Electronics and Your Slide Rule, Part I — Step-by-step to Skillful Operation (CIE Electronics Slide Rule No. 515 / Pickett N-515-T)
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CLEVELAND INSTITUTE OF ELECTRONICS / CLEVELAND, OHIO
Electronics and
Your Slide Rule
Part I
22-1
An AUTO-PROGRAMMED. Lesson
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ABOUT THE AUTHOR
Through over 15 years experience in helping students learn through home
study, Mr. Geiger has obtained an intimate understanding of the prob-
lems facing home-study students. He has used this knowledge to make
many improvements in our teaching methods. Mr. Geiger knows that
students learn fastest when they actively participate in the lesson, rather
than just reading it. Accordingly, you will find many “What Have You
Learned?” sections in this lesson, to assist you in getting a firm grasp of
each topic.
Mr. Geiger edits much of our new lesson material, polishing up the manu-
scripts we receive from subject-matter experts so that they are easily read-
able, contain only training useful to the student in practical work, and are
written so as to teach, rather than merely presenting information.
Mr. Geiger's book, Successful Preparation for FCC License Examinations
(published by Prentice-Hall), was chosen by the American Institute of
Graphic Arts as one of the outstanding text books of the year.
This is an MUQPRIGUMWET Lesson exclusive with the
Cleveland Institute of Electronics. It is your assur-
ance of the finest in technical education and training.
“Irgdemork
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& % Accredited by the Accrediting Commission : =
= +, of the National Home Study Council 3 rs
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3 Hi The Accrediting Commission has been approved by the US. 3a
% é Office of Education asa “n lty recognized accrediting z :
ee s agency’. 3
OME oF ea
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Electronics and Your
Slide Rule
Step-by-step to Skillful Operation
By DARRELL L. GEIGER
Senior Project Director
Cleveland Institute of Electronics
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esson you will learn...
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12.
13,
14,
The Scales of a Slide Rule... Page 3
Special Seales... Page 4
The Parts of Your Slide Rule... Page 5
A Slide Rule for Adding and Subtracting... Page 6
Multiplying and Dividing by Adding and Subtracting... Page 9
Multiplying With the Slide Rule... Page 10
Reading the Slide Rule Scales... Page 12
Reading With Hairline Between Marks... Page 14
Reading Other Parts of the Scales C and D,.. Page 15
Reading Other Scales... Page 16
Decimal Point in Slide Rule Operation... Page 17
Practical Multiplying... Page 19
Multiplying More Than Two Factors... Page 24
Division... Page 25
Examination. .. Page 26
ELECTRONICS SLIDE RULE NO. 515
designed by CLEVELAND INSTITUTE OF ELECTRONICS
U. S. Patent Number 3,120,342
distributed by
Cleveland Institute of Electronics
1776 East 17th St.
Cleveland, Ohio 44114
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© : Bs
Copyright 1966, 1965, 1962, 1968 Cleveland Institute of Electronica. gs
All Rights Reserved/Printed in the United States of America. z :
FOURTH EDITION /Fifth Revised Printing/October, 1966, EE
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A chat with your instructo1
This is the first of several lessons written specifically for the many
electronics men who wish to improve their job efficiency and qualify
for promotion by becoming skilled in the useof the slide rule. With
electronic equipment rapidly increasing in complexity, a good know-
ledge of the slide rule is essential toall progressive-minded men of
electronics.
Since you will be using this manual without the aid of a teacher, we
have made every effort to make each step self-explanatory. Many
illustrations are included to enable you to grasp each principle of
slide rule operation. However, if you shouldcome across any point
which you cannot fully understand, please write to me so that I can
explain it to you.
Topics 7 through 10 cover the most important subject of all... learn-
ing the proper reading of the scales. Don't be tempted to hurry
through these topies in order t3 Fet to more mreresting subjects.
No matter how much you know about a slide rule, it is of no prac-
tical value unless you can properly read the scales. We have had
much experience intraining slide rule operators, and this experience
shows that inability to properly read the scales cause beginners by
far the most trouble. Not that it is hard to learn toread the scales--
it is simply a matter of following the lesson step-by-step and work-
ing all the practice problems.
You should keep your slide rule before you at all times while read-
ing this manual and go through all the steps described on the worked
out examples. Since only practice will make you aslide rule expert,
it is important that you work all the practice problems.
