iiistance, 5.679 would become 5.68.

27^ Or, 4.568 would become

The number 8,765 would be changed to 8.77.

The number 4,637 would be changed to.

The number 78,995 would be changed to.

The number O.OOO3576 would become.

Using this system we can set any number on ourC-scale.

Using Panel 8, what letter would Indicate thenumber 29,100?

What letter indicates O.OO2906?

What letter indicates 2,913,480?

'Where on Panel 8 would you find the followingdifferent values located?

a) 0.00515 b) 5.15 c) 51,500,000 d) 515and e) 51-5

Thus, we can say that the location on the sliderule scale (does, does not) depend on thelocation of the decimal point, but only on thefigures which make up the number.

This means that our changing the numbers to conformto "our" format of a number followed by a decimalpoint (i.e., 5.67) does not affect our operation ofthe slide rule.

We have spent a long time on just locating numberson our C-scale. Now we are ready to take up multi-plication, using the C and D scales

The next section of this program covers multipli-cation with a slide rule.

27

4.57

4.64

7.90

3.58

all underhairline S

does not

B

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Panel 9

SLIDE RULE MULTIPLICATION

Now that we are able to read the scales of the slide rule tothree significant figures, we shall find that the operationsof multiplication and division on the slide rule are quitesimple and much less tedious than our work with the scales.

In most of these exercises it would be well to work alongwith each item with your own slide rule. If it is a 10-lnchslide rule, you will be able to do all the settings andreadings asked for by using the C-scale and the D-scale ofyour own rule regardless of how few or how many other scalesit may have.

Our first problem will be a simple but fundamental one:

2x3 = ?

On your own slide rule make the setting which is shown inPanel 9 (If you don't have a slide rule, then Just refer tothe panel itself.).

In this setting, the left index of the C-scale is placeddirectly over the number on the -scale.

Now move your hairline along the C-scale until it is overthe number 3. Check the answer to be sure your setting iscorrect

.

If your hairline is the same as the letter F, you madeyour setting of 3 on the D-scale instead of the C-scale.

Directly under your hairline E you will read on the D-scalethe answer, .

We have made the setting for 2x3=6.To solve this problem, we moved the of the

-scale until It was directly over the number 2.00.

28

A

i,|jii>i.i>i,i

^lIllllllllHllillllllll

2, D-scale

SeehairlineE.

6 (or,6.00)

left indexC-scale

Panel 9

5

13

14

15

16

17

Again, "break" your present setting of your slide rule,and line up your scales.

Now make the setting for the problem 3x3=?After your setting has been carefully made on your ownslide rule, check it with the answer.

Under the hairline you read the number of the answer asbeing .

If your setting was correct, and you read the correct answerfrom your slide rule (not just because you know that 3 times3 Is 91 ) and you feel you know this type of setting fairlywell, you may want to go to the next box.

If your setting was Incorrect, at first, or you want a littlemore coverage of this Important setting for multiplication,continue along in this box.

You ought to have the setting shown in Panel 10 with hairlineI. This problem is 3 x 3 = ?• To get this setting, you movethe slide of your rule until the of the -scale is

directly over the number on the -scale.

In the setting 3x3=?^ we move the left index of the C-scale until it is over the number 3.00 on the D-scale.Then we move the along the -scale until it isdirectly over our second factor which is also 3-00 on the

-scale.

For the problem 3 x 3 == ? we have set our left index overone factor on the D-scale and our hairline over the otherfactor on the C-scale. Now we read the number of the answerunder the on the -scale.

See Panel10, us4.nghairline I

on pg. 33.

9.00

left indexC-scale3.00D-scale

hairlineC-scaleC-scale

hairlineD-scale

18

19

20

21

Set your slide rule to solve the following problem:2 X 1.5 = ?

After making your setting and writing down the answer youread off your rule, check the answer.

The number of the answer which is read under hairline F onPanel 9 is .

The answer is read from which scale?

If your last setting was correct you may want to jump aheadto the next box.

If you are still a little shaky on this type of setting,you will want to go to follow-through this box.

Our problem is2xl.5=?We are to multiply (how many?) factors?

See Panel9, hair-line F.

3.00

D-scale

two

30

22

23

We have two factors, 2 x 1.5, to set on our slide rule. Weset the first factor, 2, on our slide rule by moving theindex of the -scale over this factor. (See Panel 9- )

With our first factor set under the left index of the C-scale,we move the to our second factor, (I.5), on the

-scale, and then read the number of our answer on the-scale. In this case the answer is . (See hairline

F, Panel 9.)

leftC-scale

hairlineC-scaleD-scale3.00

Make the proper setting for the following problem and deter-mine the answer from the setting of your own slide rule:

3 X 2.6 = ?

Follow these next directions carefully.

Our problem will be 2 x 7 = ?

Set your slide rule as you have before by putting the leftindex over the number 2. (Your slide position will be thesame as in Panel 9.

