Elementary Instructions for Operating the Slide Rule, Mannheim Type (K&E, copyright 1928) — pages 1–6 only
KEUFFEL & ESSER CO.
ELEMENTARY INSTRUCTIONS
FOR OPERATING THE
SLIDE RULE.
MANNHEIM TYPE
Copyright 1928 by Keuffel & Esser Co.
The Slide Rule has application in the fields of engineering, archi-
tecture, estimating, cost accounting, statistics, physics, chemistry,
astronomy, merchandising,—wherever quick calculations are neces-
sary.
It is used primarily for multiplication and division and the related
operations of proportion, percentage, and combined multiplication and
division.
Problems involving squares, square roots, and trigonometric func-
tions are also solved by means of the Slide Rule; but the beginner
is advised to confine his study to the simple operations of multipli-
cation and division on the “C” and “D” scales.
Before attempting to perform the calculations, the student should
practice the reading of the scale until he has acquired accuracy in
locating numbers without hesitation.
The C and D scales are identical and are numbered from 1 to 10,
the spaces between the whole numbers decreasing steadily toward the
right, as is brought cut in the following diagram:
poe roster ural nn
4 hope ‘ ee ee = ee) 4 .
ev eee . ia ae Cass ..
frre ;
16T SION'NT NO. 1
t
a 4 6 s ? 8 @
Fig. A,
TO LOCATE THREE-FIGURE NUMBERS ON THE C AND D SCA
STEP iy the eter agpaaeaie (The first significant figure of a number is the first
, or 2
UME the first significant figure is 1, the number will lie between the main divisions 1 and 3 2
belween 3 and 4, etc, (See figure A, Page 1.)
EXAMPLE. Rie piateioet B26 Has hetwess 256 main division 2 and indicated
since the first significant figure is 2. we: hn
: : : =
a 2 3
Fig.l. om
STEP Il.—The — Sigure locates the number on the Jad em aorsoat es gE in a similar manne
these secondary ns Indjented by the ‘racks ‘ia figure nm
am
c } I Ee ee Oe ee Se ee Se ie ee Oe
pi i G a im Rk Se eT eee b T
Fig.l. se¢o
NOTE: On the 10 In. rule, owing to the lack of space, the secondary divbio
Pome 5
:
STEP Ul.—ZJn a like manner the third figure locates the number on the third set of divisions, wh
EXAMPLE. Since the number 246 lies between the main divisions 2 and 3,
third small apace past poor ces Best pears ¢
Foner denne
Fig. 111.
IMPORTANT NOTE :—Were it practical to manufacture a rule with ten subdivisions to A 4
as have se secondary divisions. However, since the spaces grow smaller toward
into tenths throughout the ecale, Therefore : —
(a) The spaces between the secondary divisions lying be- (b) The spaces between thd s
tween Main Divisions 1 and 2 are divided in Main Divisions 2 and § :
tenths; so cach of these subdivisions has a single aloe. fifths; so each 9 eon
106 1265 138 «(1 546
10 spaces, each=]
-
STEPS I, II and III are condensed in figure TV, t
(0st)246 Lies BETWEEN 2 ANE 2
fzvo)ims serwern
sunoivisions(s
LES, there are three steps of procedure in the following sequence:
numeral that is not zero. Thus, 2 is the first significant figure of the numbers 0.0024, 24.0,
. If it is 2, the number unll liz between 2 and 3.
| by the bracket in figure I, a skeleton scale showing only the main divisions),
$ 4 6 7 8 9 BBs
4 5 6 7 8 9
IN DIVISIONS
ia between the bar and Sth secondary divisions gga <x digg second main divi-
scale with only the secondary divisions filled in. Note that there are ten of
Pd tee ed a
NDARY DIVISIONS
na between the Ist and 2nd main divisiona are the only ones numbered.
ch appear in figure [7 [—the Slide Rule Scale in its final form.
re the subdivision is in fifths, the third figure Jerre" the number finally on the
livision 2, as indicated by the arrow in it.
naa tot Sa nian aa
MPLETE SCALE
secondary division, it would certainly he done, so that each space would have a single value,
+ right end of the scale, it is practically impossible to subdivide the secondary divisions
econdary divisions between (c) The spaces between the secondary divisions for the
and 3 and 4 are divided in remainder of the scale are only divided in half; so
n has a double — each subdivision has a value of five.
