CHARTOGRAPHY
6
4
8
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ARYt ACUITY
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TEN^'lJ^S^SOiNS
rnANR J.VWARNE
CHARTOGRAPHY
IN TEN LESSONS
BY
FRANK J. WARNE
AUTHOH OP
warne's book of charts
warne's elementary course in
chartography, etc.
ILLUSTRATIONS BY H. F. CHURCH
PUBLIHHED BY
FRANK J. WARNE,
SOUTHERN RUILDING
WASHINOTON. r). C.
Copyright, 1919, By F. J. WARNE
(Authorship also protected in Great Britain and
her Colonies, including Canada)
HA^
■; TABLE OF CONTENTS
S Page
u. Preface VU
Introduction 13C
Lesson I
'-» Building the Chart
•^ Value of Table of Contents 1
(s Statistics and Chartography 3
''^'^ Definition of a Chart 3
The Statistics 4
Horizontal Lines 5
i| Vertical Lines "
i - A Choice of Methods 8
The Use of Pencil Dots 10
The Framework 10
i Lesson II
^ The Scales
'^
Statistical Variables 13
The Independent Variable 13
The Dependent Variable 14
The IIorizontHl Scale 15
Detcrrainirif,' the Vertical Scale 15
The Scale Lines Ifi
Reading the Scales 1 '
Plotting the StiiHstics 19
The Use of (iradicnlcs 20
iii
iv Chartography in Ten Lessons
Lesson III
The Curve Chart
Page
Making the Curve Heavier 25
The Horizontal Scale Unit 26
Squares Should be Equal 27
Effects of Different Scale Units 28
Dropping the Zero Line 30
Indicating the Absence of the Zero Line 31
Divisors for the Vertical Scale 33
Lesson IV
Features of a Complete Chart
The Statistical Table 37
Table Should Appear on Chart 39
The Make-Up of the Table 40
Spacing the Columns 41
The Form of the Table 42
Duplicating the Scale Units 44
The Place for the Horizontal Scale 44
Word Designation of the Scale 46
The Title 47
The Foot-Notes 48
The Neat Lines 49
Lesson V
The Bar Chart
Making Bars from a Curve 53
Making a Curve from Bars 55
Advantages of the Horizontal Bar 56
Reversing the Scales 57
Width of the Bar 59
Table of Contents v
Paob
Separation of the Bars 60
Location of the Table 61
The Bar and the Curve 62
Lesson VI
The Tools of the Chartographer
Cross Section Paper 65
The Lead Pencil 69
The Kind of Ink 70
The Ruling Pen 71
Correct Position for Holding Pen 71
Pen Points 73
The Drawing Board 74
The T-Square 75
The Triangle 75
The Engineer's Scale 77
The Dividers 78
The Essential Tools 79
Lesson VII
Accuracy in Charlography
The Use of the Typewriter 81
Drawing Letters for the Title 83
Exaggerating the Curve 86
Effects of Exaggerating the Curve 88
Advantages of Extra Squares 91
Lesson VIII
Curve and Bar Designations
Disadvantages of the Unbroken Curve 93
Curve Designations 95
vi Chartography in Ten Lessons
Page
Word Designations of Curves 98
The Peak-Top Curve 99
Determining the Scale Spacing 101
Utility of the Curve Chart 102
Chartography Based on Comparisons 103
Bar Designations 105
Interpreting the Bar 108
Some Characteristics of a Good Bar Chart .... 109
Word Designation of Scale Units Ill
Lesson IX
Value of Statistics to Chartography
The Statistical Table II4
Aids in Reading the Table 116
The Substitution of Ciphers II9
The Table of Ratios 120
Building up a Table 12l
The Percentage Increase and Decrease 123
The Zero Line 126
The Arithmetic Average 129
The Misuse of the Average 13 1
Statistical Class Limits 132
Lesson X
Primary Principles of Chartography
Planning the Chart 137
Importance of the Right Method 139
Essentials of Good Chart Making 140
Planning the Size of the Chart 141
Planning a Reduction in Size 143
The Reducing Glass 147
The French Curves 149
Checking up the Completed Chart 151
PREFACE
No attempt is made in these ten Lessons to
cover the entire field of chartography. To do so
adequately would require several large volumes.
All that these Lessons aim to do is to familiarize
the student with the primary or elementary prin-
ciples. These underlie chart plotting ajid con-
struction as applied to the curve and bar charts.
These principles are applicable to all kinds of
charts, variations being explained by the differ-
ences in the circumstances surrounding the special
problems.
These Lessons are the by-product of an experi-
ence covering a period of ten years during which
time the author has been engaged professionally in
the application of the principles of chartography
to the working out of practical problems of the
work-a-day world. In the presentation by means
of diagrams or charts of innumerable statistical
problems the author has been able to put the art
of chartograj)liy to a severe test before such
authoritative tribimals as the Literstate Com-
merce Commission, various state public utilities
and railroad coinmissions, })oards of arbitration
appointed by the President of the United States
for the peaceable .settlement of labor contro-
vii
vdii Chartography in Ten Lessons
versies and various committees of Congress. In
this professional work he has been called upon
to till entirely new fields, for there were few
authoritative guides to follow, and in conse-
quence he has been compelled to pioneer his
way amid innumerable uncharted difficulties.
Such an experience should contain lessons of
value to others engaged and about to engage in
the making of charts. In presenting this formu-
lation of the principles of chartography the
author begs leave to express the hope that these
Lessons may serve the beginner in chartography
as a safe guide over the innumerable pitfalls that
inevitably must be encountered unless he is
warned to guard himself against them.
An endeavor has been made to bring these
Lessons within a reasonable price to the student.
The cost of production of "Warne's Elementary
Course in Chartography," which was published
two years ago and the price of which was fifty
dollars for the twenty Lessons (including
"Warne's Book of Charts"), was such as to pro-
hibit a lower price, and in consequence it could not
be made to serve the class of students the author
desired most to reach. Parts of that Course have
been completely revised in these Lessons.
INTRODUCTION
The Value of Chartography
(Revised from "Wame's Elementary Course in
Chartography" and "Warne's Book of Charts")
To the average citizen statistics are as incom-
prehensible as a Chinese puzzle. To him they
are a mental "Mystic Moorish Maze." He
looks upon columns of figures with suspicion
because he cannot understand them. Perhaps he
has so often been misled by the wrong use of
statistics or by the use of incorrect statistics
that he has become sceptical of them as repre-
senting reliable evidence as to facts and, like an
automaton, he mechanically repeats "while
figures may not lie, all liars, figure," or the
equally common libel, "there are three kinds of
lies — lies, damn lies and statistics."
And yet statistics are an infallible indicator of
economic conditions — they measure the heart-
throbs of a nation's or of an industry's life-
blood. They register the conditions of any given
static situation; they point the direction of a
trend or tendency with the accuracy of the ther-
mometer in measuring the temj)erature.
1*.^'); Every business, whether organized on a large
or a small scale needs statistics — in fact, statistics
ix
X Chartography in Ten Lessons
are vital to its successful existence. Without
them the executives cannot know the status or
tendency of the economic factors which control
their affairs. This practical value of statistics
in every-day business life is coming to be more
and more correctly appraised at its true worth.
The Railway Age of February 23, 1917, says:
An officer of a western road recently made
the statement that each department of a large
railroad system should have on its staff a thor-
oughly competent man whose duty it should be
to analyze statistics. The assertion was not
made without deliberation, and it might be perti-
nent to ask whether we are getting the most out
of the statistical department. The amounts
which are spent by American railroads in com-
piling statistics bearing on the functions of the
various departments are extremely large, and no
one who knows the importance of the compara-
tive figures to the oflBcers will question the wisdom
of the expenditure. Some of the statistical data
which the railroads compile is readily analyzed,
and the important figures, such as average tons
per train, or pounds of coal per thousand gross
ton-miles, are always readily available. A closer
analysis of data which is regularly compiled
would develop important facts which are not
brought out in the routine reports. The head of a
department may desire more information than
that regularly furnished him, but he cannot take
the time to get it himself, and a clerk could not
understand its meaning or application, and would
Introduction xi
overlook important points. Great stress is laid
on the comparison of results for successive months,
and the comparison with figures for the corres-
ponding months of the previous year, but statis-
tics are no less important as a means of forecasting
results by comparing a proposed method with the
one in practice. The great expenditure for
statistics is relied upon to show the leaks and
determine wasteful methods. The field of the
statistician should be broadened and he should
give more attention to the possibility of con-
structive activity. The statistical department
has long been depended upon to keep costs from
going up. It is time we recognize that it lies
within its province to show how costs can be
brought down.
Statistics have become a vital, every-day
need not only in transportation but also in indus-
tries of all kinds, in finance, in journalism, in
social work, in public life, and in business of
every description. They are necessary to men of
affairs, publicists, economists, and even to the
average citizen if the significance of facts and the
trend of events are to be comprehended. Virtu-
ally our entire political life, both state and nation-
al, is now regulated and its course determined by
statistics. Every important branch of govern-
ment has its statistical bureaus. Large financial
institutions, industries, manufactories, railroads
and other transportation companies have their
xii Chartography in Ten Lessons
statistical departments. Innumerable associa-
tions must resort to statistics in order efficiently
and effectively to carry on their work.
This recent growth in the demand for reliable
statistics and their correct interpretation has
suddenly raised the standing of the statistician
to one of importance, and this has been accom-
panied by a corresponding increase in his remuner-
ation. Today the openings for one versed in the
fundamental laws of statistics — in their collection,
compilation, presentation, and interpretation —
are innumerable. The demand is greater than the
supply.
The value of statistics, while great, is inestim-
ably enhanced by the aid of chartography. It
supplements statistics — it supplies the best known
method for their presentation and interpretation.
In all those phases of presentation which count
for clearness and quickness of comprehension,
no other method is equal to it. It makes clear
at a glance, even to the uninformed and unin-
itiated, the significance and tendency of the fac-
tors that are portrayed. As nine-tenths of the
problem in interpretation is clear presentation
the value of the service rendered to statistics
by chartography cannot be over-emphasized.
Especially is this realized when it is remembered
that statistics, to be useful and valuable, must
Introduction xiii
not only be accurately compiled but must also be
correctly interpreted. Relatively, too much time
is spent in the collection and assembling of statis-
tical material and too little in its clear and forcible
presentation. Here is where chartography be-
comes an invaluable handmaid to statistics.
The graphic presentation and interpretation
of statistics as the basis of a recognition and an
understanding of industrial, political, financial,
social, economic, and other tendencies has become
essential to practical men of affairs as well as to
publicists, economists, and others. It can be
made of incalculable value in any line or depart-
ment of business — in that of finance, corporate
relations, internal organization, traffic, supplies,
production, prices, wages, costs, and scores of
others. It not only will repay its cost but will
be found of such great value in so many ways
that, once instituted, it will never be abandoned.
It will save in the time of the busy executive alone
more than its cost, because it will enable him to
analyze the facts and tendencies at a glance in-
stead of spending hours in studying the relations
of the figures in the different columns. It will
make more certain the correct interj)retation of
the basal information necessary to action and the
formulation of a successful pr)hcy. It will en-
large and extend his individual experience and
xiv Chartography in Ten Lessons
his accumulation of knowledge of the details and
principles of his business. It will replace vague-
ness and indefiniteness by assurance and certainty,
hazy conceptions will become clear-cut perspec-
tives, and these in turn will lead to a compre-
hensive grasp of the entire problem.
The recent development in and the growing
demand for diagrammatic statistics will continue,
and he who masters the few simple yet funda-
mental laws or rules upon which it is based will be
in a position to become an authority in his par-
ticular field and to command a comfortable in-
come.
Frank J. Warne.
Washington, D. C.
October 1, 1919.
LESSON I
Building the Chart
Value of Table of Contents — Statistics and
Chartography — Definition of a Chart — The
Statistics — Horizontal Lines — Vertical Lines
— A Choice of Methods — The Use of Pencil
Dots — The Framework.
In the Table of Contents preceding this Lesson
has been given a comprehensive outHne of the
field the beginner in chartography is to cover in
this and succeeding pages. It is a bird's-eye
view of the course of study that has been mapped
out for him in these I^essons. It should not be
passed over lightly but should be studied seri-
ously, for the reason that such a study will give
to the student at the very outset a broad per-
spective of the problems he is to encounter and
overcome.
Figuratively, he is starting on a mental journey,
with its ups and downs, its delights and pleasures,
its perplexities and obstacles — with a good deal
of play and some hard work ahead. Tlie Table
of Contents is tlic itinerary, kej)! by one who
has many times covered tlie same ground and
who thus is able to point out the significance of
1
2 Chartography in Ten Lessons
the things that are to be encountered. The
student will benefit greatly in the mastery of
these Lessons if he will frequently re-read the
Contents.
VALUE OF TABLE OF CONTENTS
The Table of Contents can also be likened to a
railroad map in the hands of one starting on a
long journey. It enables him to traverse with
his eyes the entire distance of the trip, noting
the general characteristics of the country through
which he is to pass, its mountains and rivers, and
the principal cities along the way. Thus he
secures, before he starts on the journey, a much
better idea of where he is going and becomes more
familiar with the country through which he
passes than he would if he studied the railroad
map piecemeal after the journey begins.
These ten Lessons will take the student on an
intellectual trip in the course of which he will be
called upon to exercise such mental traits as
application, concentration, observation, and im-
agination in overcoming the various obstacles on
his way to the acquisition of knowledge concern-
ing the art of chartography. He cannot reach
this desirable end without progressing step by
step in mastering its various features. And at
every step in this progress the broad view of his
Building the Chart 3
final destination which he will hav^e acquired by
a close and frequent study of the Contents will be
of material assistance to him. It will not only
enable him to cover the ground much more
quickly and with less exertion, but also with
much more satisfaction to himself.
STATISTICS AND CHARTOGRAPHY
The value and usefulness of statistics and the
relation to them of chartography, as well as the
objects of chartography, have been pointed out
in the Introduction. From a reading of those
pages it should be plain that figures in tabular
form, or which can easily be arranged in the
form of a statistical table, are essential to the
drawing of a chart — they are the reason for the
chart being made.
DEFINITION OF A CHART
The drawing of a chart therefore presumes the
existence of the statistics. It has nothing to
do with their collection or compilation. A
chart is merely a sheet of paper on which tabu-
lated facts are presented grai)hically. It is
also called a diagram or "graph." In a limited
sense it can l)e likened to a moving pi<-ture, with
this difference: In the case of the chart it is the
eye and not the picture that moves.
4 Chartography in Ten Lessons
the statistics
For the purpose of familiarizing the beginner
with the various steps in the process of making
the framework of a chart these figures are selected :
1913 1914 1915 1916 1917 1918 1919
26.7 26.7 26.4 28.1 38.2 49.5 57.2
The first line of figures represents calendar
years and the second line the average retail price
of a pound of bacon in the United States on
April 15 of each specified year. This information
is from page 77 of the Monthly Labor Review of
the Bureau of Labor Statistics of the United
States Department of Labor.
To make a chart from these figures is a simple
proposition — as simple as the alphabet, that is,
provided one knows the alphabet. It is as difli-
cult to one who does not know how as the alphabet
is to the child first beginning to lisp the letters.
That which at first appears to be a very com-
plicated and difficult thing to do comes to be
surprisingly simple after one has acquired the
necessary knowledge and facility. In the be-
ginning all that is needed is a lead pencil, an
ordinary ruler, and a blank sheet of paper.
horizontal lines
A glance at the statistical table shows there
Building the Chart ' 5
are seven prices to be recorded. These can be
represented for the present by as many lines
drawn with the lead pencil at equal distances
apart from left to right across the blank sheet of
paper. The result gives the lines A-A, B-B,
C-C, D-D, E-E, F-F, and G-G on this page.
These are horizontal lines. It is important
that the begirmer bear this fact in mind. lie
should remember that a horizontal line always
6 Chartography in Ten Lessons
extends in the direction of the horizon, that is,
parallel to the horizon. Here the horizon is
represented by the top edge of the sheet. Hori-
zontal lines are drawn from left to right, never
from right to left.
VERTICAL lines
In our statistical table we have another set of
seven figures. These represent that number of
years. So we mark off on the bottom horizontal
line G-G, by means of the inch and its fractional
units of the ruler, seven dots each an equal dist-
ance apart, the first dot starting at the beginning
of the line on the left. These dots we repeat on
the top horizontal line A-A. Next we draw
seven vertical lines connecting these dots, be-
ginning with the first dot on horizontal line G-G.
Upon completion of the last vertical line erase the
dots on the top and bottom horizontal lines.
Do not draw these vertical lines backward,
that is, downward from line A-A to line G-G. A
vertical line is an upright line, that is, it is
directed perpendicularly to the plane of the hori-
zon, as distinct from the horizontal line which,
as has been said, is parallel to the horizon.
These seven vertical lines we designate as H-H,
I-I, J-J, K-K, L-L, M-M, and N-N. Superim-
posed on the seven horizontal lines these vertical
Building the Chart 7
lines give the framework shown in the following
drawing.
K
M
N
H
M
The distinction between iiorizontal and vertical
lines should he clear to the student. The junc-
tion of a horizontal and a vertical line forms a
right angle.
8 Chartography in Ten Lessons
Another way to begin the erection of the frame-
work of a chart, and one which will likely appeal
more favorably to the student after he has ac-
quired greater knowledge of the subject, is to
draw first the horizontal lines G-G and A-A
and then the vertical lines H-H and N-N.
This gives the outline on the opposite page.
These four lines are the really important lines
of a curve chart. In relative importance they are
in this order: H-H, A-A, G-G, and N-N. The
uses to which each is put the student will become
more familiar with in subsequent Lessons. All
that is necessary for him to know now is that:
Line H-H is the vertical scale line and with its
units of measurement virtually determines the
distance the curve is to move. In other words,
all movements of the curve are measured by
this line.
Line A-A is the horizontal scale line, and in
all curve charts involving elements of time it
takes the time units. In our present problem
as to the price of bacon it provides positions for
the years.
Line G-G is the base line of the chart. Figur-
atively, it is the foundation line upon which all
the vertical lines rest and from which they start.
This base line is the zero of the vertical scale and,
whenever possible, should always be indicated
Building the Chart 9
by a cipher. All movements of the curve are
measured /ro 771 this line.
Line N-N is the least important of these four
lines, but this is not saying that it is not necessary
and useful. Its functions will be pointed out
to the student later.
10 Chartography in Ten Lessons
the use of pencil dots
With the four lines I have described already
drawn on the sheet, the beginner next divides
by dot markings the base line G-G into six equal
spaces, starting the first of the five dots the dis-
tance of one space from the left end of the base
line G-G and ending the dots the same distance
from the right end of the base line. Duplicate
these five dots at their respective distance apart
on the top line A-A. Now connect these dots
with vertical lines extending from the bottom to
the top line. This gives the five lines I-I, J-J,
K-K, I^L, and M-M.