)

Now, move your hairline along the C-scale until it is overthe second factor, 7« With this setting, what reading doyou get on the D-scale where you usually find your answer?

It is not possible to get a reading since the D-scale doesnot extend far enough.

Which index of the C-scale are you using in your presentsetting?

The C-scale has both a left index and a index.

Now shift your slide so that the right index of the C-scaleis over the number 2. Check the next answer.

Our problem was 2x7 = ?, and we have our first factor (2)set under our index. Next we will move the hairline alongthe C-scale until it is over our second factor which isthe- number .

Then we will read the number of the answer below the hair-line on the -scale, just as we did in the other problems

Check the setting you've made on your slide rule with thatof Panel 11, using hairline L.

The number of the answer which we read off the D-scale is

Since our problem was 2x7=?, we can see by inspectionthat while the number which we read off the D-scale is 1.40,this is not the correct answer. To get the correct answerfrom our number we '.vlll have to shift the .

When we shift the decimal point of our slide rule number1.40 to we get the answer to our problem, 2x7=?

7.80 - SeePanel 10,hairline V.

no reading

the leftindex

right

SeePanel 11,

7

D-scale

1.40

decimalpoint

14

31

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33

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35

36

37

Now to show you another little "twist", let's set our sliderule for the problem 7x2=?Set the factor 7 under the right Index of the C-scale ofyour slide rule. Then check the answer.

Our problem is 7 x 2 = ? We have set the first factor,

7, on our slide rule.

Now run the hairline along to the second factor, 2, along

the -scale.

Your setting should be similar to that at hairline N inPanel 12.

The number of the answer you read off the slide rule is,

Since our problem was 7x2=?, we can see by inspectionthat the decimal point should come after the 4, giving usthe correct answer l4. This is the same answer we arrivedat in the last box 1

1

The purpose of these last 3 items was to demonstrate thatparticular order of setting the factors of a multiplicationproblem on a slide rule (does, does not) affect theanswer.

Panel 12,page 37.

C-scale

1.40

does not

38

39

40

41

42

43

44

45

Set your slide rule to solve the following problem:

7 X 5.4 = ?

You'll notice that you haven't been asked to give anyanswers to these problems, but you have only been askedto give the number indicated by the hairline. The answer_to a multiplication must have the proper decimal point.The number indicated by the hairline will be, as usual,in our form of a number between 1 and .

For Instance, the number indicated by hairline R on theD-scale is .

Since our problem was 7 x 5'4 = ? we can see that eventhough the number of the answer is correct, its decimalpoint is not correct. Just by inspection we can see thatthe answer should be 37.8. We know that the slide rulewill give us the correct number of our answer, but we mustdecide on the correct location of the point in ouranswer.

In all of these problems you would do well to make the set-tings needed on your own slide rule and give the answersfrom your own slide rule, if possible.

In this box we will follow-through a complete problemincluding the proper placing of the point in our finalanswer.

Let's do the problem 7 x 1.6 = ?

In Pane b 12, and on your own slide rule, you have alreadyset the number on the -scale by putting the rightindex directly over it.

Now, in doing the problem 7 x 1.6 = ?, we move the hair-line along the -scale until we locate the number .

If you have done this on your own slide rule, your hair-line ought to be in the same position as that indicatedby letter in Panel 12.

Panel 12,hairline R

10

3.78

decimal

decimal

7.00D-scale

C-scale1.6 (or,1.60)

3^

46

47

43

49

Then, under the hairline we can read the answer on the-scale.

In this case, the number of the answer under the hairlineon the D-scale is the niimber .

This is the number -- not the correct decimal answer.

Since our problem was 7 x 1.6 = ?, we can see by inspec-tion just where we ought to put the decimal point in ournumber for the correct answer.

Select the correct answer: a) .112b) 1.12c) 11.2d) 112.

The slide rule will give us the digits in the answer, butwe must supply the correct position of theto get the correct answer^

D-scale

1.12

11.2

decimalpoint

50

51

52

53

54

55

56

57

Our next problem will deal with rounded-off numbers.

Suppose our problem was 7.0 x 50.99= ?

We would first locate the number 7-0 on the -scale andwas directly overand move the slide until the

it.

Our problem is 7.0 x 50.99 = ? We have located the 7-0and now want to set our other factor, 50.99.

This last number has (how many?) figures?

The number 50.99 has four figures, but we have found thatwe can usually set only figures on the slide rule.

So, we will have to round-off 50.99 to three figures.This will give us the number

In setting this number (51.0), we merely have to locate5.10 on the C-scale. with our hairline. Do this on yourslide rule. Which hairline on Panel 12 shows this setting?

We will read our answer on which scale?

What is the number which we read on the D-scale with thissetting of hairline Q?