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2 Hold your SLIDE RULE right!
Slide rules stick and move by jumps unless properly held when set-
ting. In Fig. A, the left hand squeezes the rule, binding the slide.
Also, it leaves the setting of the slide entirely to the right hand.
Support the body of the rule between your left palm, and the thumb
and second finger of the right hand (Fig. B). Note: no fingers
around the rule! Move the slide with the left thumb and right
forefinger. The two-way push prevents excess slide movement.
When the slide is far out of the body, support the body of the rule
with the left hand and the second finger of the right hand (Fig. C).
Do not wrap your fingers around the body, Adjust the slide with
the right thumb and forefinger, and the thumb of the left hand.
Wrong way.
Fig. B Right way
Fig.C Right woy
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Electronics and
Your Slide Rule
Part I
THE SCALES OF A SLIDERULE...Any good slide rule car-
ries a number of different scales, the exact number and type
depending upon the purpose for which it is intended. The var-
ious scales are identified by letters placed to the left of each
scale, which also indicate the purpose of the scales, The let-
ter-identifying system is the same regardless of manufacturer.
On the front of your Electronics rule, notice first the C and D
scales. They are identical, except that the D scale is on the sta-
tionary part of the rule and the C scale is on the sliding member.
These aré the basic and most important scales on a slide rule.
The C and D scales are used directly for multiplying and dividing,
and in conjunction with other scales of the rule for performing a
multitude of operations.
Notice next the CIscaleon your rule. The CI scale is the same
as the C scale except reversed; that is, the numbering is from
right to left instead of from left to right as on the C and D
scales, CI means "C Inverted". Inverted scales are printed
in red on most slide rules, so the user will not forget while
reading the scales that they progress from right to left. The
CI scale is used directly for finding reciprocals. In conjunction
with other scales it simplifies computations in many ways.
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Frovided by.Joe- Hind B scales are used with problems involving squares
Processene. Square roots. These two scales are identical, except that
the A scale is on the body of the rule, while the B scale is on
the slide. The left half of the A or B scale (the part number-
ed from 1 to 10) is similar to the C or D scale, but scaled
down to be only half as long. The right half of the A or B
scale (the part numbered from 10 to 100) is identical to the
left half, except for the higher numbering used.
The L scale is used for finding logarithms. It is particularly
useful in electronics for working decibel problems. The L
scale is different from all the rest of the scales in that it is
linearly (that is, evenly) divided.
The Sand T scales are used when working problems in trig-
onometry. Their most important use to the electronic tech-
nician is in working alternating current-circuit problems. The
S scale is used when working with sines and cosines, and the
T scale with tangents and cotangents.
2 SPECIAL SCALES, .. The scales so far discussed are found on all
good slide rules intended for engineering or technical applica-
tions. In addition, the Electronics rule has several scales intended
specifically to facilitate working many common types of electronic
provlems. These scales, Sfcourse, Wottld for be found Unwtide
rules intended for general engineering applications.
One of these special! scales is the H scale, the top scale on the
front of your Electronic rule. This scale is used for solving the
various types of resonant frequency problems. Since this, as
you will notice, is an inverted scale, it is printed in red. Below
the H scale is the 27 scale, This scale is used in solving prob-
lems involving inductive or capacitive reactance, or in any type
of problem where the factor 27 appears.
On the back side of your Electronics rule, you will find an
additional set of scales. These scales are used for quickly
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and accurately locating the decimal point in many frequently
occurring types of electronic problems. These scales are
one of the most valuable features of the Electronics rule for men
working in electronics,
THE PARTS OF YOUR SLIDE RULE... The names of the var-
ious parts of a typical slide rule are shown in Fig. 1. It is
important to know these in order to follow the instructions for
using the instrument. The slide is the movable central part of
the rule. The stationary part of the rule, in which the slide
slides, is called the body.
Fig. 1. The parts of a slide rule.
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The transparent runner that is free to move along the body is
called the indicator or cursor. In the center of the indicator
is a long fine line perpendicular to the 8Cales of the rule. This
is called the hairline, and is used for accurately locating and
reading positions on the scales. Screws in the cursor on most
slide rules make it possible to adjust the hairline, if it should be-
cume necessary, So as to maintain it exactly perpendicular to the
scales. Screws in the body of the rule, at the ends, allow the ten-
sion of the slide to be adjusted.