Repeat the pencil dots with the same space
between them on vertical lines H-H and N-N,
beginning the first of the five dots the distance of
one space from the bottom of lines H-H and N-N,
Connecting these dots with horizontal lines gives
the lines B-B, C-C, D-D, E-E, and F-F. Now
erase all the dot markings. The result is the
same as that shown on page 7.
THE FRAMEWORK OF THE CHART
This is the framework of the chart. It is
the scaffolding by means of which the curve is
to be erected or constructed. It is the skeleton
structure for supporting the curve. Without it
Building the Chart 11
the curve could not be constructed properly or
correctly; neither could the curve adequately
perform the service for which a chart is drawn.
The lines will be found to occupy positions behind
the curve, or rather to form a setting or back-
ground for it. The framework is essential for
determining the movement of the curve and
must be built up before the curve can be placed.
QUESTIONS FOR SELF-EXAMINATION
1. Describe the broad view of the field of chartography
gained from a study of the Table of Contents. What ser-
vice does this table perform for the student?
2. Describe the relation between chartography and
statistics.
3. Of what value are statistics to business? To other
activities? What is the service chartography performs?
4. Do these Lessons cover the entire field of chartogra-
phy? Why?
5. Define a chart. What is a horizontal line? A vertical
line? How is each drawn with a pencil?
6. What is the framework of a chart? How is it con-
structed?
7. What are the most important lines of the framework?
Describe their uses.
8. Of what use are pencil dots in drawing the lines?
How are these dots employed in laying out the vertical and
horizontal lines?
12
LESSON II
The Scales
Statistical Variables — The Independent Vari-
able — The Dependent Variable — The Horizon-
tal Scale — Determining the Vertical Scale —
The Scale Lines — Reading the Scales — Plotting
the Statistics — The Use of Gradicules.
The essence of a chart is in the relation which
it shows exists between two or more statistical
elements. Chartography involves a comparison.
Probably the most frequent comparison is that
of figures representing the trend or tendency of
the same or similar element or factor over a
period of time, as in the present instance of our
statistics showing the average price of bacon on
April 1.5th of different years.
STATISTICAL VARIABLES
This price is not the same for all the years —
it has the capacity of changing or varying with
the different i)eriods of time. Thus in relation
to each other these two groups of figures are
called variables.
THE INDEPENDENT VARIAHLK
A comparison being involved, one or the other
group must be made use of as the standard by
which the other group is measured or interpreted.
13
14 Chartography in Ten Lessons
The group so used becomes the independent
variable. Where the element of time enters into
the situation it is nearly always the standard and
thus becomes the independent variable.
THE DEPENDENT VARIABLE
The statistical group that is to be measured
or interpreted is called the dependent variable.
In our present problem the price of bacon being
dependent upon the specified periods of time is
the dependent variable.
The relation between or the tendency of the
units or elements of the dependent variable is
measured by scales. One of these is the horizontal
scale and the other the vertical scale. Generally
the independent variable takes the horizontal
scale. This fact is important, as a great deal of
confusion results from a violation of this simple
principle of chartography.
"It should be a strict rule for all kinds of curve
plotting," says Brinton in his Graphic Methods
for Presenting Facts, "that the horizontal scale
must be used for the independent variable and
the vertical scale for the dependent variable.
When the curves are plotted by this rule the
reader can instantly select a set of conditions
from the horizontal scale and read the informa-
tion from the vertical scale. If there were no
The Scales 15
rule relating to the arrangement of scales for the
independent and dependent variables, the reader
would never be able to tell whether he should
approach a chart from the vertical scale and read
the information for the horizontal scale, or the
reverse. If charts are always plotted with the
independent variable as the horizontal scale,
there need be no question in the reader's mind as
to how he should interpret the chart."
THE HORIZONTAL SCALE
Following out this principle of chartography
we substitute on the horizontal line A-A of the
framework on page 7 (Lesson I), in place of the
letters H, I, J, K, L, M, and N, the figures repre-
senting the years in our statistical table. This
gives the following horizontal scale line:
A
1913 1914 1915 1916 1917 1913 I9l=i
1 A
(H) (1) (J) CK) (L) (M) CM)
detp:rmixing the vertical scale
With the years representing the horizontal
scale, the average price of bacon figures — the
dci)endent variable — must necessarily be meas-
ured by the vertical scale. The units of this
16 Chartography in Ten Lessons
scale are determined arbitrarily by figures that
must have a spread sufficient to include the lowest
as well as the highest price of bacon that is to be
recorded according to the statistical table. The
lowest price is 26.4 cents in the year 1915 and the
highest is 57.2 cents for the year 1919.
It has already been stated that the lower or
base horizontal line is zero and should be indi-
cated by a cipher. This also means, inasmuch
as the vertical lines rest upon the base line, that
the beginning or start of the vertical lines must
be at zero. The framework above the base or
zero line G-G on page 7 (Lesson I) provides six
squares within which the highest number —
57.2 — of our statistical table has to be recorded.
With these facts to consider it is a simple mathe-
matical computation which shov/s that the small-
est unit that can be made for the vertical scale is
that of 10 for each square. Placing this unit
from to 60 on the vertical scale line H-H of
the framework shown on page 7 (Lesson I)
instead of the letters G, F, E, D, C, B, and A,
gives the vertical scale on opposite page.
THE SCALE LINES
We have completed both the horizontal and
vertical scales as determined by the figures of our
statistical table. Substituting these scales on
The Scales 17
the fratne-work of our chart in place of the letters
designating the lines gives the results shown on
the next page.
~H These scale lines — the horizontal and
^^' ^' vertical — are very important features
of a chart ; in fact, without them a chart
is unintelligible. They must be adapted
to the arbitrary limitations of space,
and this adaptation is readily brought
_ (Q) about by increasing or decreasing the
space allotted to each unit of each scale
to correspond to the requirements of
- (D) the particular statistical problem. The
vertical scale unit itself can also be in-
creased or decreased as the particular
~ problem requires. This scale measures,
by equal distance along all the vertical
_ ,^ lines, the units of the variables that are
being charted — it represents Vjy space
on the lines of the chart the equivalent
— (6) of an agreed uj)on element of the statis-
tics as determined by the units selected.
READING THE SCALES
The horizontal scale should read from left to
right with the earliest year to be recorded appear-
ing first and the remaining years following con-
secutively in i>oint of tijne.
40
30
20
10
18
Chartography in Ten Lessons
The vertical scale beginning at zero should
read upward from the bottom or base line to
the top or horizontal scale line.
1913 1914 1915 1916 1917 1918 1919
60i
50
AO
30
20
10
'■'
■
572
49.5
36.2
26 7
26 7
264
28 1
This arrangement "faces" the chart to the
left. A chart that faces to the right, faces in the
wrong direction, or, putting it another way, a
The Scales 19
chart that does not face to the left does not face
in the "right" direction.
PLOTTING THE STATISTICS
We are now prepared to begin the plotting of
the statistics. With the vertical and horizontal
lines drawn the proper distance apart and with the
figures of the years and vertical scale units cor-
rectl}'^ indicated by lead pencil marks, the student
next begins to plot on the respective vertical
lines, by means of pencil dots, the exact positions
of the figures of the statistical table as determined
by the vertical scale.
This scale applies similarly to measiu-ements on
all the other vertical lines as much as it does on
the vertical scale line itself. That is, any unit of
the vertical scale line, say 30 of our present scale,
has exactly the same relative position on all the
vertical lines as it has on the vertical scale line.
The first figure of om- statistical table that is
to be located on the chart is 2(5.7, representing
in cents the average jirice of a |)ouiid of bacon
on April 15, 1913. The first vertical line, wliicli
is our vertical scale line, also rei)resents that year,
as indicated by the figures 1913 at the top of the
line. Starting at the ba.se of this line at we
proceed upward to 10, to 20, and .somewhere be-
20 Chartography in Ten Lessons
tween this unit designation and the next one, 30,
must be the proper location for the figures 26.7,
THE USE OF GRADICULES
It is easy to locate where 25 should be — midway
between 20 and 30 — even without the aid of the
slight projections or gradicules which have been
inserted on the left of the vertical scale line in the
chart on page 18 for the purpose of aiding the
beginner. Each of these gradicules represents
one-tenth of the vertical scale unit, or 1, and there
are ten gradicules betAveen each unit of 10.
They perform a function similar to the sub-
divisions of the inch unit on the ordinary ruler —
thty enable the student to locate with facility on
the framework any figure of the statistical table
that falls within the round numbers of the vertical
scale units.
With the assistance of these gradicules it is a
simple matter to determine the correct location
on the vertical scale line of the figures 26.7.
This is indicated by means of a pencil dot. The
same procedure is followed in locating on their
respective vertical lines, as indicated by the
vertical scale, the remaining figiu"es for each of
the other six years of the horizontal scale.
The locating of each number on each vertical
line should be done by starting at the base or
The Scales 21
zero line and counting upward, and not by start-
ing from the position of the preceding pencil
dot. One reason for this is to prevent the
possibility of error in the location of the num-
bers in case a mistake happens to be made in
placing the first one on the vertical scale line.
Besides, it is important that the beginner should
have impressed upon his mind at the outset that
all positions of numbers charted by means of a
curve are determined in relation to the base or
zero line. This is clearly indicated on page 18.
On this drawing the numbers represented by the
pencil dots, and which are those of our statistical
table, are i)laced opposite their respective dots
to emphasize their location.
This presentation has prepared the student
for the actual drawing of the curve. This he
does by starting his pencil at the dot on the
vertical scale line representing the number 26.7
for the year 1913, and by means of a straight line
marks the space between this dot and the dot
rei)rescnting 26.7 on the second vertical line,
which latter, according to the horizontal .scale,
represents the year 1914. It .so liai)i)ens that the
average price of bacon on April 15, 1914, is
identical with the i>rice on April lH, 1013, ac-
cording to onr statistical tabic. This gives a
straight line connecting vertical lines 191.'5 and
22
Chartography in Ten Lessons
1914 at the point 26.7. The dot on the vertical
line representing the year 1915 is at 26.4, this
figure being the average price of bacon on April
15 of that year. The student connects the dot
. 1913
60
50
1914
1915
1916
1917
1918
1919
40
30
20
10
/
/
/
/
/
YEAR CENTS
1913 26.7
1914 26.7
1915 26.4
1916 28. 1
1917 38 2
1916 495
1919 572
--^
/
representing 26.7 for the year 1914 with the dot
at 26.4 for 1915. Continuing this process for
the remaining dots gives the curve shown above.
The Scales 23
In this drawing the lead pencil dots have been
erased, as have also the gradicules along the
vertical scale line shown in the chart on page
18, these dots and gradicules being of no further
use. The figures representing the price of bacon
for the different years have also been removed
from their positions opposite the dots and have
been placed in statistical table form, with the
years in the first and the prices of bacon in the
second columns.
QUESTIONS FOR SELF-EXAMINATION
1. What is the essence of a chart?
2. What are variables? What is an independent varia-
ble? A dependent variable?
3. What are scales? Describe the horizontal scale. The
vertical scale.
4. What is the relation between the variables and the
scales?
5. What scale does the independent variable take?
The dependent variable?
6. How is the vertical scale determined?
7. What is the base line? What service does it per-
form? What is the zero line? What is the relation between
the lower horizontal line and the zero line? Between the
lower horizontal line and the base line?
8. What is a square? How is it formed? What is its
function in chartography?
9. What is the vertical scale unit? How is it deter-
mined?
10. What is a vertical scale line? A horizontal scale
line? What relation to these are the vertical and hori-
zontal scale units?
11. How should the horizontal scale be read? The ver-
tical scale? In what direction should a curve chart face?
12. What is meant by plotting the statistics? How is
it done?
13. What is the relation of the vertical scale units to
vertical lines other than the vertical scale line?
14. What are gradicules? Of what use are they in plot-
ting the statistics? Where are they located? Of what use
are pencil dots in plotting the statistics?
15. How are the positions of the figures of the statistical
table on the framework determined? What service does
the zero line perform in this determination?
24
LESSON III
The Curve Chart
Making the Curve Heavier — The Horizontal
Scale Unit — Squares Should be Equal — Effects
of Different Scale Units — Dropping the Zero
Line — Indicating the Absence of the Zero Line
— Divisors for the Vertical Scale.
In drawing the curve remember to make it
heavier than any other Hne. The purpose of
this is to have it stand out prominently and so
catch and hold the eye of the reader. The
curve should he the most conspicuous of any
line on the chart for the reason that it embodies
or symVjolizes the most important facts that are
presented — it is the why and the wherefore of
the chart being called into existence. Con-
versely, the framework lines making up the back-
ground of the chart, that is, the horizontal and
vertical lines, should be drawn with a lighter
touch of the pencil to paj)cr.
The curve is a continuous, unbroken line, and
has its origin at the i)oint along the vertical scale
line that is determined for the time or other
designation of that line by the statistics and the
vertical scale. It moves across the page from
point to point on the vertical lines and in the
25
26 Chartography in Ten Lessons
direction from left to right as the respective
numbers of the statistical table determine. The
curve terminates on the last vertical line at the
point the statistics require. It takes the shortest
distance between two points and generally should
approach each slantingly.
THE horizontal SCALE UNIT
In a curve chart the unit of the horizontal
scale element — in our present case this is a
calendar year — marks a point as distinct from
space between points. Each vertical line pro-
jects or extends its horizontal scale unit down-
ward all along the entire distance of that line
even to the base or zero line. The curve cannot
and does not affect it — the curve does not move
any horizontal scale unit a hair's breadth from its
place on a particular vertical line. Or, rather,
the horizontal scale unit does not follow the
curve from its point of contact with it on one
vertical line to the point of contact with another
horizontal scale unit on another vertical line.
For instance, the year 1913 ends with the vertical
line so designated and does not cover the space
between vertical lines 1913 and 1914. Quite
commonly in curve charts this distinction is
overlooked, particularly by beginners, and the
horizontal scale element is sometimes made to
The Curve Chart 27
represent space on the horizontal scale line and
between the vertical lines. This is a mistake.
SQUARES SHOULD BE EQUAL
In a curve chart it is desirable to have the
curve move from point to point in squares or
areas of equal spacing in all directions, whether
these be large or small. This means that both
the horizontal and vertical scales should be deter-
mined upon a basis that will permit equal spacing
between the units of each scale, that is, between
the horizontal lines of one scale and the vertical
lines of the other. This allows the curve to move
up or down and from left to right an equal distance
for each unit of measurement of both .scales.
Many curve charts are being made in which this
rule is violated. It must be added, however, that
the observance of this principle is not always
possible owing to the arbitrary limitations of
.space and to the necessities of the scales. The
problem for the chartographer is to secure as accu-
rate an observance of this rule as his difficulties will
permit. He should constantly koej) in mind the
important fac-t that tlie horizontal and vertical
lines are made use of to measure the quantity or
volume or other specified quality of the .statistical
element that is charted, and that these rules of
measurement should be as fair as possible.
28 Chartogkaphy in Ten Lessons
It is recommended that the beginner at first
draw liis frame work or scaffolding lines, both hori-
zontal and vertical, exactly one inch apart, thus
giving square inches within which the curve
moves. Each scale will then have its units of
measurement one inch distant from each other.
Later on the student can practice with lessening
or lengthening this distance, keeping in mind not
to move the scale units to points less than one-
half inch or further apart than one and one-half
inches. He should not permit the units of either
scale to be separated by any greater distance than
the units of the other scale.
EFFECTS OF DIFFERENT SCALE UNITS
The student should also practice changing the
unit of the vertical scale within the inch square,
increasing or decreasing it to other selected units,
in order to observe carefully the effects these dif-
erent units have upon the movement of the curve.
In the drawing on page 22 the unit is 10. Let us
substitute for it the unit 5, as in the drawing on
the opposite page. A study of these two drawings
will disclose a number of important differences.
Probably the most important of these is the fact
that a vertical scale unit one-half as large, other
factors remaining the same, doubles the space
within which the curve moves. Conversely,
The Curve Chart
29
doubling the scale unit decreases by one-half the
distance the curve moves.
This space in the drawing on page 22 requires
1913 1914 1915 1916 I9l7 1918 19
60
55
50
45
40
35
30
/
/
/
1
/
(
/
'
9«;
vertically a fraction more than tiircc of the
squares — the Hj)rea(i in the difrcronce between
the lowest and highest numbers of the statistical
30 Chartography in Ten Lessons
table is 30.5 and with 10 as the unit this leaves
.5 more than three times 10. In the drawing
on the preceding page the vertical scale unit 5
requires a fraction of .5 more than six times 5 to
accommodate the curve, or seven vertical squares
at the very least. As the drawing on page 22
provides only six squares, another one has to be
added to the framework, as is done on the page
preceding. This is accomplished by inserting an
additional horizontal line, either above the top or
below the bottom horizontal line, and then extend- .
ing to it all the vertical lines.
With the new vertical scale unit being 5 and
with the highest number to be charted being
57.2 for the year 1919, a square must be provided
for each of the units of 5 if the scale is to begin at
zero. This demands at least twelve squares for
the vertical scale from to 60. But it is physically
impossible to accommodate this many squares
of the present size within the space limitations.
DROPPING THE ZERO LINE
The next step is to ascertain from the statis-
tical table the lowest number to be recorded.
This is 26.4 for 1915. It is clear from this that
the space occupied by all the squares below the
vertical scale unit 25 will not be needed for record-
ing the movement of any part of the curve, for
The Curve Chart 31
in not a single year of all the seven given in the
statistical table does the price of bacon fall below
that unit. Consequently, beginning the vertical
scale at 25 instead of at permits the elimination
from the framework of iSve squares. The number
that remains, which is seven, is sufficient for the
requirements.
It has been made clear in preceding lessons
that the bottom horizontal or base line of a curve
chart represents zero of the vertical scale and is
indicated by a cipher as follows:
INDICATING THE ABSENCE OF THE ZERO LINE
Such a line, of course, cannot possibly be used
as the base line with the unit of our vertical scale
starting at 25, so the zero designation is omitted.
Attention should always be called to this omis-
sion on the chart itself and this can be done by
inserting directly below the base lirje, witii its
proper unit designation, a faijit lino of dashes or
one of dots, or a wavy or slightly undulating
line, as indicated on the next page. Rulers pro-
vided with these undulations can be purchiised.
32 Chartography in Ten Lessons
The student should keep in mind as a general
principle the fact that the vertical scale begins
on the base line at 0, although he will frequently
find that this is physically impossible because of
the nature of his statistical problem. This pre-
vails more often among large numbers than with
percentages. Usually the lowest nu nber to be
charted starts at a point so high above that the
space required to show the latter on the chart is
out of all proportion to that necessary to in-
dicate the movement of the curve. Again,
frequently in such cases the vertical scale unit
determined by including zero becomes so large
that fluctuations in the movement of the curve
reflecting the trend of the statistics (which fluc-
tuations would be made clear by the use of a
smaller unit) are smoothed out or flattened so
that that which should be a curve approaches
nearer to a straight line. Thus it is not always
possible to plot a curve chart so that the zero of
The Curve Chart 33
the vertical scale will be shown and at the same
time clearly present the trend of the statistics,
which latter is the primary object of the curve.