Going back to our original problem, 7.0 x 50.99^ we mustnow place the decimal point in the correct position toget the correct answer. By inspection we see that thisproblem is approximately the same as 7 x 50, which isabout 350.

Therefore, using our slide rule number of 3.57 we wouldselect the correct answer: a) 0.357

b) 3.57c) 35.7d) 357e) 3570

It is usually possible to easily determine the decimal{point by inspection, as we have done here.

58

Set your slide rule for the following problem, and get your

answer from your own slide rule.5.00 X 2.74 = ?

D-scalerightindex

4

3—

51.0

Q

D-scale

3.57

357

13.7Panel 13,hairline S.

35

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Panel 1^

37

If your setting and your answer were correct you couldgo to the next box. If your setting was wrong, or youfeel you need more practice, finish this box. If yoursetting was okay but you read your answer wrong, you maywant to review the method used to read the slide rulescales covered in an earlier program. Look at Panel 13and set your own slide rule the same way, with your hair-line the same as S.

In the problem 5.00 x 2.74 = ?, the two factors areand 2.74.

The Is set over the factor

The hairline S (and on your slide rule) is then movedover the other factor 2.74 on the -scale.

The answer is then read below the hairline on thescale. In this case the number is

This number is not the answer, since thenot been properly placed, yet.

has

Since our original problem was 5.0 x 2.74 = ?, we can seeby Inspection that the number ought to be a little largerthan 10 (since 5 x 2 = 10). Since our number on theD-scale was 1.37, the answer (with the correct decimalpoint) will be .

Set your slide rule to solve the following problem, andget your answer from your setting correct to three sig-nificant figures, and with the proper decimal point:

75 X 220 = ?

If your setting and answer were correct you could go onto the next box.

If your setting was wrong, or you'd like more discussionon this part, finish this box.

If everything else was okay but your decimal point wasmisplaced, keep the setting on your slide m^le and go onto Item No. 70.

In the problem 75 x 220 = ?, we would first want to changethese two factors into the number form we're used tousing. This means 75 is changed to 7*5 and 220 is changedto

We will locate 7.5 on theover It.

_-scale and put the right

5.00

right index5.00

C-scale

D-scale1.37

decimalpoint

13.7

16,500,Panel l4,hairline T.

2.20

D-scaleindex

Then we move the hairline along theour second number, 2.20.

-scale until we reach

The answer is then read on the -scale.

The number on the D-scale under the hairline T (and on your

slide rule) is

Our problem was 75 x 220 = ? By inspection we see that this

is about the same as 100 x 200, which gives us a product of

Since our number under the hairline on the D-scale was I.65,

and since the answer should be "about" 20,000, the correct

answer (with the proper decimal point ) would be .

C-scale

D-scale

1.65

20,000

16,500

38

73

74

75

76

77

78

79

80

81

82

83

8^^

85

86

In setting the factors involved in a multiplication problem on

our slide rule scales it is often necessary to round-off our

numbers given in order that they may be properly set on the

slide rule.

For instance, suppose a problem was given you as follows:

3001 X 2499 = ?

How many significant figures do we usually use with the slide

rule?

In this problem of 3001 x 2499 = ? each of our factors has

four significant figures. Therefore, we will have to

"round off" each of these factors until each has only

significant figures before we can set them on our slide rule.

When we round off 3001 to a number we can set on the slide

rule, we round it off to .

On the slide rule we set 3000 as the number .

Set this number as 3-00 on your slide rule as the first factor

in multiplying.

After making your setting of this single number as a first

factor in multiplication, check the answer.

We have not yet made a hairline setting.

So we have set the first factor of 3001 x 2499 = ? Now to

set the second factor. When you round off 2499 to a number you

can set on the slide rule you get .

On the slide rule we set 2500 as the number .

Using your hairline, include the number 2.50 as the last

part of your setting of 3001 x 2499 = ?

After making your setting, check the next answer.

The number of your answer will be read on the -scale.

The number of your answer for 3001 x 2499 = ? is

Is this number 7. 50 the correct answer for 3001 x 2499?

The digits are all right, but the is not correctly

placed.

By inspection we can see that 3001 x 2499 is about the same

as 3000 X 2000. This last product is 6,000,000, so our

answer must be close to 6,000,000.

Which of the following numbers would you select as being

correct for the problem, 3001 x 2499 = ?

a) 7.5b) 7>5000c) 75,000,000d) 7,500,000e) 750,000

This is not the exact answer, of course, since our slide

rule will give us results which are correct to

significant figures. So our answer is closer to 7,500,000

than it is to 7,510,000 or 7,490,000.

Usually our work will not require any closer accuracy than

three significant figures.^

3000

3.00

SeePanel 10.

2500

2.50

Panel 10,hairlineK.

D-scale

7.50

No!

decimalpoint

d) 7,500,000

39

87

89

90

91

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Panel 15

Suppose your problem was 31^.8 x 58. 1 - ?