341 720 805
— CR scone
5 spaces, each—?2 2 spaces, each—5
velow, showing the location of the number 246-
) (ST SIGNIFICANT FIGURE 2)
a7 & STH MAIN
MO FIGURE a)
‘
‘iia hiaaaainian
LOCATION
IV. ta
re
It is advisable for the student to follow the same procedure on his
Slide Rule, locating those numbers with the aid of the hairline on the
indicator (glass runner).
Now locate 478 in the same manner, using the indicator (glass
runner) to follow each step.
I. First significant figure 4 (indicates that number lies between
4 and 5). Set indicator at 4 (fig. V.).
Fig. V.
TI. Second figure 7 (indicates number lies between 7th and 8th
ati divisions). Move indicator to 7th secondary division (fig.
.).
eeUrres & Ceerec ot eee
Fame 5
47
Fig. VI.
Ill. Third figure 8 (indicates the number lies 3/5ths of the dis-
tance between the single subdivision (half) and the next secondary
division (fig. VII.).
SEUPPEL & Coser cr. nr WADE THUS
Mantel ECT unl:
Mae i Libind if puri.
ah ae
eyter
= Fig. VIL
ee
Numbers containing a single digit are located at the main divi-
sions, as— :
aS Oe pocabenie 5 ee ———
£4} fete kab Suclant. ete i . J, 1 4 ren a MZ
ri , TF. 8 2 atin 3 — + T T
Z Z ¥ Z Pd
4 iy ca ‘ 4 cs ca , [hae 3
' = 6 7 6 @
5 a
Fig. VHI.
Two digit numbers are located like the three digit numbers, but
are finally located on the secondary divisions instead of the final sub-
divisions, as—
rntenat elope tanedndne et alainiaewmeabicidi'sg aml one bead i
4b iseohedetalt. u Dente, n ws ; owe J, " | ey eee m)
ic OM a Od : peiete ne r Foe fee famed —
/ é 7 7 7 . 7
2 7 24 a7 as 66 a4
Fig. IX.
Numbers containing a large number of digits need only be set
to the third or fourth place; since the percentage of error introduced
in the result is so minute, as to be insignificant in the majority of
problems,—especially ratio and percentage calculations, combined
multiplication and division, and multiplications involved in estimating
and appraising,
Thus, 187,575 would have to be called 187,600 and set as follows:
1876
Fig. X.
The student should practice setting and reading until he feels
confident that he can do so accurately and without hesitation, Then
he is ready to give his attention to the solution of simple multiplica-
tion problems.
MULTIPLICATION
Rule: To multiply two factors together, set the index of the C
Scale (either the right or left end figure one) adjacent to one of
the factors on the D scale and read the answer on D under the other
factor on C,
(ts7) ser c INDEX (gap) UNDER 3 ON C
i, ee
{auo) To 2 ON OD Fig. XI. (avH) READ 6 ON © ANS,
18x 26—x
(tet) BET c INDEX (ano) UNDER 26 ON Cc
nap as, *
(amo) TO 19 ON DB (aru) READ 466 ON © (aANa)
Fig. XII.
72x51—=x (ano) UNDER BI ON C (ter) Set ¢ RIGHT INDEX
WATE Use
Ul
N
(aTH) READ 3672 (ano) TO 72 ON OD
Fig. XII.
Note that in making settings to solve the last problem that
the right index must be used, instead of the left, as was used
in the first two problems. If the slide projects too far to the right
when the left index is used, use the right index.
THE DECIMAL POINT
Important: No mention has been made as to the method
of determining the position of the decimal point in the last
problems, since it has been apparent at a glance. In most cases,
however, the operator should substitute round numbers for those
appearing in the problem and determine the correct position of
the decimal point by approximation.