In beginning to read a curve chart, among
the first things to be observed is whether the
vertical scale starts at zero and if it does not to
make proper allowance for this fact in the inter-
pretation of the movement of the curve. Unless
this is kept in mind an erroneous idea or impres-
sion of the extent of the movement will result.
A chart that does not present the zero line and
fails to call attention to the omission in the
ways indicated, or neglects similar precautions,
is constructed in error. Such a chart is very
likely to be misleading no matter how excellent
or perfect its other features may be.
DIVI.SORS FOR THE VERTICAL SCALE
The selection of the vertical scale unit is thus
not without its difliculties. These the student
will learn to overcome as his experience with
varying stiitistical problems increases. lie will
learn, among other things, that particular numeri-
cal divisors are more advantageous as units than
some of the others.
The divisf)r 3, for instance, is an awkward and
inconvenient scale unit, not only for computing
on the vertical lines the measurements of the
34 Chartography in Ten Lessons
statistical element but also for calculating by
the interpreter of the chart. The divisor 2 is
much better, and 5 and 10 are nearly always ideal.
Such units as 3, 4, 6, 7, 8, and 9 are not as good as
2, 5, 10, 20 and so on, the latter group being more
easily divisible into the spaces along the vertical
lines as well as into the numbers of the statistical
table.
Whatever scale unit is selected it must permit
the inclusion within the arbitrary limitations of
the framework of the smallest as well as the
largest number that is to be charted. The unit
must be such as to permit of a spread between the
lowest and highest numbers charted sufficient to
bring out clearly in the curve the points or tend-
ency to show which the particular chart has been
designed; at the same time it must not be too
small as to result in exaggeration. It is as serious
an offense to exaggerate with curves as it is with
words. Accuracy in chart expression is as im-
portant as is the use of words in expressing
thought, and the various uses or functions of the
vertical scale unit have much to do with accuracy
in curve charts.
On a finished chart the student will not find
any dots and similar marks used as guides in
erecting the scaffolding of the framework, which
means that all such marks must be erased from
The Curve Chart 35
the completed chart. He will find, however,
that all the vertical and horizontal lines make
complete right angles at all points of junction;
that all such lines are straight lines; that they
form accurate squares; that the curve is slightly
heavier than the other lines; that the scale unit
figures are in their correct positions in relation
to their respective lines; and that the horizontal
and vertical scale unit figures do not crowd the
lines but are separated from them by the correct
spacing.
QUESTIONS FOR SELF-EXAMINATION
1. Why is the curve made heavier than other lines?
2. Define a curve. How is it emphasized in comparison
with the horizontal and vertical lines?
3. Define the horizontal scale unit. What function does
the vertical scale lines perform for this unit? What is the
relation of the curve to it?
4. What effect have unequal squares on the movement
of the curve? What relation is there between the squares
and the scale units?
5. What are some of the effects of changing the vertical
scale unit?
6. When is the zero line omitted? How is this omission
indicated?
7. Explain the reasons for omitting the zero line.
8. What effect has the omission of the zero line on the
reading of the curve?
9. What are numerical divisors? When and how are
they used? What ones are better than others?
10 What must the divisors provide for?
36
LESSON IV
Features of a Complete Chart
The Statistical Table — Table Should Appear
on Chart — The Make-up of the Table — Spac-
ing the Columns — The Form of the Table —
Duplicating the Scale Units — The Place for
the Horizontal Scale — Ward Designation of the
Scale— The Title— The Foot-Notes—The Neat
Lines.
The drawing on page 38 is a complete curve
chart constructed according to the instructions
of the preceding Lessons. The student should
examine carefully every one of its features.
Particular study should be given by the student
to the statistical table. It occupies the position
in the lower right hand corner of the drawing on
page 22 (Lesson II) but in the accompanying
chart it is located in the upper left hand corner.
In each ca.se the location of the table is adapted
to the requirements of the fjarticular chart and
each is correctly i)laced. It will be found that
one or the other of tlie.se two positions is usually
the place for the table, the lower left hand corner
and the upper right hand corner nearly always
being required for the free and unobstructed
movement of the curve.
S7
(J
38
Chartography in Ten Lessons
THE AVERAGE PRICE* OP BACON
UNITED STATES. I9I3-I9I9
1913
60
55
50
45
40
35
30
25
1913
1914
1915
CENTS
1916
1917
1916
/
YEAR CENTS
1913 26 7
1914 26 7
1915 264
1916 28.1
1917 382
1918 495
1919 57.2
/
1
/
/
/
^
1914
1915
1916
1917
1918
1919
60
55
50
45
40
35
30
25
1919
d^arkstics art rr&m Menrtily U&bo*- R«vl«<M, p, 77.
I • Av«rAg« prtc* itt dt
Apf tl IS oF *ach ywar.
This simply means that there is no arbitrary
position on the chart for the statistical table but
that its location is determined by the result of
the plotting of the curve. The only general rule
to follow is to place the table of figures in the
Features of a Complete Chart 39
particular position on the chart that disjtlays it
to the best advantage without at the same time
crowding the scale lines or interfering with the
curve. Breaking the vertical lines 1914 and 1915
and the horizontal lines 45, 50, and 55, as is done
in the accompanying chart, is not objection-
able but rather advisable in preference to these
lines extending through and breaking up the table.
"Boxing" the two columns of the table with
light lines, as in the accompanying chart, adds to
the neat appearance of the finished diagram.
TABLE SHOULD APPEAR ON CHART
Virtually every chart is based upon statistical
information. Usually this infortnation is in the
form of a statistical table or colunms of figures.
If the chart has been properly constructed and if
the figures of the table are correct, the presence
of the statistics is not e.ssential to a complete
understanding of the chart — its meaning Mill
he clear without the figures. Nevertheless it is
highly important in good chart making that the
statistics uf)on which the diagram is based should
occupy an inifjortant i)lace on the chart.
This reproduction of the fignrcs furnishes proof,
if proof is needed, of the correctness of the move-
ment of the curve as shown in the chart and will
al.so be of service to those who nuiy wish to u.se the
40 Chartography in Ten Lessons
data in other directions or to make different com-
pilations. Unless the statistics from which the
chart is made are shown upon it there is no easy
way to check up the work of the chartographer.
THE MAKE-UP OF THE TABLE
The internal make-up and arrangement of the
statistical table also require some thought from
the student. Its construction would appear at
first glance to be an easy thing to do and yet the
task has its difficulties.
All the numbers of the same statistical element
that are to be compared should be placed in the
same vertical column one under the other and not
too far apart, the digits of the tens and hundreds
and so on occupying their proper positions in
relation to similar digits of other numbers in the
same column. In the case of years, these are ar-
ranged vertically and in proper sequence of time
one under the other with the earliest year at the
top and the latest year at the bottom of the col-
umn. Nearl}^ always the years are in the first
column to the left in a table of two or more col-
umns. Vertical columns of figures read downward
from the top and never upward from the bottom.
This is in inverse order, it will be noted, to the
eading of the vertical scale units.
Each column has its proper word designation
Features of a Complete Chart 41
just above the first number, as years and cents in
the table of the chart on page 38. This is the
column heading. The space for it is usually very
limited and for this reason it should be confined to
simple words of the fewest possible letters con-
sistent with clearness as to the meaning of the
column of figures. Double meaning of words
should be as carefully guarded against as indefin-
iteness in meaning, each being a serious offense
against clearness of expression. \Mien two or
more words are necessary in the heading of a
column it is usually advisable to make of them
two or more lines just above the first number,
with each word having a line to itself instead
of all the words occupying a single line, which
latter nearly always extends the heading too far
on either side of the column of figures.
SPACING THE COLUMNS
Where two or more columns of figures are in
the same table attention has to be given to the
proj)er si)acing between the columns as well as
between the numbers themselves and their
headings. Hut in every table the number of
columns sliould be strictly limited to the fewest
possible for the purpose in view, the inclusion of
any that are not necessary detracting froni the
em[)hasis that must be given to the principal
42 Chartography in Ten Lessons
facts and tendencies shown by the statistics. The
table must be complete in itself, however, with no
vitally important factor missing. To this end
more than one comparison should not be at-
tempted in the same table.
The form of the table has to be adjusted not
only to the size of the chart but in particular to
the space available on the framework for its
presentation without interfering with the curve.
Interference by the table with the light horizontal
and vertical lines is not so important; nor is a
correct interpretation or reading of the curve
interfered with even when the vertical scale line is
broken into by the table at points which the curve
does not approach.
THE FORM OF THE TABLE
There are distinct forms best adapted to par-
ticular purposes with which the student will be-
come familiar only by practice. He will have to
decide at times whether he will include all his
data in one table or break them up into two or
more tables with a chart to illustrate each. Com-
pactness as well as proximity of the numbers for
comparative purposes are advantages which
must sometimes be surrendered at the demand of
more pressing requirements. If the table is too
large confusion to the eye results and difficulty is
Features of a Complete Chart 43
encountered in following the significance of the
separate columns. Interpretation also is particu-
larly taxing if the tabulation is dealing with a
complex mass of figures.
SIMPLICITY the guiding RULE
If the student will keep in mind that simplicity
must be the guiding rule he will usually not go far
WTong in his decisions. Much, of course, depends
upon the data that must be shown but quite often
more can be eliminated from the columns than
at first seems possible. Foot-notes as explanations
of the table often show a way out but these should
be kept at the minimum. A title to the table
separate from that of the chart is imnecessary.
Sometimes the exigencies of space limitations
combine witli the requirements of the movement
of the curve to prevent the use of the form of
statistical table that has been described and which
is shown in the chart on page 38. In such cases
recour.se has to be had to some other form, some-
times to that shown on page 4 (Lesson I) with
the years and j)rices of bacon arranged in hori-
zontal lines instead of vertical columns. At
times when this form has to be resorted to it is
not possible to f)Iace the table within the frame-
work and in .such cases a position has to be found
for it elsewhere on the chart.
44 Chartography in Ten Lessons
duplicating the scale units
In the chart on page 38 the unit figures of the
horizontal scale have been placed on both the top
and bottom lines and those of the vertical scale
on both the first and last vertical lines. This
arrangement has many advantages. While it
is not essential to the reading of the curve, at
the same time it facilitates the interpretation of
its movement in that the reading of the prices
of bacon for the first and immediately succeeding
years is permitted without requiring the eyes to
move upward to observe these horizontal scale
units; also, it permits the quick reading of the
prices of bacon for 1919 and the immediately
preceding years without requiring the eyes to
travel across the page to observe these particular
vertical scale units. The scale units arranged
along all four sides also serve to give a border-
like appearance to the framework and introduce
a little greater uniformity in place of a tendency
towards a lack of balance.
THE PLACE FOR THE HORIZONTAL SCALE
Some chartographers prefer placing the hori-
zontal scale units along the bottom line only.
My own preference is that where they are to
appear only once on the chart then the place
Features of a Complete Chart 45
for them is on the top line. That line will be
found to be much more convenient as the hori-
zontal scale line; besides, there are other im-
portant uses for the bottom horizontal line, such
as serving as the base line and as the zero line.
This preference is influenced also as the result
of more than ten years' experience in chart
making for practical commercial purposes. Dur-
ing this experience it has been observed that most
people in reading a chart start at the top with
the title and glance downward. With the units
of the horizontal scale on tlie top line the reader
early in the process of interpretation is informed
of these important facts which he must know if he
is to read the chart intelligently and correctly.
Placing the horizontal scale units on the bottom
line meets with the objection that the space
beneath this line is usually needed in most curve
charts for important exj)lanations and foot-
notes, such as credit for the source of the statis-
tical information upon which the chart is built,
notice of coj)yright, and so on. With the hori-
zontal scale figures also there that section of the
chart is likely to give the a})pearance of crowding.
Again, with the horizontal scale figures located
on the bottom line I have frequently encountered
practical difficulties hard to overcome because
the first and last of these units interfere with
46 Chartography in Ten Lessons
those of the lowest scale measurement of the
vertical lines, both sets of figures being located
at nearly the same point of the right angles formed
by these vertical and horizontal lines. As op-
posed to this, it is nearly always possible to extend
the upper part of the framework at least one
series of squares beyond the highest point to be
recorded by the vertical scale and this permits
the figures of the horizontal scale units to have a
line all to themselves without interfering with and
without interference from any of the figures of the
vertical scale.
There is no objection, of course, to reproducing
the horizontal scale figures on the bottom line
whenever there is room for them, and this prac-
tice is recommended as being advantageous,
especially in charts of unusual depth, as it facili-
tates a quick reading of the curve movement.
WORD DESIGNATION OF THE SCALE
Further assistance in the interpretation of the
chart, and especially in the reading of the curve,
is rendered if the primary characteristic of the
statistical element represented by the vertical
scale is indicated by a word designation just
inside the top border line and directly above the
center of the horizontal scale line. This is shown
in the designation "Cents" in the chart on page
Features of a Complete Chart 47
38. Such a designation states concisely to the
reader what the vertical scale figures represent —
it explains the essence of the curve. Its value
and usefulness will be impressed upon the student
as he progresses in his studies.
THE title
Another important matter to be considered
before our chart is a complete one is the title or
heading. Every chart must have a title. With-
out it the chart is almost as incomplete as it
would be if the curve itself were omitted. The
title is as much a part of the chart as are the
scale lines or table of statistics. It is more im-
portant than the beginner in chart making is
apt to realize.
The title should not contain a single unneces-
sary word. The space for it is usually limited
and too many words detract from the effect in
expressing the idea intended. Simple words of
one syllable are preferable. This choosing of
words in the selection of a title is a splendid
exercise in enabling one to secure a better com-
mand of the English language and in compre-
hending more clearly himself the essence of the
chart. The title should be so clear in its meaning
that misinterj)retation is impossil)lc, and so com-
prehensive in its scope as to cover all the import-
48 Chartography in Ten Lessons
ant data presented by the chart so that the inter-
preter will not have to look elsewhere for explana-
tion. This is not alwaj's possible and in such
cases a foot-note explanation at the bottom of the
chart is advisable, Indefiniteness in title mean-
ing is a serious offense. Similar statements are
equally applicable to any sub-title.
The position of the title is, of course, at the
top or head of the chart, as shown on page 38.
The best title is one comprising a single line but
this is not always easy to accomplish. In the
chart referred to it has been found necessary to
have two lines in the title, and in such cases the
letters of the words in the second line should be
slightly smaller than those of the first line. The
principal idea in this chart is the tendency in the
price of bacon, so its title becomes "The Average
Price of Bacon." But as this does not give the
information quite complete enough, the reader is
told in the second line that the price is for the
entire "United States" and for the years "1913
to 1919." The asterisk after the word "price"
refers the reader to the foot-notes, where it is
stated that the average price given is of April
15 of each year.
THE FOOT-NOTES
The place on the chart for the foot-notes is
Features of a Complete Chart 49
just below the base line and outside the frame-
work proper. These serve a useful purpose in
presenting descriptive information sometimes
necessary to clear up a point that has not been
brought out sufficiently in the chart, as indicated
in the use of the asterisk in the chart on page 38.
In the foot-notes there should always be a state-
ment as to the source of or authority for the
statistics upon which the chart is based. This
is shown on the chart just referred to by the
notation "Statistics are from Monthly Labor
Review, p. 77, U. S. Bureau of Labor Statistics."
The foot-notes also supply a convenient place for
the legal statement required in case the chart is
copyrighted.
THE NEAT LINES
With the drawing of the border or "neat" lines,
one on each side of the framework and usually
about one-half an inch from the horizontal and
vertical scale lines, the chart is comi)leted. These
neat lines give a sort of frame to the chart, as
shown on page 38.
In a good curve chart the principal conclusions
to be drawn from the statistical table are made
plain, all doubt as to the tendency or course of the
phenomena rei)resented by the numbers is re-
moved, and all i)Ossible errors have been elimi-
50 Chartography in Ten Lessons
nated. This ability to analyze the significance
of a table of statistics, to interpret the results
correctly and clearly, and to indicate the con-
clusions lucidly and succinctly is one of the
characteristics of chartography. The results
disclosed by a curve based upon a statistical table
quite often reveal at a glance important facts
that could not have been known except from
considerable study of the figures by an expert.
Usually an accompanying explanation or analysis
is unnecessary. If so the chart has failed of its
primary purpose.
The task of checking-up is not optional with
the student; it is compulsory — he not only should
but he must go over carefully each chart from top
to bottom.
If it is a curve chart, do all the horizontal scale
units center on the end of the vertical lines.'*
Are the respective vertical scale units on the
right in the curve chart directly opposite and at
the end of the same horizontal line as those on the
left.?
If the curve chart contains a zero or 100 per
cent line, has it been made wider or heavier than
the other horizontal lines? If the zero line is
not shown, does the bottom or base line clearly
indicate that the vertical scale does not begin
with zero?
Features of a Complete Chart 51
If it will aid in the easy reading of the curve see
that the horizontal scale figures are duplicated at
the base line.
In most curve charts it is best to have the
vertical scale figures on the right as well as on
the left vertical scale line. If only one set of
scale figures are used, however, these should be
alongside the first or left vertical line.
Do not make use of the first and last vertical
lines of a ciu-ve chart as the neat lines of the frame.
They should be reserved strictly for the vertical
scale units and should be no heavier or wider than
the interior vertical lines.
Do not forget that it is the independent variable
that takes the horizontal scale, especially in
curve charts involving periods of time.
Follow each curve from its beginning on the
left to its termination on the right to see that it is
continuously correct — that there is no "break"
in it. See to it also that the curve is a slightly
heavier line than the vertical and horizontal
lines.
1
T
QUESTIONS FOR SELF-EXAMINATION
1. Describe in general terms the most important char-
acteristics of a curve chart.
2. What is the statistical table? What is its relation to
the curve?
3. What is the position of the table on the chart? What
are its general features? What is meant by "boxing?"
4. What is the internal make-up of a table? What is a
column heading? What is meant by spacing?
5. What is the guiding rule in table construction?
C. What features of the chart affect the form of the
table and its position on the framework?
7. What is meant by duplicating the scale units? How
is this done? What are the advantages?
8. What is the position for the horizontal scale? Give
reasons supporting your statement.
9. What is the function of the word designation of the
vertical scale?
10. What Is the title? What is its location? Describe
the principles underlying the selection of words for the
title.
11. What is an asterisk? What are its uses in chartog-
' raphy?
12. What service do foot-notes perform? Where are
they located on the chart? What do they usually comprise?
13. What are neat lines? What is their position on a
chart?
52
LESSON V
The Bar Chart
Making Bars from a Curve — Making a Curve
from Bars — Advantages of the Horizontal Bar
— Reversing the Scales — Width of the Bar —
Separation of the Bars — Location of the Table
— The Bar and the Curve.