Of special importance with reference to the A, B, C, CI, and D
scales is the endscale markings on these scales, called the in-
dex marks. Each of these scales has an index on each end. In
addition, the 10 marks at the centers of the A and B scales arr
also called indexes.
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A SLIDE RULE FOR ADDING AND SUBTRACTING...A slide
rule is inherently a device for adding and subtracting. But by
4 putting properly graduated scales on the rule, the results of
this adding and subtracting can be directly read as products of
multiplication or as quotients of division. In fact, scales for
actually adding and subtracting are seldom placed on practical
slide rules, because such simple operations can be performed
quicker with a pencil and paper.
However, the best way to learn touse a slide rule and tounderstand
its principles of operation is to learn to use an adding andsubtracting
slide rule. You can construct such a rule by cutting out with a pair
of scissors the twocentimeter scales at theend of this lesson. Then
place the two calibrated edges together so that one edge can slide a-
long the other to form a simple slide rule, as in Fig. 2.
To add 243
place O om Ly opposite 2 om Ly
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Fig. 2. Using a linear slide rule to show that 2 + 3 = 5.
The scales on your paper slide rule are different from most of
the scales or your regular slide rulé iff that the divisions ofthe
former are linearly (that is, evenly) spaced, while the spacing
between the divisions of the latter is uneven. However, there
is one linear scale on your regular slide rule, the L scale. If
your regular rule had another L scale on its slide, it could be
used for adding and subtracting. To add or subtract, both of
the scales used must be linear.
Fig. 2 shows how to use your linear slide rule to find that
2+3=5. The principle of operation is quite simple. Since
the numbered divisions on the scales are in fact centimeter
marks, in adding by the method of Fig. 2 you actually show
that 2 centimeters plus 3 centimeters is equal to 5 centimeters.
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You are measuring out two centimeters and from that point
measuring on three centimeters more, making a total length
of & centimeters, You should now add various numbers to-
gether on your paper slide rule until you understand clearly
the principle of addition by this method. This will be very
helpful in learning to operate a regular slide rule.
Adding and subtracting on your linear paper slide rule are not
limited to simple whole numbers. Fig. 3(a) shows how to add
2.3 and 3.4. The 0 mark (index) of L,; is placed opposite the
mark for 2.3 centimeters on scale L,. This position is found
by noting that there are 10 minor division marks between the
main centimeter marks 2 and 3. Hence, each of the minor
division marks represents one tenth of a centimeter, so that
2.3 centimeters will be three minor division marks to the
right of the main division mark 2, as shown in Fig, 3(a).
i
uy 9 ! 2 3 tT if = 3
= 6 i At. 3 4 5 | 6 g
(a) 23 sd
23+34+:57
(b)
2.26 + 3.38= 5.64
Fig. 3. Adding two and three digit numbers with o lineor slide rule.
Opposite 3.4 centimeters on scale L,, read 5.7 centimeters
on scale L,. Hence, 2.3+3.4=5.7. Since the sum of 23 +
34 is equal to the sum of 2.3 + 3.4, except for the location of
the decimal point, the setting of Fig. 3(a) can equally well be
used to show that 23+ 34= 57. Or as another example, the
same setting can be used to show that 230 + 340 = 570, or that
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0.023 + 0,034 = 0.057. It is characteristic of most slide rule
scales that the same setting can be used for different locations
of the decimal point if the digit values are the same, as in the
above examples.
Adding 226 to 338 provides another example. Except for the
position of the decimal point in the answer, this is the same
as adding 2.26 to 3,38, which is shown in Fig. 3(b). The zero
mark on scale L, is placed opposite 2. 26 centimeters on scale Ly.
To locate 2.26 on scale Ly, the minor division mark repre~
senting 2.2 is first located. On past 2.2, six tenths of the
distance to the following minor mark, is 2.26. We must es-
timate with our eye to locate this last position, keeping in mind
that 6 is slightly over half of the distance between the two minor
marks. With practice, such estimates can be made fairly ac-
curately on a regular slide rule, but not here because of the
lack of precision in the printing process. Opposite 3.38 on
scale L, the sum, 5.64, is read on scale L,. Thus 226 + 338
= 564. You may get a value for the last digit considerably
different from 4, due to the inaccuracies of the paper scales.