Set your slide rule for this problem and read-off youranswer, with 3 significant figures including the properplacement of the decimal point before looking ahead atthe answer.

If you handled the rounding off of the number 3 '^18, andthe determination of the placement of the decimal pointto your own satisfaction, you may want to go on to thenext box.

If you want to go through a detailed discussion of thislast problem, continue on with this box.

If you want a detailed coverage of only the placement ofthe decimal point in the answer, go to Item No. 91.

Our problem was 31^-8 x 58. 1 = ?. Since we can usuallyset only figures on our slide rale, we will have toround-off the number 31^-8 to .

So, we've changed our problem to 315 x 58. 1 = ? V'e shallnow set these numbers on our slide rule, putting theright index of the C-scale over the number 3.15 and movingour hairline along the C-scale to the number 5-8l.

Then we shall read our answer on the -scale, as shown inPanel 15> The number of the answer, as read off the scaleis .

You might even read the last number as I.832, but it iscloser to I.83 than it is to 1.84.

This Is the number of our answer, as taken off the D-scale.We must now determine the proper placement of theto get the answer to our problem.

Our original problem was 314.8 x 58 . 1 = ?We could say, very roughly, that this is about the same as300 x 60. 300 X 60 = 18,000, so our answer should be closeto this value.

The number of our answer was I.83. The value of our answerought to be close to 18,000, so the answer to our problemwill be

18,300See Panel15.

3315

D-scale

1.83

decimalpoint

18,300

1^0

80 ' 90 160

In M I

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Panel 15

Skill In using the slide rule comes only from practice in

using it. In the following problems your answers ought to

agree exactly with the first two figures of the answers

given by the program. There may be a difference in the

third figure, since this third figure is often a matter of

individual interpretation.

Make your settings, read off your answer, and properly fix

the decimal point BEFORE going ahead to check your answer

with the program.

If you are confused in making any of these settings, remem-

ber the setting you used for 2x3=6, and set yourproblem the same way.

92

93

9^

95

96

97

98

Solve: 123 x 83 =

The answer would be 10,210 if you read it to four figures.

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Panel l6

SLIDE RULE DIVISION

You will find that the operation of the slide rule Individing Is even simpler than that for multiplying.

Suppose our problem was ^

To make this setting, move your hairline along theD-scale until It Is directly over the number 6.00.

This Is the number we are dividing (Into, by)

Now, leaving the hairline where It Is, directly overthe 6 on the D-scale, move the slide until the number3.00 on the C-scale Is also directly under the hair-line.

The number 3 Is the number we are dividing(Into, by).

Now your setting on your slide rule should look Justlike Panel l6 with hairline E.

Can you see where we read the answer to our problemof ^ - ? ?

We read the answer on the

of the C-scale

_-scale, under the left

From your own slide rule, or Panel l6 (with hairline

E), we read the answer. In this case, to be

Notice that this setting that you have Just made Isexactly the same as that used for the problem2x3=6. So, If you forget which number goes onthe D-scale and which on the C-scale, all you haveto do Is make this fundamental setting, as we haveIn Panel l6, with hairline E, and you can tell whatgoes where.

Into

by

D-scale

Index

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F Panel l6

For Instance, In Panel l6, hairline E, we see that thenumber we are dividing into is always set on the

-scale.

The number that we are dividing b^ is set on the

-scale directly over the first number.

These two numbers are accurately lined up through

the use of the .

The answer of a division problem on the slide rule

is merely read off the -scale directly below the

left (or right) of the C-scale.

Now "break" your present setting on your slide ruleby lining up the C and the D scale indexes.

7_ _ oOur next problem will be3-5

Our first move is to slide our hairline along the

-scale, and locate the number 7, since we aredividing into this number.

Now, with the hairline over 7 on the D-scale, slip

your slide until the number 3-5 on the -scale isdirectly under the same hairline. 3«5 is the number

we are dividing (by, into).

Now we look for our answer down on the -scale, .

under the of the C-scale.

The answer, in this problem, is .

Panel l6, hairline F shows the setting.

D-scale

C-scale

hairline

D-scale

index

D-scale

C-scale

by

D-scale

left index

h3

Panels 17-20 after next page.

Set your slide rule for the following problem andread-off your answer:

32.3 = 9

"ir 1.5

Panel 17 with hairline G shows the proper setting forthe problem in the preceding box.

If you made this setting without any trouble, and gotthe correct answer you may want to go on to the nextbox.

If you want to go through more discussion of thissetting, continue on in this box.

Our problem was 32.3 ^33

(Panel 17 with hairline Gshows the setting.

)

Our first step is to locate the number we are dividing

(into, by).

Using the hairline, we locate the number we are

dividing into on the -scale.

In this case, it is the number 52.3- In Plate 17 it

is shown at the hairline with the letter .