Emphasis thus far has been placed on the curve
as the method of expression offered by the art of
chartography. But tliere is also the bar. Many
of the principles of construction already explained
in describing tlie curve apply with equal force
to the bar chart. In fact, there are many points
of similarity between these two different kinds of
charts.
MAKING BARS FROM A CURVE
This tlie student will be able to realize clearly
by taking a curve chart and drawing vertical
bars from its base line to the points of the curve.
This has been done in the chart on page 54. It
is merely the result of taking the curve chart on
page 38 (l/csson IV) and with as few changes as
possible transforming it into a bar chart.
In order to secure a bar for each of the seven
years it is necessary to add another vertical line
5S
54
ClIARTOGRAPHY IN TeN LeSSONS
to the right of the one for the year 1919 and
extend to it the top and bottom horizontal lines.
The horizontal scale unit for each year is moved
to the right from its former position at the top
of a vertical line so as to occupy space between
the vertical lines and to be above the top of the
bar. No change is made either in the unit of
measurement of the vertical scale or in its location.
The Bar Chart 55
making a curve from bars
This procedure enables the many points of
similarity between the curve and the bar chart
to be quickly recognized. This similarity will
all the more be indelibly impressed upon the
mind of the student if he will take the vertical
bar chart on page 54 and diaw a continuous
curve from left to right touching the tops of all
the bars. Then if he will cut out a piece of blank
paper so that its upper edge conforms roughly
to the curve he has drawn he will find, by placing
this on the bars, that the latter are hidden from
view and that the curve remaining in sight ex-
presses just as clearly the tendency shown by the
bars. In other words, his cut piece of blank paper
has simply restored the original curve chart on
page 38 (Lesson IV).
This procedure also emphasizes strikingly the
essential difference between these two kinds of
charts. Tliis difference lies primarily in the fact
that the horizontal scale of a curve registers points
on lines while the horizontal scale of a vertical
bar chart registers space beiireen j)oints on lines.
But in changing the curve to the bar we have
not secured a good bar chart. In the first place
the bars are entirely too wide to represent such
.small amounts as cents. In the .second place the
bars take up entirely too much space — the same
56 Chartography in Ten Lessons
ends can be accomplished by the use of a narrower
bar. In the third place the result is a vertical
bar, that is, a bar standing upright on its end,
A horizontal bar, that is one lying on its side and
extending from left to right, is preferable.
ADVANTAGES OF THE HORIZONTAL BAR
This preference is based on an experience of
years in meeting the every-day problems of
chartography. It convinces the writer of the
greater utility of the horizontal bar. Quite
probably there are occasions when it is advisable
to have recourse to the vertical bar, but at the
same time where there is a choice between the
two the horizontal bar will be found to be more
advantageous. It gives greater opportunity for
the display of letters and figures where the limita-
tions of space or other considerations require that
these be placed on the bars themselves. In
such instances, in order easily to read the words
or figures on vertical bars the chart usually has
to be turned half way round to the right, whereas
if the bars are horizontal the figures and letters
read in the natural direction. In brief, with the
vertical bar the chartographer will encounter more
difficulties than with the horizontal bar in the
placing of his table, figures, and letters. The
ability to select advisedly in those cases where it
The^Bar'Xhart 57
might be advantageous to employ the vertical
bar will come to the student with practice and
experience. It is recommended that in the mean-
time he confine himself to the practice of the
horizontal bar.
Such a bar chart is presented on the foUow^ing
page. It will be observed, from a comparison
of its statistical table with that of the curve chart
on page 38 (Lesson IV), that it is constructed
from the same set of figures.
REVERSING THE SCALES
The horizontal bar has necessitated a reversal
in the location of the scales in comparison with
those of the curve. Instead of the independent
variable — the years — occupying the horizontal
scale position it takes that of the vertical scale,
and the dependent variable — the prices of bacon
— becomes in turn the horizontal scale. This
permits of the measurement of the movement of
the bars from left to right and not from the bottom
up, as with the vertical bar. Otherwise we could
not secure the advantages of the horizontal bar.
In a horizontal bar chart the figures of the
vertical scale, quite froquontly comprising periods
of time, are located directly to the left of the
beginning of the bars, the figures for each year
being centered adjacent to their respective bar.
58 Chartography in Ten Lessons
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The Bar Chart 59
The last digit of the number should not be per-
mitted to crowd the end of the bar too closely.
WIDTH OF THE BAR
It will be noted that the bars are narrower
in the chart on page 58 than in the one on page
54. This feature of the bar is important. Just
how narrow or how wide or deep the bar should be
will depend upon a number of factors, such as
the nature of the particular statistical problem,
the arbitrary limitations of sj)ace, and so on. No
definite rule can be given except that all the bars of
a chart must be of uniform width, they should be
sufficiently wide to be easily seen, and they should
convey an impression of the volume or quantity
represented. P'or instance, a bar representing
billions should be wider than one representing
millions; the latter wider than one representing
hundreds of thousands; and the latter of greater
width than one rc})resenting thousands, and so on.
Wide bars are preferable to too narrow ones.
In l)egirming to draw the bars the sttident
should i;i<licate on the sheet by light lead pencil
lines instead of dots the width and length of each
bar, the former being arbitrarily determined by
the number of bars that is to go in the available
space and the latter by the quantity or volume
each bar rei)resents as determined by the statis-
60 Chartography in Ten Lessons
tics and the scale unit. It is first advisable to
determine from the statistics and the horizontal
scale unit the length of the shortest and the
longest bar. All the other bars fall within the
limits these two set. Begin plotting the chart
with the bar for the earliest year at the top and
just beneath the horizontal scale line, outlining
the bars downward as the years determine. These
skeleton bars should then be filled in black by
rotating the pencil point within the outlines.
separation of the bars
Between each bar representing the statistical
element of the vertical scale there should be a
separation sufficient to distinguish it from the
preceding and following bar. In the chart on
page 58 this has been done by leaving in the
original drawing a space equal to one-tenth of an
inch. Usually this is too much spacing. Besides,
it requires a greater amount of painstaking labor
than should ordinarily be given to a bar chart.
How this labor can be eliminated the student will
be informed in a succeeding Lesson.
The bar chart on page 58 shows the vertical
lines extending from the points of the scale
units on the top horizontal line to the base hori-
zontal line except where the bars and the statis-
tical table intervene. These extend downward
The Bar Chart 61
the units of measurement of the horizontal scale
to each of the seven bars at the various points of
contact of the vertical lines with the bars. Ordi-
narily these vertical lines should not be extended
between the bars but to the first bar only that
interferes with their further extension. These
lines are permitted to be seen on this chart merely
to inform the student as to the purpose of the
vertical lines in a bar chart. All sections of verti-
cal lines tliat have been drawn within the bars
should be pencilled out of observation as the body
of the bar is pencilled in.
LOCATION OF THE TABLE
The location of the statistical tal)le in the upper
right hand corner is that which will usually be
found best adapted for this use. This is true be-
cause this position, as a general thing, is opposite
the shortest bars and thus has the largest area of
unoccupied space. The lower right hand corner
is frefpiently taken up with the extension of the
longest bars rei)resenting tlie largest numbers
to be charted, and the upi)er and lower left hand
corners always contain the })eginning of the bars.
In cases where the extensions of the bars from
the earliest to the latest years show a decrease
instead of an increase, the statistical table s}K)nl(l
be located in the lower right hand corner. 'J'he
62 ClIARTOGRAPHY IN TeN LeSSONS
table should be "boxed," that is, enclosed in a
light frame composed of two vertical and two
horizontal lines connecting at their ends and form-
ing right angles.
Separating the nunibers from their table and
placing them on the individual bars adjacent to the
figures of the years will sometimes be found advan-
tageous.
THE BAR AND THE CURVE
As between the bar and the curve chart the
latter will be found to be much more useful as
well as more adaptable to a larger number of statis-
tical tables or problems. It is true that in many
instances either may be employed with equally
successful results. The bar chart, however, is
the most common at the present time not only
because it is the simplest to construct but also
to interpret. Its advantage lies in its simplicity —
the amount or quantity or statistical element is
simply represented by the length of the bar. This
gives only one dimension to be read and in conse-
quence there is little ground for misinterpreta-
tion. As a general statement the bar method
should be used where the numbers represent large
volumes or quantities.
At the same time there are special problems in
chartography which the curve chart alone will
The Bar Chart 63
solve to the best advantage. Just what are the
particular characteristics of these problems the
student will learn by experience. The kind of
chart that will best bring out the true significance
of a statistical table is the one to select. It can be
said generally that with statistical tables having
numbers representing very large amounts, such
as billions and millions, the bar chart is preferable.
Conversely, where the numbers represent small
amounts, such as hundreds and tens, the curve
chart is usually the best. One reason for this is that
the bar conveys the idea of volume to a greater de-
gree than does the curve.
The difference between these two kinds of charts
is strikingly presented by Brinton in his Graphic
Methods for Presenting Facts. He first com-
pares bars representing years or other intervals of
time with j)rogress photographs. Though the bars
and progress photograi)hs are valuable, he says,
they give information only in spots. Then he says:
"A moving-picture machine shows pictures so
rapidly that the pictures blend into a continuous
narrative in the eye and the brain of the observer.
What the moving-[)icture is to separate progress
photographs, the curve is to detached bars repre-
senting time. In just .so much as the moving-pic-
ture is superior to separate pictures shown by
lantern slides, in just that much is a curve superior
64 Chartography in Ten Lessons
to a series of horizontal or vertical bars for the
same data. Unless a person knows thoroughly
how to read and how to plot curves he cannot
hope to understand the graphic presentation of
facts."
Brinton also says: "A curve permits of finer in-
terpretation than any other known method of
presenting figures for analysis — it gives informa-
tion which many persons might not fully grasp if
only a column of figures were used." And again
the same author says: "One of the chief advan-
tages of the curve method of presenting informa-
tion is that a curve forces one to think."
It will be found that plotting the curve is sim-
pler than plotting the bar. It also consumes less
time. Many chartographers prefer the curve to
the bar method of presenting statistics because
it not only brings out the fluctuations from year
to year more clearly to the eye but also enables
the reader to grasp more readily the tendency
shown. The curve is gradually supplanting the
bar in popular usage because of its greater clear-
ness, and this tendency is likely to grow stronger
as its advantages over the bar are more generally
recognized.
QUESTION FOR SELF-EXAMINATION
1. Describe the similarities and dififerences of the curve
and bar chart.
LESSON VI
The Tools of the Chartographer
Cross Section Paper — The Lead Pencil — The
Kind of Ink — The Ruling Pen — Correct Posi-
tion for Holding Pen — Pen Points — The Draw-
ing Board — The T- Square — The Triangle —
The Engineer's Scale — The Dividers — The
Essential Tools.
If the beginner has profited to the full extent
from a careful and painstaking study of the pre-
ceding Lessons he is now qualified to drop the
blank sheet of ordinary paper, the lead pencil,
and the common ruler and take up the real
materials and tools of the chartographer. The
proper use of these materials and tools will
measurably facilitate and make less difficult
the mechanical work of chart making and will
also result in much better workmanship. It
permits of the chart becoming permanently
valuable as well as of its rei)roduction in any
number desired.
CROSS SECTION PAPER
The most imi)ortant of the essential materials
is the cross section or coordinate paper. A
sample illustration is shown on the following
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Tools of the Chartographer 67
page. This section paper comprises minute
squares formed by horizontal and vertical lines.
On the most commonly used section paper each
minute square measures one-tenth of an inch.
One hundred of these squares make up a larger
square of one inch, the border lines forming the
square inch being slightly heavier than the other
horizontal and vertical lines. Section paper can
also be secured that has other rulings, such as
eight minute squares each way or sixty -four to
the square inch, and six each way or thirty-six
to the square inch.
Cross section paper thus presents a system of
squares whose lines permit the easy measurement
or determination, by means of space or distance
on the sheet, of the quantity or volume or what-
ever element it is the statistical table represents.
By combining squares, space units of measure-
ment as extended in both directions as the par-
ticular i)roblem requires are readily determined.
A sufficient quantity of section })aj)er for most
charting purposes can be obtained at almost any
first-class stationery store. If a large number of
different charts is to be made the varying scales
will likely require different subdivisions of the
square inch and as it requires too nnich detail
labor for the chartograi)licr himself to draw these
subdivisions, it is advisable for quantity produc-
68 Chartography in Ten Lessons
tion to keep on hand a supply of coordinate
sheets with the diflPerent ruhngs. Even then the
chartographer will not always have paper with
the ruled spaces exactly corresponding to his
requirement, and in such cases he will have to do
the ruling himself.
In sheet sizes the section paper is usually 17
by 22 inches. These sheets can be cut to meet
almost any ordinary requirement; or two or
more can be pasted together along the edges to
meet the demand for a larger surface than that
commonly required. Built-up sheets of paper can
also )e formed from remnants by pasting. If a
larger section-ruled surface than 17 by 22 is
frequently required it will be advantageous to
purchase the coordinate paper in rolls, in which
form it is also prepared commercially.
The section paper used should be of the best
quality. There are cheap grades on the market
but these do not take the ink satisfactorily and
have other defects, so that in the long run it pays
to purchase the better grade at little higher
prices. Of course, a higher price does not neces-
sarily mean a better grade, but it usually does.
The section paper best adapted to ordinary
chart work has the horizontal and vertical lines
ruled in blue ink. On some section paper these
lines are in green or purple but these colors are
Tools of the Chartographer 69
not so desirable, as they are likely to reproduce
lines on the photographed chart that should not
be showTi. Paper with a soft surface should
also be avoided as it will not take the ink properly,
and from now on we are to make all our charts
with pen and ink instead of pencil.
THE LEAD PENCIL
This does not mean that the student will have
no more use for the lead pencil. In fact, he will
continue to have constant need of it. The lead
should )e neither too soft nor too hard — it should
not be so soft as to crumble, or so brittle as to
snap in two or so hard as to penetrate or puncture
the drawing sheet. The best grade for general
use is HB.
Virtually all points of measurement, such as
the distances from unit to unit of the scales and
those of the curve and each bar, should first be
indicated on the section sheet by light lead pencil
marks or dots. This use of the dots will facilitate
the drawing of the lines, curve, and bars in ink.
The entire curve and an outline of each bar might
with advantage first be drawn in light lead pencil,
the ink being later superimposed after the student
has satisfied himself that his pencil markings
correctly represent the data. The dots and other
lead pencil markings can be erased after the ink
70 Chartography in Ten Lessons
has dried. It is much easier to correct a mistake
made in lead pencil than one made in ink. The
curve itself is made finally with the draftsman's
ruling pen. The neat lines of the frame are
drawn in ink after the framework of the chart has
been entirely completed.
THE KIND OF INK
The best black ink for charting purposes is
Higgins' American India. In purchasing ask the
dealer for waterproof quality. This, when it
dries, is insoluble and will not smear or spread in
case the sheet is brought in contact with water,
as is often the case when the chart is to be re-
produced by the blue-printing process. Another
favorable quality of this ink is exhibited in the
process of drying areas on charts, such as bars, as
it dries with a flat or "dead" surface. Such a
surface is highly desirable in case the chart is to
be reproduced by such photographic processes
as zinc-etching, photo-lithography, and so on.
"Chin-chin" ink, also an India ink and noted
for its opacity, can be used to special advantage
in cases where the chart is to be reproduced by the
blue-printing process. While special mention is
made of these two inks, there are also other India
inks on the market equally as good for ordinary
charting purposes. With the smaller bottles is
Tools of the Chartographer 71
usually supplied a beveled quill inserted in the
cork which is used in filling the ruling pen.
THE RULING PEN
This ruling pen is an invaluable tool to the
chartographer. It has two blades or tines the
relation of each to the other being controlled by
an adjusting screw. The manipulation of this
screw permits the drawing of lines of varying
widths. The use of the ruling pen should be con-
fined to line and curve work. Some pens have a
lever attachment which permits the cleaning of
the tines without disturbing the gauge at which
they may be set. This lever saves the time re-
quired to make the proper adjustment again and
prevents the possibility of the chartographer
resuming work with a different adjustment of the
tines.
CORRECT position FOR HOLDING PEN
The ruling i>cn should be licld in such a j)osition
a.s to be in a plane i)eri)eiidicular to the surface
of the drawing sheet, the tips of the thumb and
forefinger grasj)ing the pen at the adjusting
screw. This is illustrated on the following page.
Holding the pen in this way permits, when
necessary, the manipulation of the screw by
slightly raising the pen from contact with the
72 Chartography in Ten Lessons
sheet. In ruling lines or curves the hand or
fingers should not touch the paper, nor should
the elbow rest on the sheet. The movement of
the pen is not from the hand but is a free elbow
movement and is from left to right and from bot-
tom to top of the sheet.
Tools of the Chartographer 73
Failure to observe these instructions will result
in the points of the tines wearing away unevenly
and the pen then develops what is referred to by
draftsmen as a "shoulder." This usually means
that this particular pen must be discarded for
line and curve work as it is no longer a "true"
instrument or tool. These old pens can be used to
advantage, however, in filling in bars, they being
operated in such cases somewhat as one would a
small brush. It is not impossible to remove a
"shoulder" from a ruling pen. This can be done
by using a small oil-stone or razor-hone. The
stone or hone can also be used to advantage in
keeping the points of the tines sharp and true.
In this process of sharpening be careful to hold
the ruling pen against the surface of the stone or
hone at an angle of about forty-five degrees,
grinding the points with a gentle rotary motion.
Follow this by rubbing the points of the tines on
any glass surface. .\n examination of the
points should then find all "burrs" or unevenness
to have been removed.
PEN POINTS
In addition to the ruling pen and as a substitute
for it in many uses, the .student will need pen
points and, of course, a penholder or holders.
For fine line work and small lettering Gillett's
74 Chartography in Ten Lessons
No. 303 is recommended. Esterbrook's No. 14
bank pen point is also good for lettering. Gillett's
No. 291 will also be found satisfactory, especially
in mapping work.
The student is no doubt familiar through per-
sonal experience with the fact that most pen
points when first dipped in ink repel or throw off
the ink. This is likely to result in blots or spots
if it occurs on a sheet of drawing paper. To
obviate this it is suggested that the pen point be
held for a moment in the flame of a match before
being put to use for the first time.
THE drawing board
The effective use of the section paper, the pen-
cil, the ruling pen, the pen points, and the ink
makes necessary that the student also have a
drawing board. This is nearly always made of
neatly glued strips of soft wood, usually white
pine, with a hardwood ledge of an inch or so on
each end. The board can be secured in varying
sizes ranging from 12 by 17 inches to 31 by 42
inches. Larger sizes can also be purchased. The
board rests unattached on the desk or table and
can be moved about freely with the section paper
temporarily attached to it by means of thumb
tacks. In case the student prefers a drawing table,
this can be had in various makes and designs.