Subtracting on your paper slide rule is merely a matter of
working backwards from the process used for addition. Thus,
to subtract 3 from 5 set 3 on scale L, opposite 5 on scale Ly»,
and then opposite 0 on scale L, read the answer, 2, on scale
L). The scale settings are exactly the same as for adding 2+
3, as shown in Fig. 2. Similarly, by setting 3.4 of scale L,
opposite 5.7 on scale L,, the difference between the two,
2 3, is read on scale L, opposite-Oon'scale L; The setting
is the same as in Fig. 3(a).
You should practice adding and subtracting with your paper
slide rule until the principles and methods are clear to you.
It is important not just to learn how to add or subtract, but
also to understand why the sums and differences are obtained
when the operations are performed as described.
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= One way to add 2+ 3 would be to measure off two feet on the
‘ floor from some starting point and there make a mark. From
& this mark, measure off three feet more in the same direction
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and make a second mark. Now measuring the distance from
the starting point to the second mark, it is found to be five
feet, so that 2+ 3 must equal 5. Your paper slide rule is
just a somewhat less clumsy method of adding two distances
in the same way.
MULTIPLYING AND DIVIDING BY ADDING AND SUBTRACT-
ING,..Since a slide rule is inherently capable only of adding
and subtracting, multiplication and division must be reduced
to addition and subtraction if a slide rule is to be used for the
purpose. If you have studied logarithms, you will probably
remember that it is possible to do this, but you need not be
familiar with logarithms to understand how.
In algebra, it is shown that numbers with the same base can be
multiplied together by adding their exponents. Thus, 3? x 3° =
3?*+3= 38, For proof, note that 3?=3x 3=9, 33=3x3x3
= 27, and 38 = 3x 3x 3x 3x3 = 243, Since 9 x 27 = 243,
3? x 3? is proved equal to 3°. As another example, 2‘ x 2° =
2°, which you may verify as an exercise. Asa further exam-
ple, take 10? x 10° = 105, which shows that 100 x 1,000 =
100,000. In this last example, the base is 10. More advanced
mathematics shows that any number can be written as 10 with
the proper exponent. Here are some examples:
100 = 10? 500 = 107 6 2 = 10°
131.23 = 107+ 118 762 = 102: 8 3 = 10°47"
200 = 10?- %! 1,000 = 10° 6 = 10°78
The exponents in the examples above are called logarithms.
Thus in the expression, 762 = 10°*°**, 2,882 is said to be the
logarithm of 762. Logarithms are found by consulting tables
of logarithms, constructed for that purpose, but how this is
done need not concern us. The important point at this time is
that any two or more numbers can be multiplied together by
adding their logarithms. Thus, since 131.23 = 10% '"8 and
762 = 107", we can multiply 131, 23 by 762 by merely adding
the exponents of the powers of 10 (logarithms). Hence, 131.23
x 762 = 10? 118 + 2.882 = 198 = 100, 000.
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10 Working ina similar manner, 2 x 3 = 10% ™! x 10°47 =10%- 78
= 6. Providing we know the logarithms of the numbers involved,
the process of multiplication thus reduces to one of simple ad-
dition. And since division is the opposite of multiplication,
the process of division reduces to one of subtraction.
6 MULTIPLYING WITH THE SLIDE RULE...Using the paper
slide rule you have constructed, you can multiply 2 by 3 by
adding their logarithms, 0.301 and 0,477, and then noting that
their sum, 0.778, is the logarithm of 6. Since we would or-
dinarily not know the logarithms of the numbers to be multi-
plied or divided without looking them up in tables, this method
is certainly impractical. However, by marking directly on
the slide rule the numbers to which the logarithms correspond,
the necessity of knowing or referring to logarithms is elim-
inated, as you will see shortly.
To find 2x3:
set /eft index scale C opposite 2 on scale D
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then opposite 3 on scole Co read 6 on scale D
Fig. 4. Finding 2 « 3 — 6 (or finding 6 =~ 3 = 2).
We will now multiply 2 x 3 using your Electronics slide rule.
On the body of the rule there is one linear scale, the L scale,
corresponding to the L, scale of your paper slide rule. To
multiply 2 x 3, it is necessary to add 0.301 to 0.477. Set the
i hairline of the indicator over 0.301 on the L scale, and then
== set the left index of the C scale under the hairline, as shown
#2 jin Fig. 4, the dashed line indicating the position of the hair-
22 line at this time. But notice that the hairline is also over 2
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on scale D. Hence, it was not necessary to first know the log-
arithm of 2 and then set the hairline to this value on scale L.