With the hairline set over the number we are dividinginto on the D-scale, we slip the slide of the slide

rule until the number we are dividing (into,by) on the C-scale is directly under this samehairline. In this case, the number is 35'

into

D-scale

by

The answer to the problem is then read on the -scale D-scale

under the of the C-scale. In this

case the answer is

left index

1.3

Set your slide rule for the following problem,get your answer:

22

23

24

25

26

27

28

29

30

31

32

33

Panels 17-20 on next page.

If your setting was not correct, at first, or you

would like to have a little more discussion and

practice on the setting for division, we'll go through

this setting in detail.

42Our last problem was -^ - •?

Our procedure is always the same. First we will set

the hairline over the number we are dividing into

-scale. (Do this).(42) on the _

Now our hairline is set over 42 on the D-scale. Now

move the -scale until the number we are dividing

by (56) is directly under this same hairline.

While this was being done, the hairline (was,

was not) moved.

After making its first setting, the hairline is not

moved.

Now all we have to do is to read the answer on the

-scale

.

The answer is indicated, in this case, by the

of the C-scale.

See Panel 18, hairline H, for proper setting.

The number of the answer on the D-scale for this

problem is 7-50.

42By inspection of the problem, -f^ , we can see that the

answer will be a little less than 1, or

Solve: ^& = ?

If you had this correct, go on to the next box.

If you did not get this answer, or if you want more

practice, continue in this box.

195Our last problem was y^ =

The setting of this problem is shown in Panel 19,

using hairline V.

Which was the first number you should have set the

hairline over?

This number is "set" first on the -scale by

moving the over it.

After the hairline is in this position it

(is, is not) moved again for this problem..

Our problem is Îv ^"^^ ^^ have already set the number

195 on the D-scale.

-scale along untilOur next step is to slide the

the number is under the hairline.

Our final step, then, is to read the answer on the

-scale, under the of the

-scale.1^5

D-scale

C-scale

was not

D-scale

right

index

0.75

1.42(Or, 1.423)

195

D-scale

hairline

is not

C-scale

137

D-scaleleft indexC-scale

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Panel 17

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Panel 20

hi

Panels 17-20 on preceding page.

Under the left index on your slide rule, and inPanel I9, you can read the number of the answer to

three figures as being .

(Since the scale is a large one at this part of theslide rule, it is possible to read a fourth figure, ifyou want to, giving us a number of 1.423. The lastfigure is 3, since the number is about a third of theway from 1.420 to 1.430.)

105Going back to our original problem, ^§7 "= ?, we can

see that in this case the answer is more than 1 and

less than 2, so the correct answer is ,

1.42

1.42

On your own slide rule, solve the following problem:

28.31 ^ 9

1.90

If your answer was correct, if you rounded off yournumbers OK, if you made your settings correctly, andhad the decimal point of the answer in the rightplace, you may want to Jump to the next box.

If you want to go over this problem in more detail,continue below.

Our problem was

to set is

28.311.90

• The first number we will want

This number has four figures, and we can usually only

set figures on the slide rule.

Therefore, we will round off 28. 3I to the number

This is the first number we will set, and we will set

it on the -scale.

We set this number 28.3 on the D-scale by moving the

until it is directly over the number.

Once the hairline is set, we move itagain.

Then we take our second number in our problem, I.90,

and locate it on the -scale by moving the slide

until it is directly under the which wehave been careful not to move.

Now we have 28.3 on the D-scale and I.90 on the C-scaleboth under the same hairline (as shown in Panel 17,hairline K), and we can now read the number of our

answer directly on the -scale under the

of the -scale.

In this case, the number of the answer on the D-scale

under the left index is .

Our problem was i'qq = ? Since -.

qqis approxi-

mately the same as 3090

we can see by inspection that

the answer should actually be

15.0

28.51

3

28.5

D-scale

hairline

do not

C-scale

hairline

D-scaleleft indexC-scale

1.50

15.0

k8

46

47

48

^9

50

51

52

53

54

55

Solve:20,69834.53

(In this problem, be sure to write down your answer,

Including the correct decimal point, before exposing

the answer given by this program.)

If you are satisfied with your handling of this last

problem, go on to the next box.

If you'd like more drill on these divisions settings,

finish out this box.

20,698 o,

Our problem was WJy^ "=

Since we can usually set only figures on the

slide rule, we will have to round-off these numbers.

The number 20,698 would be rounded-off to ,

and 34.53 would become .

Thus our original problem of|^[^|

Is changed to

^QfÔO 3Q that we can set it on our slide rule.34.5

In making the setting on our slide rule we shall first

set the number on the -scale by

moving the over it.

Then, being careful not to move the , wewill set the number we are dividing ^by (34.5) on the

C-scale by slipping theis under the hairline.

until the number

Now we read the number of the answer on the -scale

Our setting should be the same as shown in Panel 20,Hairline I.

The number of the answer is directly under the

of the -scale.