Tools of the Chartographer 75
the t-square
The drawing board or table facilitates greatly
the use of the T-Square, another tool of the char-
tographer which he will find invaluable. It is
so-called because of its resemblance to the cap-
ital letter T. For all purposes of accurate line
drawing not involving measurement it supplants
the ordinary ruler. A T-Square fitted with trans-
parent ruling edges is reconmiended, as it permits
the draftsman to see adjacent portions of the
section sheet that would be hidden if a wooden
straightedge were used. It fits in snugly and
along either ledge of the board or table accurately
by reason of the head piece of the T-Square ex-
tending beneath the blade with its ruling edges.
This permits of a true base line as well as other
horizontal lines. Upon this base line, with theT-
Square in position, true vertical lines are erected
by means of the Triangle.
THE TRIANGLE
The use of the Triangle is largely confined to
making vertical and horizontal lines. Do not
attempt to draw these lines with the ordinary
ruler if any degree of accuracy is desired as such
an attempt will most likely result in inaccuracy.
Accuracy, it should be remembered, is one of the
cardinal principles of good chartography.
76 Chartography in Ten Lessons
Fia I
Fie.a
Tools of the Chartographer 77
The illustration on the preceding page shows
some of the uses to which the Triangle is put when
operated in connection with its running-mate, the
T-Square. Triangles are obtainable in numerous
sizes and angles, the standard angles being 45
degrees and 30 by 60, the latter commonly called
"Thirty" by draftsmen.
THE engineer's SCALE
Important uses will also be found in chart
making for the engineer's rule or scale. It is an
equilateral triangle in shape, that is, all its sides
are equal; it is usually made of hardwood, 12
inches in length (although different lengths are
procurable), and has three edges each with two
measuring surfaces. These six surfaces are laid
off into multiples of 10, with 10, 20, 30, 40, 50, and
60 units to the inch, and in consequence they
provide measurements of almost any fraction of
an inch that can l)e quickly applied to varying
scale units of less than an inch. The engineer's
.scale is admirably adapted to linear measure-
ments, that is, to measurements pertaining to or
of the nature of a line or in one direction.
The engineer's triangular scale is not to be
confused with the architect's triangular scale, the
latter having tlie inch divided into units of fourths,
eighths, sixteenths, thirty-seconds, and so on,
78 Chartograpiiy in Ten Lessons
and which is of Httle use to the chartographer.
The student is cautioned against making use of
the engineer's rule for ordinary ruUng purposes,
as this use wears away the ruled edges and in
time makes inehgible the sub-divisions of the
inch.
THE DIVIDERS
Assistance in the drawing of a chart is also
rendered by the use of the compass or dividers.
It consists of a handle from which extends two
prongs each having a sharp point. In the handle
is a joint, either a pivot or tongue, which permits
adjustments between the two points up to several
inches. This enables the draftsman to "step-
off" or gauge accurately any measurements on
lines or charts that are to be transferred to other
lines or charts. Greater accuracy will be se-
cured from the use of the dividers than from that
of the ordinary ruler for this purpose.
Every draftsman has use for kneaded rubber,
art gum, and the "ruby" or red rubber eraser for
erasure purposes. A hard rubber or gritty eraser,
such as the ordinary typewriter eraser, should
not be used. A supply of pins, clips, thumb
tacks, and the like will also come in handy.
THE ESSENTIAL TOOLS
The following summarizes the more important
tools needed in chartography :
Tools of the Chartographer 79
One drawing pencil HB.
One ruling pen.
Six Gillett's No. 303 and six Easterbrook's
No. 14 pen points.
One bow or compass pen with interchangeable
pen and pencil points and extension bar.
One bottle Higgin's waterproof black drawing
ink.
One drawing board or table.
One T-Square.
One six-inch celluloid 45 degree triangle.
One twelve-inch engineer's triangular rule.
One dividers.
These tools can each be bought separately but
a material saving is made by purchasing a com-
plete set of drawing instruments at the outset.
The price naturally varies according to the quality
but an expensive set is not necessary for good
work. The outfit of the chartographer may be
simple or elaborate according to individual taste.
A few well selected instruments of standard make
is recommended at first. Where the begiinier
confines himself to a limited number of tools he
becomes familiar with the "feel" and balance
of each instrument and, as a result, soon learns
to liandle it with confidence and skill. This
applies especially to the drafting or ruling pen.
QUESTIONS FOR SELF-EXAMINATION
1. What is cross section or coordinate paper? What ser-
vice does it perform in chartography?
2. What is the function of the lead pencil in chart
making?
3. What is the ruling pen? Describe the correct posi-
tion for holding it. What is a "shoulder" and what causes
it? How can it be prevented?
4. Describe the drawing board and its uses.
5. What is the T-Square and what are its uses? The
Triangle?
6. What is the engineer's scale? How and for what
purposes is it employed?
7. Describe the dividers and its uses.
8. What are the essential tools in chartography?
80
LESSON VII
Accuracy in Chartography
The Use of the Typeivriter — Drawing Letters
for the Title — Exaggerating the Curve — Effects
of Exaggerating the Curve — Advantages of
Extra Squares.
In placing on the chart the figures of the scale
lines, the statistical table, the foot-notes, and
other figures and letters the use of the typewriter
enables the chartographer to meet many of the
exactions encountered in the practice of his art.
This is especially true when a large number of
different charts has to be made for reproduction
in quantities by means of one of the photographic
processes.
THE USE OP THE TYPEWRITER
If a long-carriage machine is not available and
if the coordinate sheet is too large for the ordinary
typewriter the sheet can })o cut in two and after-
wards pasted together. This makes necessary
the exerci.se of care in handling the sheet after-
wards or else the typewritten figures will "rub."
This work on the typewriter should be done after
the lines and curve or burs are comj)leted.
Another j)ractice that has many advantages is
81
82 Chartography in Ten Lessons
first to typewrite the numbers and words on
separate slips of paper and then paste these
securely in their proper places on the section sheet.
This plan should be followed if the chart is to be
reproduced. It enables corrections to be made
more easily and does not wrinkle or otherwise
damage the sheet. If the chart is not to be
reproduced, the letters and figures should be
written according to the first plan, that is directly
on the coordinate sheet itself.
Typewriting the table directly on the chart or
on a separate slip of paper and later pasting this
on the sheet, requires considerable painstaking
care. The tyj^ed figures and letters must be
clean, decimal points separating the digits must
be in column order equally exact with the fig ires
themselves, units of tens or hundreds and so on
must be under each other, and all in straight
columns with headings appropriately placed at
the top of each. In pasting the slip on the sheet
exactness is required so as to avoid the appearance
of "skewness." Corrections can more easily be
made with the figures and letters on the slip
than with them directly typed on the coordinate
sheet.
In the employment of the typewriter for plac-
ing words and numbers on a chart that is to be
reproduced by a photographic process, care must
Accuracy in Chartography 83
be exercised in seeing to it that the ink of the type-
writer ribbon is of a quality that will reproduce.
I knoAv of the experience of a fellow chartographer
who had in progress a rush contract for several
hundred different charts on each of which was
to be rei)ro<luced a statistical table. He failed
to have pro})er attention given to overseeing the
typing of tliese tables, with the result that not
one would reproduce because the right kind of ink
was not used, In itself the kind of ink may be a
small matter but the consequence of not using the
right kind is likely to prove serious and costly.
DRAWING LETTERS FOR THE TITLE
Virtually all the figures and letters required on
a chart can be i)laced in their proper positions
by means of the typewriter with the exception of
the title letters. These lalter are usually larger
thaji those of the typewriter, although even for
the title the capitals of the tyj^ewriter can some-
times be made to serve the requirements. As a
general thing, however, the use of the typewriter
for the title letters is inadvisable.
It is this lettering for the title that is among
the exactions of chartograi)hy with which the
beginner is likely to have some difliculty. He
mu;st learn how to make the kind of letters
required. This is not so difficult as might at
84
Chartography in Ten Lessons
first appear; in fact it is qujte simple, ahd by a
little practice the student can soon become pro-
ficient in this phase of the work.
In making these larger letters the minute
squares of the coordinate sheet are of material
assistance. After determining upon the size of
the letter required, the horizontal and vertical
lines of each letter are drawn by the ruling pen
and with the aid of the minute squares. The
curved corners are first left blank, as illustrated
in the following:
mwmi
Then the curved corners are filled in with a free
hand pen.
For the guidance of the beginner in chartog-
raphy the letters of the alphabet are reproduced
on the opposite page as samples of plain and
easily made letters based upon the above instruc-
tions as to how they are to be drawn. No
attempt is made to present other than a simple
utility alphabet, all the letters with the exception
U L
86 Chartography in Ten Lessons
of I, M, and W being approximately of the
same width. Illustration is also given as to the
drawing of large figures.
EXAGGERATING THE CURVE
The beginner in chartograpliy, however, should
know how to make letters and should not neglect
to become proficient in this direction. Practice
in lettering teaches painstaking accuracy, and
this is demanded of the good chartographer.
In chart making he will have many opportunities
for acquiring this personal asset.
Especially is this true in the process of determin-
ing and plotting the scales for the curve chart.
He must be certain that his vertical scale does
not permit of the exaggeration of the movepient
of the curve. This exaggeration easily results
in not allowing for the vertical scale the same
amount of space per each scale unit as for the
horizontal scale, and vice versa. In other words
the movement of the curve can be exaggerated
either vertically or horizontally.
"The scales of any curve chart should be so
selected," says Brinton, in Graphic Methods for
Presenting Facts, "that the chart will not be
exaggerated in either the horizontal or the ver-
tical direction. It is possible to cause a visual
exaggeration of data by carelessly or intentionally
Accuracy in Chartography 87
selecting a scale which unduly stretches the chart
in either the horizontal or the vertical direction."
"The beginner in curve plotting and in curve
reading," continues Brinton, "is apt to be
somewhat puzzled by the different effects which
may be obtained bj' changing the ratio between
the vertical scale and the horizontal scale. It
is difficult to give any general rules which would
assist in overcoming the beginner's confusion.
Ordinarily the best way to get facility in making
the proper choice of vertical and horizontal
scales for plotting curves is to take one set of
data and plot those data in several different ways,
noticing the changes which the different scales
selected give in the proportions of the chart.
Just as the written or spoken English language
may be used to make gross exaggerations, so
charts and especially curves may convey exag-
gerations unless the person preparing the charts
uses as much care as he would ordinarily use to
avoid exaggerations if presenting liis material
by written or spoken words."
"A person reading charts must take great
care," concludes Brinton on this point, "that
he does not give too much weight to the actual
appearance of the curve on the page, instead of
basing his conclusions on the |)erccntage increase
or decrease as ju<lged from the figures of the ver-
88 Chartography in Ten Lessons
tical scale. The proper choice of scales for curve
plotting is largely a matter of judgment, and the
judgment can be trained very greatly if it is kept
in mind to examine every curve chart which
comes to one's attention to see whether the verti-
cal and horizontal scales have been selected so that
the chart gives a fair representation of the facts."
EFFECTS OF EXAGGERATING THE CURVE
The effects of an exaggeration of the vertical
scale can be seen from a study of the chart on the
opposite page. The units of the vertical scale
are there purposely made twice the distance apart
than are units of the horizontal scale. The result
is an exaggeration to the eye, in the rise and fall
in the movements of the curve across the sheet,
of just twice what these movements should be.
In order that the student may comprehend
clearly for himself just what this exaggeration of
the curve means, it is suggested that he draw on
the chart on page 89 in light lead pencil a broken
or dash curve that conforms to a scale by which
the distance between the horizontal lines is re-
duced one-half. In other words, he is to give to
each horizontal and vertical scale unit exactly
the same space.
Rearranging the vertical scale units accordingly
the unit 7 falls on the vertical line at a point half
IMMIGRATION TO UNITED STATES BY MONTHS, 1918
Tboosaiids of Ixalgruiti
Jan. Feti. Mair. Ipr. Kay June Jul; Aug, Stpt. 0«t. (OT. Mo.
1«
\
Iknth Iiimlgranti
Ju. 6,3S«
Mb. 7,388
lUr. 6,510
Apr. 9,641
Miy IS. 217
JtUM 14, £47
Jnl^ 7,780
tag. 7,863
sept. 9,997
Oct. 11,771
HOT. 8,499
Dee. 10,748
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90 Chartography in Ten Lessons
way between the unit 6 and the present 7, and the
point now marked by the latter becomes the
place for the scale unit 8. Proceeding upward
in this manner cross out with the lead pencil each
of the old vertical scale units and substitute the
new units according to the revised plotting. Re-
produce in lead pencil this new scale also alongside
the extreme right vertical line. Connect these
new left and right vertical scale points by horizon-
tal lines in light lead pencil. Next draw the
curve from point to point of the vertical lines as
determined by the revised units.
It will now be found that this new curve moves
up and down exactly one-half the distance of the
original curve. The new curve starts at a
point on the left vertical line just above the pre-
sent scale designation 6 and ends at a point on the
right vertical line half way between the present
scale units 8 and 9. These vertical scale units
represent thousands of immigrants, as explained
in the word designation just above the horizontal
scale line.
It is important to remember in connection with
the exaggeration of the curve that the arbitrary
limitations of space imposed upon the chartog-
rapher does not permit him in every case to choose
the scale that might have been chosen if there
were no factors to consider other than the exact
Accuracy in Chartography 91
presentation of the statistics. His problem is to
present the facts as clearly as possible within the
arbitrary limitations of space imposed upon him.
Sometimes he will find himself in a quandary in
his endeavors to include all the necessary data
without exaggerating one or the other of the
scales.
ADVANTAGES OF EXTRA SQUARES
Reducing by one-half the space allowed the ver-
tical scale unit in the chart on page 89 brings the
lowest and the highest points of the curve within
a space of less than three inches, thus decreasing
horizontally as compared with the old curve the
size of the area within which the curve moves
without affecting its size vertically. Plotted in
this way results in an awkward size for the cliart.
This can be overcome by providing at least two
series of squares both below the lowest and above
the highest i)oints recorded by the movement of
the curve. In such cases the vertical and hori-
zontal lines forming the squares are drawn just as
if they were to be used to indicate a stage in the
movement of the curve. This extension of the
area of the squares should also be regulated so as
to accommodate the placing of the statistical
table without crowding. It will nearly always be
found feasible in plotting the vertical scale to
92 Chartography in Ten Lessons
provide for at least one series of squares vertically
into which the movements of the curve do not
enter. This will be found to be advantageous in
a number of ways. It adds to clearness of expres-
sion as well as avoids the appearance of crowding.
If the exaggeration of the scale in the chart on
page 89 had been in the horizontal instead of the
vertical measurement, just the opposite effects to
those noted would have resulted. It is suggested
that the student draw a chart in which he gives
twice the space to the horizontal scale unit that he
gives to the vertical scale unit, using the data in
the statistical table of the chart on page 89.
QUESTIONS FOR SELF-EXAMINATION
1. Describe the various uses of the typewriter in chart-
ography.
2. How are large letters drawn by hand?
3. How is the curve exaggerated? What are some of its
efifects? How can these be avoided?
4. What are the advantages of extra squares?
LESSON VIII
Curve and Bar Designations
Disadvantages of the Unbroken Curve — Cun>e
Designations — Word Designations of Curves —
The Peak-Top Curve — Determining the Scale
Spacing — Utility of the Curve Chart — Chartog-
raphy Based on Comparisons — Bar Designa-
tions — Jnterpretiyig the Bar — Some Character-
istics of a Good Bar Chart — Word Designation
of Scale Units.
It is plain that if a number of curves on the
same chart are each drawn as an unhroken curve
much confusion will accomjjany efforts to interpret
the tendencies shown, as most likely the curves
cross and re-cross each other. This is illustrated
in the chart on the following page.
DISADVANTAGES OF THE UNBROKEN CURVE
Let the student try to follow each curve from
its beginning on the left vertical scale line to its
termination on the right vertical scale line. It
is hardly possilde that he acconiijlislies the task
successfully in every case by ending on the curve
he starts out upon, as indicated by the initial
abbreviation of the name of the railroad. Even
if he does succeed he will have .spent a great deal
98
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Curve and Bar Designations 95
more time than should be required to interpret
such a chart correctly. Among the aims of
chartography is to prevent confusion and to aid
comprehension at a glance, and the reading of a
chart should not have placed in the way obstacles
like those illustrated on the opjjosite page, es-
pecially when the obstacles have no reason or
even excuse for being. A study of the chart
should quickly convince the student of the dis-
advantage of using the same kind of unbroken
curve for two or more statistical elements on the
same chart. Reading the chart in question is
only slightly aided by placing at the left and right
vertical scale lines the abbreviations of the names
of the different railroads which the curves
represent.
CURVE designations
Attention is thus called to a practical condi-
tion confronting tlie chartographcr which would
be replete with difficulties did he not have re-
course to a sinijjle device to overcome them.
This is the enij>loyment of difroront designations
for two and more curves.
In contrast with the utibrokon or straight line
curves of the diart on j)agc 04, those of the chart
on page 96 should be studied. 'I'he latter com-
pare as many as nine sei)arate an<l distinct sta-
AVERAGE PRICES'OF MEAT PRODUCTS
UNITED STATES, 1913-1919
C«nti
19U
XI
BACon
Zi
Sirloin
Rirund 3t«aX
Pork Chopa
l.Amb
20
Onok ItoAet
—
191} 1914 191S 1916 1917 )9L« 1919
Bacon >&.' 26.7 26.4 28.1 M.i 49.5 i7.2
Han 26.6 26.6 25.} 31.2 36.5 44.6 52.9
Sirloin Ste«» 26.4 26.4 25.1 27.0 }1.7 36.6 43.7
BounO StMlt 22.3 23.0 22.3 24.0 26.9 34.5 40.5
Porn Chop» 21.4 21.6 19.7 22.5 30.6 36.6 41.4
Umb 20.2 19.3 21.0 23.0 27.6 36.3 39.9
016 fiM«t' 19.9 20.1 19. » 21.0 25.2 29.3 34.6
OIUOK RoMt 16.2 17.0 16.0 21.2 21.2 26.5 29.4
puts B««f 12.2 12.4 12.2 12.6 l«.l 19.9 22.6
/
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840M
45
Sirloin
Por* Chop*
RouaA St*4ll
35
mil II044I
90
CBuok lout
25
Plato BooC
to
Stall etico or* froa MooVtly Labor Bavltv, pp. 77.
U 5 euroau of Labor SUtlotlca.
* Ataraga prico l* of
April 13 of aach yaar
Curve and Bar Designations 97
tistical elements, presenting two more curves
than are in the chart on page 94, and yet there is
not the slightest difficulty or confusion in tracing
the nine curves from their beginning to their
termination. This greater clearness and ease of
interpretation is almost entirely due to the fact
that a different designation is given to each curve.
If this had not been done it would be almost as
difficult to follow the curves in the chart on page
96 as in the chart on page 94 — the curves of the
former would also be lost, as to the reading of
their movement, at the points where they cross
and re-cross one another.