You can accomplish the same thing by setting the index of
scale C opposite 2 on scale D.
Our next step is to set the hairline over 0.477 ona linear scale
on the slide. But since the slide does not have a linear scale,
this cannot be done. However, if it did have one, 0.477 would
come opposite 3 on scale C. Hence, set the hairline over 3
on scaleC, asshownby the indicator position in Fig, 4. Read-
ing under the hairline on scale L, 0.778 is found to be the sum,
which is the logarithm of 6. Hence, 2 x 3= 6. Again, it is
not necessary to consider the logarithm 0.778, because the
answer 6 can be read directly on the D scale.
The slide rule manufacturer has marked on the C and D scales
the natural numbers, each number being located on the rule at
the point where the logarithm would fall on a linear scale. In
that way, it is not necessary to refer to logarithms when using
a slide rule to multiply or divide.
To summarize: To multiply 2 by 3, set the left index of scale
C opposite 2 on scale D. Then opposite 3 on scale C, read 6,
the answer, on scale D, Or another way: Set the left index of
scale C opposite 3 on scale D. Then opposite 2 on scale C,
read 6 on scale D.
As another example, to multiply 1.5 by 3, set.theleft index of
scale C opposite 1.5 on scale D. Then opposite 3 on scale C,
read the answer 4.5 on scale D. See Fig. 5. We get 4.5 as
our reading on scale D, because the hairline sits on the half
mark between 4 and 5.
Dividing is, of course, just the opposite of multiplying. To
divide 6 by 3, place 3 on scale C opposite 6 on scale D. Then
opposite the left index of scale C, read 2 on scale D. See
Fig. 4. Or to divide 4.5 by 3, first set the hairline over 4.5
on scale D. Then set 3 on scale C under the hairline. The
answer, 1,5, is then read opposite the left index of the C
scale on the D scale. See Fig. 5. The purpose of using the
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1]
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12 hairline is to fix the point 4.5 on scale D, so we won't lose it
while locating 3 on scale C andbringing it to the proper location.
To find 1.5 x 3:
set left index scale C opposite /.5 on scale aD.
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Fig. 5. Finding 1.5 % 3 = 4.5 (or finding 4.5 3 — 1.5).
READING THE SLIDE RULE SCALES... Before the slide rule
can be put to any practical use, it is first necessary to learn
to read any value from the scales. We will begin first with
the C and D scales, which are identical. Slide rule scales are
somewhat more difficult to read than simple linear scales be-
cause of the unequal spacing between divisions. Consider first,
readings that fall between 1 and 2 on the scales C and D.
A view of this pa'rt of scale D appears in Fig. 6. The vertical
@8hed lines represent various positions of the hairline. This
section of the rule is divided into 10 main subdivisions, mark-
ed 1.1, 1.2, 1.3, etc, For example, the hairline at position
G reads 1.7 on scale D.
Each of the main subdivisions just discussed is further divided
into 10 secondary subdivisions. For example, you will findthe
space between 1.2 and 1.3 on your rule divided into 10 parts.
These are not numbered because the division marks are too
close together to permit it. These secondary subdivisions be-
tween 1.2 and 1.3 make it possible to read values from the
slide rule between 1. 2 and 1.3.
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Fig. 6. Reading the section of the C or D scale between 1 ond 2.
For example, when the hairline is in position B of Fig. 6, the
reading is 1.23. The last digit 3 is obtained by noting that the
hairline is 3 secondary subdivision marks past 1.2. Similarly,
the reading for the hairline at point C is 1. 28 (here the hair-
line is 8 secondary subdivisions past 1.2). As further exam-
ples, the reading for hairline A is 1.12, for position F is 1. 64,
and for position H 1,94. Reading positions D and E will be ex-
plained in the next topic, You should, of course, set the hair-
line of your slide rule to these various positions as you study
the text.
WHAT HAVE YOU LEARNED?
Referring to Fig. 7, read the nine different settings of the
hairline.