The number of the answer we read at this place on the

D-scale is.

Now we have to decide on the proper placement of the

in order to get our final answer.

Our original problem was -j^' ^, . This is about the

same as lo^^ and this quotient, we can see from

inspection, is about 700close to 700.

So our answer should be

Since the number of our answer is 6.00 (taken off theD-scale under the right index), which of the followingwould you select for the final answer to this problem?

6.0060.06006000

600

20,7003^.5

20,700 (2.07)D-scalehairline

hairline

slide

D-scale

right index

C-scale

6.00

decimalpoint

600

^9

56

57

58

59

60

61

62

63

64

65

66

The problems which follow are presented with theiranswers, but with no discussion. In working these onyour slide rule, your first two digits or figures ofyour answer ought to agree exactly with the answergiven by the program. The third digit may not be thesame as that given as the answer, since some interpre-tation and interpolation is needed to get this thirddigit. However, your third digit ought not to bemore than a value of one away from the answer whichis given.

For example, if the program answer is 91.7, then youranswer might be 91.8, or 91-6, and still be OK. How-ever, if your answer was 91. 9 or 91.5 it would notbe close enough to be correct.

Solve 53727H

Review Items 28 to 35 if this gives you any difficulty.

solve: |I| .

Review Items 28 to 35 if this was difficult for you,

Solve 9.45

Solve 30.1

745

Solve; 0.007650.0515

Items 36 to 46 cover a similar problem,

Solve222.2~T7T5 •

Items 36 to 45 cover a similar problem,

Solve:2.8856023.5

'

If the decimal point bothers you, you might want touse powers of 10.

Solve:8225

900.5

Solve: 42,8356.896

If this gives you trouble you might want to reviewItems 47 to 55.

solve: ^^^^^3-^34^

644.9

Review Items 47 to 55 if this was difficult for you

Solve 41.15

8.55

Items 35 to 45 cover a similar probler

1.93(to threefigures)

0.732

2.37

0.04o4

0.149

193

0.000480 or

4.8 X 10'^

9.13

6,200

38,100

4.81

50

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Panel 21

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SLIDE RULE EXTRACTION OF SQUARE ROOTS

Our final operation with the slide rule will be theextraction of square roots. Strangely enough, thisoperation, which Is one of the most difficult opera-tions In arithmetic. Is one of the simplest of allthe slide rule operations.

Look at Panel 21 at the top of this page

This Is a slide rule which has had the removed,

In Panel 21, how many different scales are shown?

v/hat letters are used to designate these threescales?

We will not use the K-scale. In this program wewill use only the scale and the scale.

slide

3

A, D, andK

A, D

What letter points to the left index of the D-scale?

'What letter Indicates the left index of the A-scale?

Suppose the letter F indicates the number 1

the letter G will indicate the numberThen

The letter J indicates the number

The letter K indicates the numberpoints to the number .

This is true, even though it is labeled as 1

and L

E

F

2

6

9

10

52

M Q R S T U

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Panel 21

10

11

12

The A-scale Is really a double scale. The firstpart of this "double" scale runs from F to L, andthe second part runs from L to the letter .

The left part of this A-scale, from F to L, is

exactly the same as the right part of this scalewhich runs from to .

The middle point of the doubled A-scale is markedwith the letter

L to V

13

14

The

K L

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Panel 21

19

20

21

22

Set

M N P Q R S T U

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ill II III 1 1 111) I iTl II itlllilllll I I II

Panel 21

30

31

32

33

34

On the right hand part of the A-scale, set yourhairline over the number 25 and find its squareroot.

We all know the square root of 25 is 5> but youwant to get this answer from your slide rule.

If your setting was correct and you read the answerof 5 from your slide rule, you may want to go tothe next box.

If you're not too sure about your setting, finishthis box.

Our problem was to extract the square root of 25-We did this by setting 25 on the A-scale. Set 25on the A-scale under your hairline.

This setting is Just half-way between 20 (indicatedby the letter M) and the number (indicated bythe letter 0).

With this setting for 25 we can now read the squareroot of 25 directly under the same hairline on the

-scale.

I

The reading under the hairline on the D-scale is

Panel 21,hairline K.

30

D-scale

5

35

36

Make the proper setting on your slide rule toextract the square root of 49. 'What answer do youread from your slide rule ?

If you obtained this answer from your slide ruleand had no trouble with your setting, go on tothe next box.

If you had trouble with this setting on your sliderule, you'll want to go through the steps inthis box.

Our problem was to extract the square root of 49.Our first step is to set the hairline over 49 onthe -scale. A-scale

55

K L

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Panel 21

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37

38

39

Set your hairline over 49 on the A-scale. (Checkthe next answer.

)

Notice that P is 40 and R Is 50 and Q Is ninesecondary divisions from 40 to give us the settingfor the number

.