Quite frequently the student of chartography
will encounter the problem of having many
curves to compare. While this difficulty is met
in part by employing different designations for
the curves, there will be occasions when even
this method will result in confusion. Under such
circumstances, instead of attempting to draw all
the curves on a single chart, it will be found
advantageous to make two or more charts. One
set of the group of figures should be .selected as a
common basis for the comi)arison and the curve
re[)resenting this set or statistical element in-
.serted on all the charts, this curve taking the
.same unbroken or straight line designation on
each chart. It i.s a mistake to j)lace a larger
98 Chartography in Ten Lessons
number of curves on one chart than can be read
quickly and without confusion to the eye in
tracing their movements. Where the curves lie
close together or are constantly crossing and re-
crossing each other, more than five or six are
likely to result in this confusion.
It is in making clear just such problems as
those presented in the chart on page 96, where a
number of different statistical elements must be
compared, that the advantage of the curve method
over the statistical method becomes apparent.
To grasp quickly and comprehendingly the mean-
ing of each of the nine different columns of figures,
not only in relation to its own element over the
period of years but also in relation to each of the
elements of the other eight columns, is prac-
tically an impossibility to most minds. And
yet one of average intelligence can easily read
the trend or tendency of these prices of different
kinds of meats when interpreted by the curves.
WORD designations OF CURVES
Not only from the point of view of interpretation
but also of mechanical construction the chart on
page 96 is recommended for close study. Note
the word designations of the curves to the left
and right of the vertical scale lines. This inser-
tion of the word designation alongside the point
Curve and Bar Designations 99
of contact of the curve with the vertical scale
lines lends to easy reading of the chart. It
requires, however, extending the space between
each vertical scale line and its respective neat
line, and this is not always possible. In such
cases the curve designations with their word
descriptions should be placed at some convenient
place on the framework itself as a sort of key or
legend. Quite frequently a good place for the
legend will be found to be just beneath the bottom
horizontal line and above or between the foot-
notes.
The different designations that can be em-
ployed for curves should be practiced by the
student until he has acquired facihty in drawing
them. To assist him in this the following page
of designations is presented. These have been
made considerably larger than is necessary for
the curve on the chart.
THE peak-top curve
The student is cautioned against making use of
what is called the "stairway" curve. This makes a
flat or step-like c-ontact at tlie point <letcrniined by
the scale. All curves, as has btieu said, should
approach the j)oint of contact slantingly and
direct from the j)oint previously touched on the
vertical line. The great advantage of this
Curve and Bar Designations 101
peak-top curve is brought out on charts contain-
ing two or more curves which approach each other
at or near the same points. In such cases the peak-
top permits of easy separation of the two curves
and does not result in confusion caused by in-
ability to follow the curves, which latter is inevit-
able when two flat-top or stairway curves ap-
proach each other at the scale unit points.
DETERMINING THE SCALE SPACING
In determining the vertical space a number of
curves should occupy every one of the columns of
figures in the statistical table is examined to ascer-
tain the lowest and highest numbers that are to
be charted. That is, for this purpose all the differ-
ent columns representing the comparable statis-
tical elements are considered as if they were only a
single column.
Take, for illustration, the table of the chart on
page 96. The lowest number of cents represented
in any one of all seven columns is 12.2 in the col-
umn for the year 1913. This number also api)cars
in the colunui for the year 1915. The largest
nuinlx^r of cents in any one of all the columns is
57.2 in the column for the jear 1919. Thus the
spread for all the numbers in all the columns is
from 12.2, the j)rice of plate beef in 1913 (also in
1915), to 57.2, the price of bacon in 1919, or a max-
102 Chartography in Ten Lessons
imum spread for all the figures of 45. With a verti-
cal scale unit of 5 this spread requires at least ten
squares vertically with the base line starting at the
unit 10. Starting at would require two addi-
tional squares below the scale unit 10, but if this
were done there would not be space enough any-
where on the framework for the inclusion of the
statistical table. Our squares are thus more
valuable at the top, so we provide two additional
there to accommodate the table,
UTILITY OF THE CURVE CHART
By this time the student should have become
impressed with the great utility of the curve
method in chartography. In comparing the
tendency over a period of time of two or more dis-
tinct but, related statistical elements it is far
superior to the bar method in chart making and
incidentally is also superior to the statistical me-
thod. While a trained statistician could interpret
satisfactorily the tendency from a study of col-
umns of figures, no one else could perceive the
movement as clearly as it is convincingly demon-
strated by curves drawn in relation to each other.
This is particularly true when more than two
curves representing different columns of figures are
compared, as in the chart on page 96. These
curves not only show the variations in each of the
Curve and Bak Designations 103
items for each year compared with the other years
and with the other items but they also give a
comprehensive perspective of the entire movement
during all the years; they show the status of
each of the items in relation to every other item
for each year and at the beginning and through
to the end of the period of time. Thus it is that
chartography can be said to "speak" a language
easily made intelligible to the mind through the
eye.
CHARTOGRAPHY BASED ON COMPARISONS
The curve also strikingly emphasizes the fact
that the art of chartography is based upon rela-
tions or comparisons. There can be no chart
without a comjjarison of some kind. And as the
very nature of statistics involves a relation be-
tween or a comparison of groups of facts, it is
not too much to say that chartography is the art
best adapted to expressing this clearly and con-
cisely.
"Comparison is, in general, the final goal to-
ward which all statistical studies tend," says King,
in his Elemenls of Siatifitical Mclliod. "Com-
parison is necessary to give us clear ideas of the
relationship of things in time and space. It is also
essential in determining whether phenomena are
connected or independent and in establishing
relations of cause and efifect. We may wish to
104 Chartography in Ten Lessons
study: 1. Changes of a single variable. 2. The
structure of different groups. 3. Changes in two or
more variables."
Brinton, in his Graphic Methods for Presenting
Facts, puts it this way: "One of a business man's
chief assets is his ability to show things to others
in their true proportions. He is continually mak-
ing contrasts, and holding up for comparison
different propositions which come up in his daily
affairs. The graphic method lends itself admir-
ably to use in making comparisons. It is surpris-
ing how much clearer even simple comparisons of
only two or three items will appear when their
numerical value is put in graphic form rather
than in figures."
In every chart, then, a comparison or relation of
some kind is involved. This comparison may be
with the same statistical element for two or more
periods of time; it may be of two or more differ-
ent elements for the same or different periods of
time. It may be a comparison of total or abso-
lute amounts, of increases or decreases, of the rate
of change. It may be a relation of one or more
elements expressed in proportions to a common
total, and so on.
Graphic methods must, of course, show compar-
able facts only and these in their true relations
and profKjrtions in order to present the correct sit-
Curve and Bar Designations 105
uation. They represent the best kno'VNii scheme
for presenting contrasts and in this way indelibly
impressing their significance upon the mind. Hav-
ing recourse to curves differentl}' constructed
permits some of these comparisons to be made
much more clearly than if the chartographer
were limited to the unbroken or straight line
curve.
bar designations
DiflFerent designations for different statistical
elements or factors apply with equal significance
to the bar as to the curve chart. The simplest
designations are plain black and white which are
usually employed where only two groups of
figures or statistical elements are involved. The
plain white bar is secured simi)ly by outlining it
on the section sheet and without filling it in with
the ink. But it is not as satisfactory as a cross-
hatched bar, that is, one with the outline filled
in by drawing liglit diagonal lines.
One use of designations in bar charts is illus-
trated in the chart on page 106. The student
should write out on jiajjcr a careful analysis of
this chart, not only from the point of view of its
construction but al.so from that of interi)retation.
Another and probably the most common use
of designations in bar charts is illustrated on
page 107. It shows the employment of the black
OPERATING REVENUES AND EXPENSES
PENNSYLVANIA RAILROAD
UlUoM of BolUn
100 us
1*0*
ino
i«u
itu
itu
IfU
ins
iti«
•M
«Vl » n «« trm Mpert* of R&llroat
to lat«r»taM eoBwo* CooniMioB
<
10
K
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I
t
i
1
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8
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t3
108 Chartography in Ten Lessons
and white as parts of a whole bar. In this chart
the total freight traffic of the Norfolk and Western
Railroad Company has been separated on the
percentage basis between bituminous coal and
all other commodities transported. The com-
parison involved is expressed as a ratio. The
changes over the period of years of the coal
traffic in relation to the total traffic, as well as
also in relation to the traffic in all other com-
modities, is seen by comparing the black portions
of the bars with the total bars, reading from left
to right. Similar changes in the proportion of
the traffic of other commodities to the total
freight traffic is shown by comparing the white
portions of the bars with the total bars, reading
from right to left in order better to secure an
idea of the differences in the length of the white
sections. The proportion of each designation
to the total bar in any one year and the changes
as between years are clearly indicated.
In this chart each of the series of horizontal
bars represents by 100 per cent the total amount
of all freight traffic for each of the designated
years. Consequently all the bars are of the same
length. No information is given as to the
numbers representing the absolute amount of
traffic of the road, which it may naturally be
assumed varied in the different years — it may
Curve and Bar Designations 109
have increased or decreased from year to year
and if these numbers were charted they would
likely give bars of varying lengths. All that the
chartographer is interested in, so far as the sta-
tistics enlighten him, are the changes in the pro-
portion of the two components which together
comprise the total freight traffic for each year.
SOME CHARACTERISTICS OF A GOOD BAR CHART
The chart on page 107 is a good illustration of
this kind of a bar chart. The title is concise and
yet comprehensive. The sub-title — that of the
particular railroad — is well placed and well
spaced. The figures for the years are directly
under each other and are spaced sufficiently from
the bars, while the figures for the black and white
portions of the bars are directly in proper column
form on each of the six bars. The reader is told
at the top of the framework tliat the figures
rej)resent per cents, and at the bottom among the
foot-notes that the statistics have been "Com-
j)iled from Hei)orts of the Railroad to Interstate
Commerce Conunission." The group of bars is
.so spaced as to avoid the appearance of crowding.
The designations of the bars are clearly distin-
guished between " Bituminous ('oal" and "Other
Commodities" by' means of the legend beneath
the bars. The neat lines |)roperly frame tlie
series of bars.
a:
<
o
z
g
a:
lu
u.
O
o
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o
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z
o
IJL
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Curve and Bar Designations 111
When more than two statistical elements have
to be indicated on a bar the chartographer has
recourse to an almost unlimited number of differ-
ent designations. Some of these, shown in the
chart on the opposite page, indicate the extent
to which variation in bar designations can be
carried. The effect of the use of these different
designations is for the purpose, of course, of
causing the areas to stand out in contrast with
each other. The student should practice until
he becomes proficient in making these designa-
tions.
In the chart on page 89 (Lesson VII) and in the
one on page 106 will be found a simi)le device and
yet a valuable aid to chartography. This is the
word designation of the vertical scale unit of a
curve and the horizontal scale unit of a bar chart.
In the chart on page 89 (Lesson VII) this
designation is "Thousands of Immigrants." By
its use the chartographer is al)le to droj) from each
of the vertical scale units all the ciphers repre-
senting thousands. That is, instead of the vertical
scale starting with the unit 0,000 it })ogiiis with 6,
the interpreter of the chart knowing from having
read the word designation that this unit G means
6,000. So with the horizontal scale unit of the
chart on page 106. There the word designation is
"Millions of Dollars" and this permits the drop-
112 Chartography in Ten Lessons
ping of six ciphers from each of the horizontal
scale units — it allows the scale to begin with
the unit 100 instead of requiring 100,000,000.
To reproduce the additional six ciphers after each
one of the horizontal scale units would over-
burden the horizontal scale line with figures even
if s]iace could be found for all of them.
Making use of the word designation of the
scale so as to drop the ciphers from the scale line
itself has many advantages and should always be
employed where the numbers represented are
more than three digits, that is, thousands and
over. The designation should be clearly pre-
sented in an easily observable place on the chart,
even when the table of figures would seem to
make this unnecessary, so that the chart can be
quickly read and easily understood without
reference to the statistics from which it is made.
Usually the best position for the word designation
is just beneath the top neat line and centered
above the horizontal scale line.
QUESTIONS FOR SELF-EXAMINATION
1. What are the advantages of various designations for
different curves?
2. Describe the peak-top curve.
3. How is the scale spacing determined?
4. Describe the utility of a curve chart.
5. What is the basis of chartography?
6. Discuss the uses of various designations for different
bars.
LESSON IX
Value of Statistics to Chartography
The Statistical Table — Aids in Reading the
Table — The Stibsfitntion of Ciphers — The
Table of Ratios— Building Up A Table— The
Percentage Increase and Decrease — The Zero
Line — The Arithmetic Average — The Misuse
of the Average — Statistical Class Limits.
It should be clear by this time that a most
important asset in the practice of chartography
is a knowledge of statistics. The mere mechani-
cal act of drawing lines and curves and bars on
section paper is the work of the draftsman and
does not of itself make a chartographer. In
these Lessons it has been assumed that the infor-
mation is already at hand in proper form for the
drawing of the chart — that the collection and
comi)ilation of the statistics have been correctly
done and that the figures have been checked
and verified so that there is no question as to their
accuracy and trustworthiness.
This assunii)tion has l)een necessary for the
reason that statistics are a distinct field of study in
themselves, with sulj-divisioris as to methods of
collection, of comj^ilatiori, of tiibulation, of comjju-
tation, of arrangement, of presentation, of inter-
ns
114 Chartography in Ten Lessons
pretation, and so on. This field is entirely too
extensive to be presented in these Lessons even
in merest outline, and for a knowledge of its
principles the student should have recourse to
standard books on the subject. All that can be
done here is to make the briefest reference to a few
only of its features which most vitally concern
the beginner in chartography.
THE STATISTICAL TABLE
Conspicuous among these is the arrangement of
the statistical elements in the table. The prin-
ciples underlying this have necessarily been dis-
cussed briefly in preceding Lessons. But there
is one other point in particular to which attention
must be called. This is the more or less common
practice — fortunately it is becoming less common
as the rules of good chartography become more
widely disseminated and better known — for
charts to appear in otherwise first-class publica-
tions with the statistical table having the latest
date at the top and with the earliest period of time
at the bottom of the column.
A chart made from a table arranged in this
way reads backwards from the latest to the
earliest year. In order to interpret it from the
earliest year and in sequence of time it has to be
read from right to left, which is the wrong way to
Value of Statistics to Chartography 115
read a chart. Invariably this arrangement is at
first glance misread, as the natural inclination of
the reader is to assume that years are arranged
in proper sequence. Where they are not so ar-
ranged too much time is lost before this is realized.
The first impression on the interpreter of the
chart in such cases is exactly the reverse of that
intended and which would have been received
by him if the correct method of arranging the
statistical elements in table form had been fol-
lowed. In consequence, one of the fundamental
purposes of the chart method of disseminating
knowledge is violated. Such a practice should
not be indulged in even in exceptional cases.
RECONSTRUCTING THE TABLE
Whenever the chartographer has a table of
figures to chart in which the latest year or period
of time api)ears at the top of the column, he should
rearrange or reconstruct the table in correct col-
umn form with the earliest year at the top before
he begins plaruiiiig his chart.
The justification for presenting the latest year
first in the column is that it is of greater impor-
tance compared with the other years recorded.
As a matter of fact, no one year in a series of years
that charts a tendency is of any greater impor-
tance than the other years. It may be of greater
116 Chartography in Ten Lessons
importance in the mind of some particular indi-
vidual or individuals as to the significance of the
data it discloses but in itself as a year it is only of
equal importance with every other year. Besides,
chartography offers other and much better
methods for placing emphasis on particular statis-
tical elements.
AIDS IN READING THE TABLE
It may be advisable, where large numbers are
the basis of a chart, to substitute ciphers as the
last two figures in tens of thousands, the last
three in hundreds of thousands, and the last five
in millions. By raising or lowering the last
preceding digit before the cipher, sufficient
accuracy is obtained for the purpose of most
cha ts. The advantage of this is that the ciphers
enable the mind to grasp more quickly the signifi-
cance of the numbers. In financial statements,
however, this practice has objections.
Necessary space on the chart for the columns of
figures can sometimes be secured by dropping
entirely the last three or six digits and substituting
at the head of the columns a word description of
the amount represented, such as thousands or
m illions and so on as the case may be. This elimi-
nates the confusion to the eye of numerous digits.
While this practice is not only admissible but
also advisable in designations of the scales it should
Value of Statistics to Chartography 117
not be allowed to become general in tabulations,
not even where the value or volume or quantitj'^ is
so large as to run into seven or more digits, as long
as there is space on the chart to show the complete
numbers without crowding.
Assistance in the direction of facilitating the
rapid reading of a statistical table and in enabling
a quicker grasp of its significance, is rendered in
cases of long columns of figures by breaking up
the numbers into groups of fives with double the
space separating each group. For illustration,
instead of presenting the table on the chart like
this:
Year Population
1900 75.994,575
1901 77,747,402
1902 79,365,396
1903 80,983,.390
1904 82,601,384
1905 84,219,378
1906 85,837,372
1907 87,455.366
1908 89,073,360
1909 90.691,354
1910 92,309.348
1911 93,927,342
1912 95,545,.S36
191.S 97,163,.330
1914 98,781.324
1915 100.399.318
1910 102,017,312
118 ClIARTOGRAPHY IN TeN LeSSONS
It might better be presented as follows:
Year Population
1900 76,000,000
1901 77,700,000
1902 79,400,000
1903 81,000,000
1904 82,600,000
1905 84,200,000
1906 85,800,000
1907 87,500,000
1908 89,100,000
1909 90,700,000
1910 92,300,000
1911 93,900,000
1912 95,500,000
1913 97,200,000
1914 98,800,000
1915 100,400,000
1916 102,000,000
These figures represent the population of
continental United States as reported by the
Bureau of the Census of the United States Govern-
ment in its bulletin on mortality statistics for
1916. Using them as a basis, the student is
instructed to draw with a lead pencil a curve or
bar chart, whichever he determines, applying to
his task the instructions he has received up to this
point.
Value of Statistics to Chartography llf)
THE SUBSTITUTION OF CIPHERS
This substitution of ciphers for other digits in
large numbers does not affect the accuracy of the
chart for the reason that the change made by it
in any number is so sHght, compared with its
total, as to be lost in the results of the appUca-
tion of the scale unit to its measurement. Be-
sides, it has a distinct advantage in that it does
not accord to the statistics any greater import-
ance than the method of their compilation war-
rants. No one who is familiar with the methods
of taking or enumerating the decennial census of
the population of the United States and of esti-
mating its growth for intermediate years believes
for a single moment that this population, say, in
1916, was exactly 102,017,312 to the last digit of
accuracy. While no criticsm of these methods is
here intended, it is bul stating the fact that they
are not so perfect as to record to the last figure
the exact population. Most statistical tables at
best are api)roximations and do not represent
absolutely accurate and indisputable facts to the
point of minute measurement.