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ANSWERS
A. 1,00 B, 1.02 C,. 1,06 D. 1.17 E, 1.35
F, 1.40 G. 1.71 H. 1,80 I. 1.89
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14 READING WITH HAIRLINE BETWEEN MARKS...When the
hairline is in position D of Fig. 6, it does not coincide with
any of the marks on the rule, but is halfway between the mark
for 1.42 and 1.43. The reading therefore is 1.425, the last
digit 5 showing that the hairline is past the mark for 1.42 by
0.5 of the distance from 1. 42 to 1. 43.
In position E of Fig. 6 the hairline is between 1.56 and 1.57.
By careful inspection we might estimate it to lie to the right
of 1.56 by 0.3 of the distance between 1.56 and 1.57. With
that assumption, the reading obtained for this setting would be
1.563. The last digit 3 here is only an estimate. Someone
else equally experienced with a slide rule might estimate 2
for the last digit. A third person might estimate 4. Thus the
reading for position E might be variously given by different
operators as 1.562, 1.563, and 1.564. This is characteristic
of a slide rule; the last digit in the reading is often subject to
a slight error. However, for practical applications the ac~-
curacy of a slide rule is nearly always sufficient.
From the above it is evident that the accuracy of results with
aslide rule depends to some extent upon the ability of the user
to properly estimate values when the hairline does not coin-
cide exactly with any of the division marks on the rule. You
ean quickly obtain this neccssary skill with practicc, provid-
ing you are careful to always do the best estimating job you can.
WHAT HAVE YOU LEARNED?
Referring to Fig. 8, read the different settings of the hairline.
Take care in estimating the final digit, An experienced read-
er will get one of the acceptable readings given in the answers
to this exercise. Since you are a beginner, you may be farther
in error than these answers allow. Providing you are doing
the best you can, you need not be concerned about this.
PEPE CHH ITE LO HOR ORS TYYY
Fig. 8.
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ANSWERS 15
The best answer for each reading is given first, but all of the ans-
wers given areacceptable, even for an experienced slide rule oper-
ator.
A. 1,014, 1,013, 1.015 B. 1.056, 1.057 C. 1.096, 1.097
+ 1,128, 1.127 E. 1.155 F. 1.195, 1.196
- 1,228, 1.227, 1.229 H. 1.263, 1.262, 1.264
1,297, 1.296, 1.298 J. 1.336, 1.335, 1.337
1,373, 1.372, 1.374 L. 1.426, 1.427 M. 1,472, 1.473
1,523, 1.522, 1,524 O. 1.566, 1.567 P. 1.615
1,668, 1.667 R, 1.726, 1.727 S. 1.783, 1.782, 1.784
» 1,844, 1.843, 1.845 U. 1.895, 1.896 V. 1,943, 1.942
1,992, 1.991, 1,993
TaD
nOzR
=
READING OTHER PARTS OF THE SCALES C AND D...We
will now consider reading that portion of scales C and D of the
slide rule between 4 and 10, Fig. 9 is a view of that section,
Each of the principal divisions in this part of the rule is di-
vided into 10 subdivisions. Because of lack of space these
subdivisions are not numbered. Each subdivision is further
divided into two secondary subdivisions to assist in estimating
the final digit when the hairline lies between two subdivision
marks.
>
oo
a
xo
—n
oe
—--O
z
_
---%
r
=
ss sis 622 || lott
Fig. 9. Reading the portion of the C ond D scales between 4 ond 10.
The reading of A in Fig. 9 is 4,3, since the hairline lies 3
subdivision marks to the right of 4. Similarly, the reading of
J is 7.7. The reading of D is 5.35, since the hairline lies on
the mark that divides the space between 5.3 and 5. 4 in half.
The reading F is 6.22, the final 2 being, of course, estimated.
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_
oO
In reading the position of the scales C and N hetween 2 and 4
you willnotice that each principal subdivision is further divided
into five secondary subdivisions. Figure 10 shows this part of
the rule. The reading for position E is 2.6 and for position N
3.8, Position F reads 2.74, position K reads 3.28, position A
reads 2.15 and position I reads 3.07.
AO ERE FGHIy KY HY
' ' ’ ’ | ' ‘
' ' t ' 4
'
26 274 307 3b8 3.8
2.15
Fig. 10. Reading the portion of the C and D scales between 2 and 4.
WHAT HAVE YOU LEARNED?
Read the hairline positions B, C, E, G, H, I, K, L, andM in
Fig. 9 and positions B, C, D, G, H, J, L, and M in Fig. 10.