Now, with our hairline set over 49 on the A-scale(hairline Q In panel 21) we can read the square rootof 49 on the -scale as being 7.

Panel 21,hairline Q.

49

D-scale

40

41

42

43

Now we'll try a tricky new setting. Set your hair-line over the number 4 in the right hand part of theA-scale, or in the same position as indicated by theletter P in panel 21. With the hairline in thisposition, what reading do you get on the D-scale?

Is the square root of 4 equal to 6. 31?

Now move your hairline to the left section of theA-scale on the number 4 as indicated by hairline I.

With the hairline in this position, what readingdo you get on the D-scale?

Is the square root of 4 equal to 2?

Thus, it is Important to set your number in thecorrect section of the A-scale.

6.31

Kg!

2

Yes

44

45

Notice that we set the number 4 in theof the A-scale to get its square root.

How many digits are there in the number 4?

section left

one

56

M N P OR S T U

iiî 1 11

i 1 1

1

Iliiit'iMliMiT 1*1I il I 1 1 iTmiTiiiiT

K6

47

48

49

50

51

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I

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Panel 21

Notice that we set the number 25 (see hairline N)

In the section of the A-scale to get its

square root.

How many digits does the number 25 have?

So, if a number has one digit, (for example, 4) we

use the left section. If a number has two digits,

(for example, 25) we use the right section.

Suppose a number has three digits, (such as 225)

which section of the A-scale would you guess that

it should be set in?

Correct Section ofthe A-scale to use

LeftRightLeftRight

Consider the following:

Numberof Digits

1

2

3

5

How should the blank be filled in?

Look at that chart again.

If the number of digits in a number is odd, the

number is -set in the section, and if the

number of digits in a number is even , the number

is set in the section of the A-scale.

So, for an even number of digits, the

is used; for an odd number of digits, the

section is used.,

section

right

two

left section

left

left,right

right,left

57

52

53

54

55

56

57

58

59

60

E F

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I I I II

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Panel 22

Suppose we are to find the square root of 3J+6.

How many digits are there In 346?

Is this number of digits odd or even?

Is this number set In the right section, or theleft section of the A-scale?

Set your slide rule to determine the square rootof 346, and read off your answer from your sliderule.

In which section would you set the number 16,700,000to extract its square root?

This is true because it has an even number of digits.

On your slide rule determine the square root of152,000.

If your answer was correct (with the correctdecimal point), skip this box and the two followingit.

If you got the number of the answer (3.9O) but areuncertain as to how to get the correct decimal pointfor the answer, go to the next box.

If your answer was 123 (or a similar wrong answer),continue on in this box.

Our problem was to find the square root of 152,000.How many digits are there in this number?

Is this an odd number of digits, or an even numberof digits?

Since the number of digits is even, this number(152,000) should be set in the (left, right)section of the A-scale.

58

3

odd

left

Panel 22,hairline G,18.6

right section

390.

even

right

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Panel 22

61

62

If you did not get this last answer, or you areconfused about this point of right and left sectionsof the A-scale, review Items 44 to 52.

If you understand which section the number 152,000Is to be set In, go ahead and set It.

What Is the number of the answer you get for thesquare root of 152.000?

Panel 22,hairline H.

3.90

63

64

65

66

67

Our next task is to get the decimal point in theproper place. If you can already easily do this,skip this box. In extracting square roots, one ofthe things we must always do is to group the digitsof our number into pairs, starting at the decimalpoint. For instance, if we "pair up" the digitsin the number 234,456 we get the following pairs:

23 4-4 56

"Pair up" the digits (figures) in the number 125,098.

In pairing up the digits in the number 379, we get

3 79, since we start our pairing from the decimal

Pair up the digits (figures) in 35,065-

Starting at the decimal point, we can pair off thenumber O.O345 as follows: 0. 03 45

How would you pair off the number O.OOO876?

This pairing off makes it easy to determine thedecimal point of our square root. For each pair ofnumbers in the number there will be one digit inthe square root.

How many digits (or figures) will there be in thesquare root of 16,7000,000?

This is true since there are four pairs of digitsin the original number.

12 50 98

point

3 50 65

0. 00 08 76

four

59

E F

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11 1 1

1

1 1 1 1

1

1 1 1 1 r1

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1 1 1 a

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Panel 22

68 How many figures will there be In the square rootof 0.0016?

Now we will get back to our original problem ofgetting the square root of 152,000.

69 Pair off the number 152,000.

70 How many pairs does it have?

71 How many digits will it have in its square root?

Back at item 62 we determined that the number ofthe answer of this square root problem is 3.9O.

72 Now, knowing that the square root has three numbersin it to the left of the decimal point, what is thesquare root?

two

15 20 00

3 pairs

3

390

If your number for which you wish to extract thesquare root is less than one (0.00234, for instance)you can determine which section of the A-scale inwhich to set it by merely counting the number ofzeros to the right of the decimal point.