All that can be expected of chart()graj)hy is that
it indicate clearly the general trend or tendency of
statistical elements. The chartographcr should
be on his guard against i)ermitting the curve or
bar to convey an impression of a greater degree of
120 Chartography in Ten Lessons
accuracy than is warranted by the statistical
information.
THE TABLE OF RATIOS
In deaHng with tables of ratios it is always
advantageous to carry the digits at least one place
beyond the decimal point. The advisability of
this should be so clear as not to need to be dis-
cussed. If, for instance, by not including the
last digit of the two ratios 67.6 and 32.4 of the
1912 bar in the chart on page 107 (Lesson VIII)
each portion of the whole bar falls short of its
correct measurement and the total 100 per cent
bar is incomplete. It is hardly ever necessary
to carry the digits further than two decimals and
in most cases one digit beyond the decimal point
answers all practical purposes.
Frequently decimals exceeding one-half may
be raised to a whole number and under one-half
lowered to a cipher. Where the digit is exactly
one-half whether it is raised or lowered will
depend upon the particular circumstances. Per-
centages or ratios are a problem in mathematics
and it is to that science the student should have
recourse for more complete knowledge of the
principles involved.
As percentages or ratios are derivative figures
it is of advantage, if it does not over burden
the chart, to place also on the fj-amework the
Value of Statistics to Chartography 121
original figures from which they are derived.
Where a choice as to exclusion has to be made it
should be in favor of the retention on the chart
of the derivative figures upon which it is based.
BUILDING UP A TABLE
Both the original and their derivative figures
appear in the table of the chart on page 122.
This chart also illustrates the use of the ciu-ve in
expressing ratio. The problem is to show the
income of the Pennsylvania Railroad Company
in relation to its securities, that is, the rate earned
by the latter for each year from 1909 to 1916,
both inclusive. The basal information as to
securities and income was secured from the annual
reports of the company filed with the Interstate
Commerce Commission in Washington, D. C.
The amount of bonds representing funded debt
and the capital stock were added to ascertain
the total of all securities for each of the years.
This gives the second column of figures in the
table to the chart. In order to ascertain the
total income that is f)roperly related to these
securities the amount of interest paid on funded
debt was added to net corjiorate income for each
year, which gives the third column. This in-
formation enables us to ascertain the rate of
income each year by dividing the amounts repre-
RATE OF INCOME ON RAILWAY SECURmES
i«i»
PENNSYLVANIA R. R.
ini ml iMs itit
/
/
/
/
1
1
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\
f
1
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i
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1
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s
^^
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/ /
/ /
/ /
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orti2«2^.
.
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—
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M
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—
ttrttM lnn> ud Far
0«pl«»l K
t Corp«r«i*
ttr
'««- IMlvtKU iBWrwtA OnA
Stock
taooa*
o«in
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l*» 6M,«a3,MD »3,4«.6T« t.M
H4.4M.BO0
9.«M,3ll
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1710 T06,979,TTJ 62,2^,600 T.41
411.296. 974
O,04»,l«
t.Tl
1911 ri«,SCa,m 4ft, 104.606 «.I4
Ut,443.93B
4,6U.023
7. 47
1912 T14,6ai,60T 4T,4»,U& 4.44
4M,«77.900
T.NU.eSl
ft.U
inj ra9.0l9.ti4 S0,4U.S11 4.«I
4»i.soa,4n
U),6M.4TS
e.u
ItU T4S.10SJ1B 48.947.004 4.11
4»9,t66.70O
l6,3fl7,TT8
7.H
^
in* •U.Ul.aTO 43.41t.su t.U
49».203,600 -
n,u«.ui
4.64
h™
in« 9n,us.sT4 a.4«4.'9< t.ti
4M.n4.Toa 1
I3,733,43t
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1 1
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!
Value of Statistics to Chartography 123
senting capital obligations into the amounts
representing net corporate income and interest
for each of the corresponding years. The result
is the fourth or ratio column of the table. The
other column of ratios — the seventh of the table
— is ascertained by dividing the amounts repre-
senting capital stock into the amounts represent-
ing net corporate income.
It should be noted that the only comparison
made by the two curves of the chart is based
upon the two columns of ratio figures. It would
better assist comparison in the statistical table
if these two columns were placed alongside each
other, but this cannot be accomplished with
clearness in reading without making another
table with the column of years duplicated and
with awkward headings above each ratio column.
This latter is due to the words expressing the
exact meaning of the ratio column taking up a
great deal more space in width than is occupied
by the three digits and the decimal point. Thus
to place adjacent to each other the columns that
are compared is likely to commit an ofFense more
serious than is the vainc of tlic advantage to be
gained.
the pp:rcentage increase or decrease
Quite a different percentage chart is presented
on pa^e 124. It shows the rate or per cent of in-
PRINCIPAL ITEMS OF OPERATING EXPENSES. 1008-IOiS
BAL-nMORE » OHIO
Pl^orM r*pr«a«at ^ar ctnti.
laor^a** or Atortvm It ov«r I90ft
i«ot tuo \ni lau 11U
B<Jl> 41>d TIM
rui
Pr*l«kt Cu-a
Pftaaanflvr Cara
■ 8.M
• 9.5T
• ».92
"10.93
•IT. 19
•Ji.ia
•a.M
42.(9 <T.*6
«i.ta 43. ai
U.ll 'U.BO
It. 43 ^4.M
11.30 19. Tl
U.«0 14.34
• 1.34 • B.«3
■ 3.96 • t.9»
sa.KS
so. 23
12.96
22. TS
10. Tt
22.53
' 3.06
6.40
-f
U>oow>ttv«» *
Mill* «nd n«a
Puel
Freight Car* *
poadvay tni Trftck
Pa«a«in0*r Cart*
CmtMM Cnm K«^rt« of liilr<M4
'Ropairt, r«fi««tti9. an4 do9recl«tloo
Value of Statistics to Chartography 125
crease or decrease. This arithmetical principle is a
most valuable aid to the chartographer, for without
it many curve charts that are now possible could
not be made. This is true in most cases where
the difference between the numbers to be com-
pared is considerable, that is, where some are
large and the others small numbers, as a chart
of these absolute amounts is impossible owing to
the requirements of space necessarj^ to indicate
the "spread" between the highest and the lowest.
But by resolving these \'urying amounts into per
cent increases or decreases, as the figures deter-
mine arithmetically, statistical elements are
secured which permit of a common measurement
and in consequence of a comparison of relative
movements over a period of years.
The percentage increase or decrease in our chart
of each element for each year from 1908 to 1913 is
based upon the amount for 1908. In consequence
every curve starts from the same point at zero on
the 1908 vertical line, because it is plain that
there could be no increase in 1908 over 1908. As
the per cent figures for every element show a
decrease in 1909 over 1908 every curve extends
downwarrl bellow the zero line to the respective
points of contact with the vertical line for 1909.
For each of the following years the curves
separate more or less widely according to the
126 Chartography in Ten Lessons
tendency as indicated by the figures for the
different elements.
Taking the year 1913 for illustration, there is
an increase over 1908 in every one of the prin-
cipal operating expense items. It also shows
that the expense of buildings, fixtures, and so on
had increased faster relatively than that of steam
locomotives, or of rails and ties, or of wages, and
so on; that the expense of passenger cars had
increased less rapidly than that of any of the
other items, and that this expense was greater in
1913 than in 1908.
THE ZERO LINE
The chart on page 124 presents also the zero line
feature of chartography based upon percentage
increase or decrease figures and not on absolute
amounts. It is one that the student is likely to
have frequent occasions to make use of. This line
is indicated by the cipher designation on the
vertical scale lines.
The zero line is in reality the base from which
the curves move up or down as the numbers of
the statistical table and the scale units determine.
It practically represents the amounts of each of
the eight elements in the year 1908 as indicated by
the line drawn horizontally across the chart, for
the increase or decrease is "over" that year or
line. In other words, the movement of the
Value of Statistics to Chartography 127
curves for any one and all of the six years in rela-
tion to the zero line is determined by the rela-
tion of the amount in each year to the amount in
1908. Thus the fluctuations in the curves from
year to year should be read or measured from this
zero line and not from the slopes of the curves
themselves.
Facility in tlie interpretation of such a chart is
aided if it is clearly indicated that all the move-
ments of the curves above the zero line mean
increases over the base year and below that line
decreases compared with that year. This is accom-
plished by inserting the Mords "Increase" and
"Decrease" alongside the vertical scale lines on
either side of the zero line. This shows clearly that
the vertical scale reads upward from the zero line
for increases and downward for decreases.
Assistance in the clear interpretation of such a
chart is also rendered by making the zero line
slightly heavier or wider than the other horizontal
lines connecting at other units of the vertical
scale lines and at the same time not as heavy or as
wide as the curve or curves themselves. This
wider zero line calls the reader's attention to the
fact that he must interpret the movements of the
curves from the zero and not from the lowest or
ba.se line.
In cases where the figures to be charted show
128 Chartography in Ten Lessons
no decreases and in consequence it is not necessary
to extend the curves below the zero line, then
this line becomes also the lowest or base line at the
bottom of the chart and all the movements of
the curves are above that line. In such cases it is
not necessary to employ the terms "Increase" and
"Decrease" above and below the zero line. Nor
is it necessary in such cases that the zero line be
made wider than the other horizontal lines.
While the chart on page 124 designates with a
cipher the horizontal line from which the move-
ments of the curves are measured, as a matter of
fact this line is not a zero line but a 100 per cent
line. This is true arithmetically for the reason
that in reality it represents the total amount of
each element or item for 1908. These were taken
as the base from which the figures for each of
the other years were ascertained. Arithmetic
exactness requires that this line be designated as
a 100 and not a line. But in this case chartog-
raphy takes liberties with arithmetic for the sake
of securing greater clearness in interpretation.
Experience has taught that because of the general
lack of knowledge on the part of many of those
for whom charts are prepared, confusion leading to
misinterpretation, and this to misinformation,
results whenever the 100 per cent designation
is employed in place of the cipher.
Value of Statistics to Chartography 129
THE arithmetic AVERAGE
In the chart on page 124 the basis upon which
the respective percentages have been computed
is, as has been said, an amount for a single year.
Wherever possible this basis should be the average
of the amounts for a number of years, and this is
nearl}^ always feasible when the number of years in
the table comprises ten or more. This average is
ascertained by adding the amounts for the years
selected and dividing the total thus obtained by
the number of these years. The percentage in-
crease or decrease is then computed for each of
the years from this average amount. This is not
advisable for the statistics in the chart on page
124, as tlie numbei- of years is only six. In those
cases where it can be done there will likely be
found a material difference between the move-
ments of curves over a period of years thus dis-
clo.sed compared with the movements shown with
only a single year as the base.
The advantage of taking the average for a
number of years as the base for computing in-
creases or decreases is found in tlie fact that this
average smooths out the irregularities of high and
low or of large and small amounts which may have
been comjiriscd in the difrcrent years. If a
single year only is used as the ba.se it may be that
in that particular year unusual influences or
130 Chartography in Ten Lessons
forces were at work to change unduly its total in
comparison with preceding or following years
and in consequence it is out of normal relation to
the amounts of the other years.
An illustration of this as to many phases of
railway operation, for instance, is the fiscal year
1908 extending from July 1, 1907, to June 30,
1908, both inclusive. The records for that fiscal
year include the effects of the panic in the latter
part of the calendar year 1907. The railroads
were very seriously affected by this disturbance
in business and financial conditions and their
traffic and revenue fell off strikingly. In con-
sequence, any comparison of the operations and
finances of subsequent years based upon the single
year 1908 would show tendencies that might not
and would not be showTi if a year that did not
record a panic was used as the base. Averaging
a number of years escapes this possibility of
statistical error and in consequence avoids
misrepresentation in chartography.
The proper use of the average is an important
asset to the chartographer. This average reper-
sents or indicates the usual or common occurrence
or status. It is, primarily, as has been stated, a
problem of arithmetic. Quite often, if not always,
it is simply an arithmetical standard, non-existent
in actual reality and yet one around which other
Value of Statistics to Chartography 131
facts tend to approximate or conform and by
which they are measured or compared. Such,
for instance, as the average height of men, or
the average price of a pound of bacon, and so on.
THE MISUSE of THE AVERAGE
The average can be as much of a sinner when
improperly made use of as it is a saint when
projjerly employed. To the chartographer the
use of the average has its pitfalls against which he
must be constantly on his guard. While it is
indispensable at times, it has its limitations and
shortcomings and these must be known if he is
to make the best use of it and not be inveigled
by its attractions into grievous errors.
Quite freqiieiitiy the average comi)riscs ele-
ments radically different from each other whose
irregularities or dissimilarities have disappeared
or been smoothed out to such an extent that it
does not represent any measurable status or even
approximate situation of the actual facts, and in
consequence can have no other effect than to mis-
lead. This is illustrated, for instance, in statistics
giving tlio average amount of stock hold j)er
stockholder in the railways of the I'nitod States.
In 1914 this average was stated as .^L'^O.^H.
It was obtained by dividing the total number of
stockholders — ()':^2,284 — into the total i)ar value
132 Chartography in Ten Lessons
capital stock outstanding— $8,685,764,000. Of
course, such an average is absolutely meaningless.
It is merely an arithmetic average. No such
amoimt of stock approaches even in the slightest
degree to the actual facts in the case. The
fallacy in any practical use of this average can be
demonstrated by a simple illustration from almost
any railroad.
Let us take the Wabash for an example. In
1915 a single stockholder — the Equitable Trust
Company — owned $28,744,000 of the stock of
this railroad. With nine others, these ten largest
stockholders together held $59,449,200 of the
stock, or more than sixty-four per cent — nearly
two-thirds. In view of these very large single
holdings of stock by a very small number of
stockliolders — these ten owning by themselves
an average of $5,944,920 — any arithmetical com-
putation representing the average amount held
by each stockholder cannot fairly represent the
situation as to the ownership of stock in the
Wabash Railroad Company,
THE STATISTICAL CLASS LIMITS
In such cases as this instead of making use of
a meaningless average there is the possibility of
recourse to a separation of a group of figures into
class limits in order that the facts of a given situa-
Value of Statistics to Chartography 133
tion may be more accurately presented. This
should always be taJcen advantage of whenever
possible.
Applied to the preceding illustration it simply
means the separation of the total number of
stockholders into groups or classes according to
selected amounts of stock held. The first step
in this statistical process is to determine upon
the limitations for the different classes. These
are purely arbitrary. To obtain them, round
numbers are most desirable, as these give clear
cut groups. These numerals form what are
technically known as boundary lines of the classes.
The difference between them is called statis-
tically the class interval. These class intervals
should all be equal or uniform.
The number of clas.ses and the numl)er in
each class become statistically what is called a
frequency tal)le.
By thus dissecting the statistics a number of
verj' interesting and highly important facts is
usually disclosed which the j^resentation of the
average does not indicate as being j)resent. A
knowleflge of these facts is es.sential to a correct
and comi>Iete presentation of the actual situation.
These facts indicate that the chartograjjlicr
must excrci.se his best judgment in the i)resen-
tation of the average. He cannot be permitted
134 Chartography in Ten Lessons
to excuse himself by hiding behind statistics.
Charts that reflect inaccuracies and irregulari-
ties of mathematical computation to the extent
of being misleading cannot be explained away
because, in truth, they never should have been
made. This is a high standard to attain, for
quite often the chartographer must depend almost
entirely upon his statistics for a truthful presen-
tation of the facts, and if the statistics are faulty
it seems rather unfair to hold the chartographer
to strict responsibility for any misleading result.
Nevertheless, the chartographer should be as
scrupulous and as exacting in the use of statistics
as in the use of the English language in maintain-
ing a high standard for truthfulness and exactness.
A sufficient variety of curve and bar charts
have been presented in the preceding Lessons to
impress upon the student of chartography that
his most important task is the planning of the
chart. It should be done before he touches pen
to paper in beginning the drawing of the chart.
With this planning successfully accomplished the
remaining details of the work of execution or
construction becomes a relatively simple matter.
In this planning the student should first know
thoroughly the real meaning or significance of
the table of statistics he is to chart — he must
"see" clearly the vital point of comparison the
Value of Statistics to Chartography 135
chart is to bring out. It is of advantage in com-
prehending this point if the student will roughly
sketch several different charts, both curve and
bar, before he attempts to lay out the curve or
bar in ink. He will be surprised at the difference
in results shown by the various methods, and
can then select the one which best illustrates the
significance of the statistics. More time rela-
tively should be given to the planning than to
the actual drawing of the chart. The time
devoted to the latter will be greatly shortened
if the planning has been done correctly. Be-
sides, it will also save time lost tlirough changes
and alterations usually made necessary where the
planning has been neglected.
QUESTIONS FOR SELF-EXAMINATION
1. What is the value of statistics to chartography?
2. What is the statistical table? How should it be
arranged?
3. Describe some of the technical aids to the interpreta-
tion of a table of statistics.
4. What are ratios? How are they computed? How
arranged in table form?
5. Describe the construction of a statistical table.
6. What are the important differences between ratios
and percentage increases or decreases?
7. Of what value to the chartographer are percentage
increases or decreases?
8. Describe the zero line and its use in charts showing
percentage increases or decreases.
9. What is the average? How is it computed? Describe
its advantages and disadvantages.
10. What are statistical class limits? What are boun-
dary lines of the classes? What is the class interval? A
frequency table?
1S6
LESSON X
Primary Principles of Chartography
Planning the Chart — Importance of the Right
Method — Essentials of Good Chart Making —
Planning the Size of the Chart — Planning a
Reduction in Size — The Reducing Glass —
The French Curves — Checking up the Chart.
Chart-making for commercial and other pur-
poses is still in its infancy and in consequence
has not yet been systematized. Statisticians who
are employing it to an increasing extent as an
aid in the presentation of facts are in disagree-
ment, or rather are not in accord, as to the
superiority of different methods. Give a group
of statisticians who are also familiar with chartog-
raphy a set of figures to chart and^ there will
likely be as many fliffcnMit kinds of charts widely
divergent in methods as there are statistic;ians.
Thus the same information will be charted in
many different ways. While variety in charting
is possible where numerous illustrations must be
made, at the same time some methods are better
than others in bringing out the facts more clearly.
Variety of effect is permissible and sometimes
desirable in order to avoid monotony in presen-
tation and to retain attention.
187
138 Chartography in Ten Lessons
a choice of methods
The value of the chart method being in ex-
pressing clearly the meaning of a statistical table,
the problem of the chartographer is to select the
one method from among the many that will best
express this meaning. Particularly is this true in
the use of charts by the large corporation. Pre-
pared usually for the executive whose time is
limited and of great value, the chart must be so
drawn as to give to him instantly the true sig-
nificance of a mass of statistics which he has not
the time to analyze in their details. The efiicient
and successful executive must decide quickly and
of course correctly. The information furnished
him on the chart must not only possess an ac-
curate background but it must also be presented
to the best advantage if he is to make the right
decision and avoid "guess work." The busy
executive is more and more being compelled to
place greater dependence upon the chart analysis
of statistics.