ANSWERS
Figure 9...
B. 462, 4.69 C. 4m96, 2.97 E. 5.88, 5.87 G. 68748, 6749
H. 6.86, 6.85 I. 7.28, 7.27 K. 8.47, 8.48 L. 9.20
M. 9.77, 9.76
Figure 10...
B, 2.26 C, 2,37, 2.38 D. 2.48 G. 2,85 4H, 2.95, 2.96
J. 317 L. 3.43 M. 3.60, 3.61
READING OTHER SCALES... The principles of slide rule read-
ing brought out above in learning to read scales C and D will
enable you without further study to read the other scales on
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the slide rule. However, in reading the CI scale it must be
remembered that this scale is the C or D scale in reverse,
and therefore must be read from right to left, rather than from
left to right as for the other scales. For example, the reading
of position B on scale Cl in Fig. 11(a) would be 8.9.
Laan
1] '
Boia vibenre
A Cc F 4
B ke " at we gi re so | ey Jo | 0 | ay: SE
cl f) sain Paieg “to 947 low @ ew Edt sdapest ava al mit ober I t
c i aad olstsl @slststs litt ieLotely lybplalebebielals | \ g *
|
Fig. 11.
DECIMAL POINT IN SLIDE RULE OPERATION, ..In reading
the hairline position in problems and examples up to this point,
the decimal point has always been considered. This was done
to help you understand the theory of reading positions on the
Tule. In actual problems the position of the decimal point is
generally ignored (except when finding square root) during the
slide rule manipulations. After the digits forming the answer
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are obtained from the rule, the correct decimal point position
is found by some non-slide rule method. Various examples in
the remainder of this manual! will show how this is done.
While position Dof Fig. 9, for example, has been stated as the
setting for 5.35, it is also the setting for 0.00535, 0.535, 535,
53500, etc., since the decimal point is normally not considered.
WHAT HAVE YOU LEARNED?
Read the B, the CI and the C scales for each of the hairline
positions A through G in Fig. 11(a), (b), and (c).
Since the slide rule does not locate the decimal point, do not
show the decimal points in your answers to this exercise, or
at any other time when using the slide rule unless the intended
position for the decimal point is known or can be determined.
ANSWERS
Scale B Scale CI Scale C
Figure 11(a)
A. 1126 944 1060
B. 1266 889 1125
Cc. 1425 839 1193
D. 1606 790 1266
E. (802 746 {341
F, 202 704 1421
G. 227 664 1507
Figure 11(6)
A. 493 449 222
B. 553 425 235
Cc. 622 401 249
D. 702 378 265
E. 788 356 281
F. 884 337 297
G. 994 318 315
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Figure 11(c)
A. 241 204 492
B. 271 1921 521
Cc. 304 1813 552
D. 341 1711 585
E. 383 1614 620
F. 431 1523 657
G. 485 1436 697
PRACTICAL MULTIPLYING...You have already learned to
multiply some simple values, like 2 x 3. Now that you have
learned to read the scales on the rule you can multiply any two
numbers.
Example... 1
Multiply 12. 46 by 236
Solution... See Fig, 12
(1) Set the left index of scale C opposite 12.46 on
scale D.
(2) Set the hairline of the indicator over 236 on
scale C.
(3) Read the digits of the answer, 294, under the
hairline on scale D.
To locate the decimal point: 10 x 250 = 2500. Hence, 12.46
Explanation, ..
In making the settings required in steps (1) and (2), the decimal
points in the original problem are ignored. This is true also
in reading the digits making up the answer in step (3).
Fig. 12(a) shows the setting for steps (1), (2), and (3) in skel-
eton form, and Fig. 12(b) is a photograph of the portion of the
rule covering this setting.