73 In the number 0.00234, how many zeros are there tothe right of the decimal point?

74 Is this number of zeros odd or even?

If this number of zeros is even, the number is seton the right section, and if it is odd, it is set

75 on the section.

two

even

left

76 In which section of the A-scale would you set thenumber 0.00234 to get its square root?

Did you count to see that 0.00234 has an evennumber of zeros to the right of the decimal point?

right section

60

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1

77

78

79

80

81

82

83

84

To extract the square root of 0.000206, you wouldset it In the (left, right) section of the

-scale.

Did you note that 0.000206 has three zeros to theright of the decimal point ?

The simple rule to remember is that if a number lessthan one has an odd number of zeros to the rightof the decimal point, it is set on the sectionof the A-scale.

If the number of zeros to the of the decimalpoint is even, the number itself is set in the

section of the A-scale.

In which section of the A-scale would 0.0000101be set?

This is true because it has an even number ofzeros after the decimal point.

In which section of the A-scale would you guessthat 0.l6 should set?

Will the number O.OO875O be set in the rightsection or the left section of the A-scale?

Make the proper setting for extracting the squareroot of 0.008750 on your slide rule.

The number of the answer which is read off theD-scale is

We are extracting the square root of O.OO875O, andwhen we pair off this number we get .00 87 50. Sincethis number contains (how many) pairs, andsince each pair gives us one digit or figure in thesquare root answer, we will have at leastdigits in our answer. The number of our answer is

9.35^ so the correct square root would be 0.0 .

The zero after the decimal point of our last answeris there because our first pair was a double zeropair.

61

iiiiiiliiiit

IWFPJ

III 1 1 it

Panel 22

leftA-scale

left

right

right

right section

right section

right section

Panel 22,hairline J,

9.35

3

3

0.0935

85

86

87

88

89

90

91

92

E F

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11 1 1 II II II

'2

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II 1

1

1

3III II

11 1 1

1

1 1 1 1

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^t I I I I I I I I ilihhliliililili

Panel 22

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11 1 1 1

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Extract the square of l8,500.

If your answer was correct, go to the following box,

If your number was correct, but the decimal pointwas off, go to Item 8£.

If your number was Incorrect, finish this box.

The number we were to take the square root of was18,500.

It has an (even, odd) number of digits, andshould be set in the (right, left) section ofthe -scale.

Make the proper setting on your own slide rule.

-scaleThe number of the answer is read from theas being .

In the number l8,500 we could point off (howmany) pairs?

There were three pairs, so there will be digitsin the square root.

So, our correct answer (taken from the number ofthe answer, I.36) will be .

Extract the square root of O.OOOOI68.

If your answer was correct, go to Item 104 .

If the number of your answer was correct, but youare not sure about the placement of the decimalpoint, go to Item 99 -

If your answer was not correct, go to Item 93 «

62

136

oddleftA-scale

Panel 22,hairline F.

D-scale1.36

1 85 00,

3 pairs

three

136

0.0041

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iii|iiniiiii| .i|iiM|iiii|iiii|nii{Mii|iiii{iiii]iiiM

'i'

93

94

95

96

97

98

99

100

101

102

103

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1

m tpyrpi

III 1 1 it

We are to extract the square root of 0.0000168.

How many zeros are there to the right of the decimalpoint?

Is this (answer) odd or even?

In which section of the A-scale should the number0.0000168 be set?

If this is not clear to you, re-do Items 73 to 8l.

Make the setting on your slide rule to get the squareroot of 0.0000168.

'/fiiich hairline shows the proper setting for0.0000168?

The setting of E is wrong, since it is in the leftsection.

With the proper setting for 0.0000168, what numberdo you read for its square root?

Now we need to properly place the decimal point.

Take the number 0.0000168 and pair it off.

That last zero is merely added to pair off the 8.

How many pairs are there?

How many places will the answer have?

Since our first two pairs are zeros (.00 00 l6 80),our first two places will also be

.

Since the number we read off the D-scale is k.l,the answer with the correct decimal point will be

If this last answer is not clear to you, go backto Items 6_3 to 71 for a review of decimal pointplacement

.

63

J

Panel 22

four

even

right section

Check panel22.

4.10 (on theD-scale)

0. 00 00 16 8o

4

zeros

.0041

104

105

106

107

108

109

In the following exercises, make the proper settingson your slide rule, write down your answer, placethe decimal point in its proper place BEFORE youcheck the answer in the program. This will give youyour best practice. In case you have trouble withany of these problems, reference is made to the partof this program which you might want to review.

Extract the square root

A similar problem starts

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PROGRAMMED SLIDE RULE - Archive...6 5 6789 5 6 789 n Ir.rj^ R ST Panel1DiagramofaSlideF^le (showingonlytheprimary scaledivisions) 3Whatistheotherscaleontheslidecalled?C-scale