To locate the decimal we round off very roughly the values of
the original problem. Thus 12. 46 is roughly equal to 10, and
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To find 12.46 X 236°:
set /eft index scala C: opposite fast 2: scale D_
=) pocescneseeeseceesceene 236
| H i
£ i
c oN Pad 2 i 4 5S
- .. ot —— root + + rH a Pio es ee | rt rf
0 T ot) r2i ts 4 is 16 17 192 | oe . 4 4 6
' i 4
4 i i
tf {
1248 | 294 Le +
(a) then opposite 236 on scole C read 294 on ‘Stole
( a" } Tm 7 ™ T ’ T ; rT T TTT
’ j H ; Py ° , + 4 : ‘ we
| ‘ . aa leh ‘ : - mn ees z oy teas en 2 ‘adam see . ~ je" o ress aed
. ‘ L lub. satel F riot — - ~ noe - n n sureties’
\ t a — * ai Ey e *, 7 © & ” 9 ; * ine
i C 1 RE RE Sr : 1 1 apes wa if x Z : 28 i " : ie : a ve yi
a o ‘ai ‘ i " ' a " ite "e - vt eng } rm r J " | ais | . 4 Rae fis
} wows ny : is ‘ aoe) 5 eee so pity dyin, oft,
DES Segond io ps SR
“oo anos mn .
Fig. 12. Using slide rule to show that 12.46 X 236 = 2940 {or finding that
2940 + 236 =
12.46).
236 is roughly equal to 250. Since 10 X 250 = 2500, the answer
to the original problem must be of the order of 2500, which
would make it 2940.
*
Multiplying 12.46 by 236 with a pencil gives an exact answer of
2940.56. Rounding this value off to three significant figures
gives 2940, the same as the slide rule answer above. You
shouldnotsuppose that the slide rule answer of 2940 1s usually
a less satisfactory answer than the exact answer 2940.56.
It
is only less satisfactory if the nature of the problem requires
an accuracy greater than three significant figures, and this is
electronics work.
seldom the case in
Example... 2
Multiply 0.004728 by 8. 62
Solution... See Fig. 13
(1) Set the right index of scale C opposite 862 on
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plained in this course,
scale D.
*Locating the decimal point by means of a rough calculation, as shown here, [8 the
method used byall expert slide rule users, Mechanical methods of locating the deci-
mal point, as occasionally taught, have serious disadvantages and will not be ex-
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(2) Set the hairline of the indicator over 473 on
scale C.
(3) Read the digits of the answer, 408, under the
hairline on scale D.
To locate the decimal point: 0.005 x 9 = 0.045. Hence,
0.004728 x 8.62 = 0. 0408,
Explanation...
The procedure in this example differs from that of Example 1
in that the right index of scale C is used for this example, while
the left index was used for Example 1. You should try to work
this problem using the left index as in Example 1. You will
find that part of the slide needed extends beyond the body of the
rule so that a reading cannot be obtained.
In step (2) the number 4728 is rounded off to 473, since this
part of the scale will not read to four figures.
To locate the decimal! point, 0.004728 is rounded off to 0. 005
and 8.62 is rounded off to 9. Hence, the correct answer is
somewhere around 0.045. We place the decimal point in the
answer digits, 408, in the position that makes the answer
closest to 0.045. That would be 0. 0408.
ee ed
The examples above show that both the left and the right indexes
on the C scale are used in working problems in multiplication.
If the wrong index is chosen for any particular problem. it will
not be possible to set the hairline on the desired position on
scale C, because that part of the scale extends beyond the body
of the rule. In that case the problem must be started over
again using the other index. With a very little experience you
will know at once which index to use for most problems. How~-
ever, even an experienced operator sometimes finds he has
chosen the wrong index.
Example 2 above was worked by placing the index of scale C
opposite 862 on scale D. This problem could also have been
worked by placing the index of C opposite 473 on D, and then
the hairline over 862 on scale C. You should work the prob-
lem in this manner, verifying that the answer is the same as
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To tind 6,664726 w 6.62:
set right index scale C opposite 862 on Jeole 2
473 Eo Regia noe const i mE, ey
i408 --— — i e62
Seite eal
then opposite ee on scale C racd 408 on seole D
Fig. 13. Using slide rule to show thot 0.004728 X 6.62 = 0.0408.
obtained in Example 2. There are thus two ways of multiply-
ing any two numbers together.
One method results in the slide being moved farther out of the
body of the rule than does the other method. While it would
make little or no difference in the simple problems so far
given, it is generally the best practice to choose that method
which results in the slide being moved the least distance out of
the body of the rule. In more involved problems tais will some-
times result in a saving of labor.
WHAT HAVE YOU LEARNED?
Perform the indicated multiplications:
1...3 x 277 5...11.18 x 0.46
2...2.41 X 3.87 6...8,624 x 3,719
3...69.5 x 5.78 7..