As has been made clear, in the practice of
chartography there is a choice of widely varying
methods. No general rule can be given for
determining which of these methods is the best
for any particular purpose, but practice will
enable one to form his own judgment as to selec-
tion, and through experience he will learn to
Primary Principles of Chartography 139
choose the method best adapted to each of the
varying problems.
importance of the right method
The importance of selecting the best method is
emphasized by Brinton in his Graphic Methods
for Presenting Facts. He says: "After a person
has collected data and studied a proposition with
great care so that his own mind is made up as to
the best solution for the problem, he is apt to
feel that his work is about completed. Usually,
however, when his own mind is made up, his
task is only half done. The larger and more
difficult part of the work is to convince the minds
of others that the proposed solution is the best
one — that all the recommendations are really
necessary. Time after time it hapi)ens that
some ignorant or presumptuous member of a
committee or a board of directors will upset the
carefully thought out plan of a man who knows
the facts, simply because the man with the facts
cannot present his facts readil}' enough to over-
come the opposition. It is often with impotent
exasperation that a person having the knowledge
sees some fallacious conclusion accojited, or some
wrong policy adopted, just becau.se known facts
cannot be marshalled and presented in such a
manner as to Ije effective.
140 Chartography in Ten Lessons
"Millions of dollars yearly are spent in tb^
collection of data, with the fond expectatiofi
that the data will automatically cause the con cc
tion of the conditions studied. Though acrv
data and real facts are valuable, when it
getting results the manner of preseni
ordinarily more important ti-an the factb .
selves. The foundation of an edifice is of vasi
importance. Still, it is not the foundation but
the structure built upon the foundation who-
gives the result for which the whole work \N'ae.
planned. As the cathedral is to its foundation so
is an effective presentation of facts to the data."
ESSENTIALS OF GOOD CHART-MAKING
The primary essentials of good chart-making
are simplicity and clearness. The curves or bars
of a chart are employed to express and to com-
municate ideas, just as words are used in the
English language. The fewer the ideas it is
attempted to express in a single chart, the better.
In fact, a single chart should aim to express only
a single idea. This is diflBcult to accomplish,
as the essence of a chart is a relation or a compari-
son and this usually involves more than one idea.
The aim, however, should be to construct the
chart so that all but the dominant idea it is
intended to express or communicate is kept
Primary Principles of Chartography 141
subordinate or in the background. There should
not be a single unnecessary mark or figure or
word on the completed chart, and if its full
meaning cannot be grasped quickly, then it has
failed of its object.
There is a common and quite general violation
of ^hese principles. Chart-making is not at all
'omplex; it does not involve a knowledge of
nigher mathematics for correct presentation and
interpretation. There are a few definite rules
which, if once understood, result in the ease and
facility that may be likened to a knowledge of
the alphabet, once acquired. Much of bad chart-
making and of confusion in interpretation flows
from a violation of the few simple princii)les.
PLANNING THE SIZE OF THE CHART
One task that will likely confront the student
with as many peri)le.\ities as any other will be
the working out of the size of the chart within
the limitations of the sheet and the requirements
of the statistics. Only practice will enable him in
time to overcome most of these didiculties. Hut
as a .sort of guide for meeting some of these prob-
lems there is presented in the following paragraph
a practical illustration.
The size of the sheet for the completed chart is
arbitrarily fixed for us at 12 by 16 inches. At
142 Chartography in Ten Lessons
least two of the 16 inches are required as a margin
on the left of the sheet (the chart appearing
lengthwise) for binding. Usually an inch margin
on the remaining three edges is advisable. This
leaves 13 of the original 16 and 10 of the original
12 inches as the size within which the chartog-
rapher is to work, or a size 10 by 13 inches. The
neat lines of the frame and the letters of the title
must come within this size. Usually one-half inch
is sufficient for the title letters, and in our particu-
lar illustration it is required that the title appear
lengthwise of the sheet. This reduces the size to
9.5 by 13 inches. Between each of the neat lines
and each of the scale lines one-half inch will
usually be sufficient — this is a reduction in both
dimensions of another inch. Sometimes a full
inch is required below the lower horizontal line
for the footnotes. Of course these spacings are
subject to being increased or decreased according
to the requirements of varying problems. The
original size of 12 by 16 inches has dwindled by the
above mentioned processes to 8.5 by 12 inches as
the size of the framework proper.
The arbitrary limitations of space within which
the chartographer is confined in his work cannot
be removed from among the difficulties of the
practice of the art. All that he can do is to learn
by experience to make the best adjustment pos-
Primary Principles of Chartography 143
sible in each particular problem. This is true
no matter what the size is that is determined upon.
And having made the decision the chartographer
will soon learn to adapt himself to the limitations
of space and to forego something that is desirable
in order to adjust his work to the exigencies of the
requirements.
In most cases where a number and variety of
charts are to be filed for reference or bound as
exhibits it is quite important that the size for all
the sheets be made uniform. This does not neces-
sarily mean that the worker will have the same
size for the original of all the charts themselves,
but it does mean that the completed charts shall
all be on slieets of the same size. This permits of
uniformity in size for all completed charts and
assists in securing neatness and orderliness in
office records. Completed charts on sheets of
different sizes are awkward in handling and easily
damaged.
PLANNINO A REDUCTION IN SIZE
Where the original <lrawing is to be reproduced
by one of the .several j)hotograi)hic i)rocesses and
printed from plates, the chartographer has a
.special problem of reduction in size to .solve. In
such casos the i)f'ri-aiid-ink charf should always be
considoral)ly hirgor than the final r<'i)r<Mliiction.
Most charts will stand a reduction in size of from
144 Chartography in Ten Lessons
one-third to one-half and in cases even more, and
will be improved in appearance by the process.
A reduction in the size of the original drawing
tends to smooth out the rough places or minor
irregularities of lines, curves, bars, figures, and
letters and results in a much cleaner effect.
Virtually all the charts in these lessons have been
reduced approximately one-half from the size of
their original drawings.
In ascertaining the dimensions for the size
of the original drawing simply apply the rules of
proportion. Only four factors are involved —
the width and length of the reproduced chart
and the width and length of the size that
must be drawn to secure the reproduced size.
Assuming our problem to be the one mentioned
on page 142, we know the width and length of
the reproduced size — the former is 10 inches and
the latter 13 inches. We know also how much of a
reduction we desire to secure — whether one-
third or one-half and so on. Selecting a reduction
of one-third gives us the arbitrary width of the
original as 15 inches. It is the length of the
original that must next be learned.
Our known figures give us this formula:
10 : 13 :: 15 : X, which reads 10 is to 13 as is 15 to x.
Working out this formula we learn that 13 times
15 equals 195 and this number divided by 10 gives
Primary Principles of Chartography 145
19.5. This latter thus represents our unknown
fourth quantity, which is the dimension of the
length of the original drawing. The size of the
original must then be 15 by 19.5 inches to secure a
reduced size of 10 by 13 inches.
In the above illustration the number 10 and the
letter x are known as extremes and the numbers 13
and 15 as means. In any proportion the product
of the extremes is equal to the product of the
means, that is, 10 times x, the latter being 19.5,
is 195, the product of the extremes, and 13 times
15 is 195, the product of the means.
It is also true that the product of the extremes
divided by either mean gives the other mean, as
for instance: The product of the extremes is 195
(10 times 19.5) and 195 divided by 13, one of
the means, gives 15, the other mean, or 195 divided
by 15 gives IS. Again, the product of the means
divided by either extreme gives the other extreme.
For illustration: 13 times 15 is 195, the product of
the means, and divided by 10 gives 19.5, or by
19.5 gives 10.
Another simi)le method for ascertaining the
reduced dimensions from the original is illustrated
on the following i>age. The larger rectangle is
our original she. From its lower left hand corner
a diagonal line is drawn in light lead jjencil to the
upper right-hand corner. This is line C-C. This
Primary Prixciples of Chartography 147
diagonal line is then connected by a vertical line
starting at any point on the base line A-A, such as
the broken line shown. From the junction point of
the broken line and the diagonal line draw another
broken line at right angles to the vertical line and
extending to line D-D. The rectangle thus cir-
cumscribed in the lower left hand corner will be
found to be in exact proportion to the larger rec-
tangle, or the size of the original.
In planning a reduction in the size of the
chart from the original, care should be exercised
in .seeing that all the lines on the original are made
sufficiently wide to stand the reduction in line
width due to the decrease in size. In our preced-
ing illustration on j)age 144 the lines would be only
one-tliird as wide in the completed as in the
original drawing. Therefore, all the lines and
curves and .so on of the original must be made
wider than would be necessary if the chart were
not to be reduced. Failure to allow for this reduc-
tion in the width of the lines and curves and let-
ters and figures is a common mistake made by the
beginner in chartogrni)hy which should be
guarded against if the best results are to be
secured.
TIfK UKDrriNfi c;la88
A valnable aid in this branch of tiic work is the
reducing gla.ss. It nuiy l>e .said to be the opposite
148 Chartography in Ten Lessons
of the magnifying glass, decreasing instead of
increasing the size of the object observed, the
lens being ground concave instead of convex.
A convenient size is one with a single lens about
one and three-fourths inches in diameter. This
permits the lines, figures, and letters on a chart
to be seen in sizes from one-half to one-fourth
smaller than their originals.
In observing the parts of the chart for an in-
dication of the size of the proposed reduction the
most accurate method is to hold the glass at
different distances above the sheet so that looking
through it with the left eye two or three or four
squares, depending upon the amount of reduction
desired, equals one square as seen by the unob-
structed right eye. Thus by superimposing and
comparing the images of both eyes the required
reduction can be measured. This enables a
comparison of the width of lines, figures, and
letters as originally placed with their width after
reduction and permits the determination as to
whether they must be made still wider or heavier
or larger in order to meet the reduced size.
Even with the use of the reducing glass the be-
ginner is likely to find at first that his lines,
curves, figures, letters, and so on when reproduced
do not appear to be as heavy or as large as he had
anticipated.
Primary Principles of Chartography 149
Without the emploj'ment of these rules and
aids in reduction one has to depend largely upon
guess work as to whether the chart and its parts
will present a proper appearance when reduced,
and guess work, as has been said, should be
eliminated from chartography. The student
must not forget that accuracy is a valuable
mental quality which is useful elsewhere than in
chartography', and if the practice of this art
teaches it to him he has gained an additional
asset of great usefulness.
THE FRENCH CURVES
Another tool that the student may find useful,
especially in cliarting curves, is what is known as
the "PVench curves." These are on sale at any
first-class store dealing in drafting instruments.
While they do not always in their entirety fit into
the complete curve the student luis to make, they
can be shifted forward or backward so as to cover
fairly accurately the lead-j)encil dots measuring
the points of contact of flie curve. Usually
they give a clean, smootli curve if care is exercised
in their use.
In most charts where the scale niiils permit the
curve to move regularly uj) or down across the
sheet, the curve appears smooth without sharp
movements that result in peaks. In all the
150 Chartography in Ten Lessons
illustrations in these Lessons these curves have
been drawn in freehand, and this method is
recommended as satisfactory. This peak-top
does not indicate as minute a degree of accuracy
in the figures upon which the curve is based as
does the smooth curve.
OTHER MECHANICAL AIDS
One serious drawback in making the letters by
hand is the length of time required, even after one
becomes proficient in lettering. Under conditions
where the number of charts to be drawn is large,
efficiency is best served and the cost of produc-
tion materially reduced if recourse is had to a
small printing press with about three fonts of
type of 18, 12, and 10 point, commercial Gothic.
The moderate expenditure will soon be com-
pensated by using for other work the time saved
from lettering by hand. Printed letters photo-
graph satisfactorily in almost any process of
reproduction.
Another recourse instead of drawing letters by
hand is to make use of gummed black paper
letters and figures which are for sale at first-
class stationery stores. These can usually be
pasted quite neatly on the chart that is to be
reproduced, if a light pencil line is made for a
guide along the bottom of the spacing for the
Primary Principles of Chartography 151
letters. This pencil line must of course afterwards
be erased.
CHECKING-UP THE COMPLETED CHART
After the drawing has been finished there
remains for the student a very important task.
The explanation of this task in detail involves
describing the concrete application of all the
rules and principles of chartography that have
been observed in the construction of the chart.
This is true in the .sense that the student must see
to it, by a rigid and thorough checking-up of the
lines and figures and letters and so on before the
chart leaves his hands, that all these rules have
been strictly applied. As related to the check-
ing up of certain features of the curve chart,
this ta.sk ha.s already been referred to in I^esson
IV, pages 50 and 51. The immediately follow-
ing statements apply particularly to the bar chart.
Each bar should extend to the point on the
chart that its statistical number as measured by ^
the scale determines — it should neither fall short
of this i)oint nor extend beyond it.
Be sure that each bar is f)roperly spaced from
adjoining bars.
In making the bars of a chart it is quite often
possible that all the space to the right of the
vertical scale or column of years and to the left of
152 Chartography in Ten Lessons
the ends of the bars, and from the horizontal
scale line to the base line, can be made black
with a small brush dipped in India ink, the ends
of the bars being squared with the pen. After
the ink dries the bars can easily be outlined and
separated from each other according to the ver-
tical scale units by drawing horizontal lines in
Chinese white. This expedient enables a great
deal of work to be done in a comparatively short
space of time, and the results are highly satis-
factory. When the India ink is used in this way
it is advisable to apply two or more coats or
washes in order to insure a uniform density of
surface.
Chinese white is an opaque composition which
may be thinned down to desired consistency by the
addition of water. Besides its use in separating
bars out of a block of black, Chinese white is also
excellent for concealing black ink lines or marks
where erasure is impracticable.
The scale units should be correct at each of the
points of measurement and neither to the right nor
left of their proper places.
The chart should imclude the statistical table
from which it has been made.
If it is found impossible to include the statistical
table on the chart it should be on an accompany-
ing or attached slip or sheet.
Primary Principles of Chartography 153
The table of figures should be correct and neat
and properly located and boxed without crowding.
The period of time column both in the table
and adjacent to the bars must be correctly and
properly alligned.
Be sure that no mistake has been made in copy-
ing any figures on to the chart.
The statistical table involving periods of time
should be presented with the earliest period first.
The source of the statistical table should in
every instance be given, preferably in the foot-
notes.
Instead of checking up the movement of the
bars or curves from either the statistical table on
the chart or the scale figures tl)emselves, reference
should be had to the original figures.
All additions, subtractions, multiplications,
divisions, and so on derived from the statistical
table should be computed at least twice and by
different f>ersons.
See that all horizontal lettering reads from left ^
to right and all vertical lettering from the base
of the chart uj>ward.
The title should l>e clear and concise and yet
comprehensive. It should have every word
spelled correctly and shouhl contain the fewest
possible words consistent with clearness of ex-
pression. It sometimes happens that the title
154 Chartography in Ten Lessons
can be improved in these directions over the first
selection of words after the student has been
working with the statistical material. Words as
well as letters in the title should be evenly placed
and spaced — none of them must be askew.
THE PROCEDURE IN CHECKING UP
It is an advantage in checking up a chart to
start with the title, next the horizontal scale, then
the vertical scale, the table of statistics, and then
relate the movement of the curves or bars to
these factors. The horizontal and vertical lines
forming the background of the chart must not be
overlooked as to their proper distance apart.
The foot-notes and the neat lines require equally
careful attention.
Make sure that the neat lines are wider or
heavier than the vertical and horizontal lines of
the framework.
Foot-notes should be as brief as possible con-
sistent with clearness, should read from left to
right, and should not be askew.
In selecting the designations for the curves and
bars, have the most conspicuous been made to
correspond with the particular statistical element
it is desired to emphasize? For instance, in bar
designations the solid black is generally more
noticeable.
Primary Principles of Chartography 155
Check carefully the key or legend designations
with those of the curves and bars to see that
they correspond accurately.
Have the proportions been correctlj^ determined
for the required reduction?
Be especially careful that all lead pencil and
unnecessary ink marks, used as guides or other-
wise, have been erased or removed. If not, in
case of reproduction these are likely to photograph
and thus affect disadvantageously the neat ap-
pearance of the chart.
CLEANLINESS ESSENTIAL TO NEATNESS
In handling a chart keep the hands clean,
especially from the drawing ink which will smear
the sheet. .Vn aid to this will be found by keeping
the ink bottle on a })lotter which will absorb drops
and i)revcnt them from getting on the drawing
board or table. Blot immediately every ink spot.
Never fold a rhart. Keep the .sheet flat or
roll it. A folded chart cracks or crea.ses the sheet
and breaks the lines, bars, curves, and .so on.
All checking and verification should be done
also by some f)iic other than the |>orson who drew
the chart so that there may \)v greater certainly in
the detection and correction of errors. For
even the best chartograjjher nuikes mistakes.
The student should assure himself before per-
156 Chartography in Ten Lessons
mitting the chart to leave his hands as completed
that in all respects it is in condition to receive his
final O. K.
PLOTTING THE CHART IN ROUGH OUTLINE
After the chartograplier has completed his
checking up he should devote several minutes to a
consideration of the possibility that he might
have selected a different method which would
have brought out the point of the statistics more
clearly. He will have fewer regrets if he adopts
and consistently follows the practice of first
plotting his chart in rough outline in lead pencil
at the very outset of his work. He should apply
this to several methods before finally determining
upon any. He will find that though this practice
takes a little time at first it will in the end greatly
expedite his work.
It should never be forgotten that as chartog-
raphy primarily supplements statistics with the
object of making them clear and comprehensible
at a glance, a chart that is not more clear in
exposition than the statistical data upon which
it is based has missed its object. Also it should
be remembered that the chart " tells the story " —
it should need very little explanation, if any.
Instructions to the lithographer should be clear
and definite. These may be written on a slip of
Primary Prixciples of Chartography 157
paper and attached to the drawing with a dip,
but a safer plan is to write them on the coordinate
sheet itself, preferably on the back.
Before sending the drawing to be reproduced
be sure to cut away the margin of the sheet where
the thumb tacks have held it in place on the
drawing board, as these punctures are likely to
show in the reproduced chart. Even when the
drawing is not to be photographed, such punc-
tures in the paper detract from the neat ap-
pearance of the finished chart.
Before deciding upon the uniform size of .sheet
for a number of different kinds of charts it is
advisa})le to consult the lithographer in order that
a size may be selected which permits of the least
possible waste or loss in cutting from the larger sheet.
It is imf)()rtant also to examine closely into
the quality of the {lajjcr of the reproduced chart.
The preservation of the chart depends to a large
degree upon this quality. Paper containing
sulphite pulj) or other chemicals suffers rapid
deterioration. U'ithiri a short time such paper
becomes brittle and di.scolored, and these defects
seriously affect the preservatif)ti of chart records
for any length of time. A high grade linen bond
paper, although it costs more i)er sheet, is less
expensive in the long run.
The checking up of the completed chart as well
158 Chartography in Ten Lessons
as the details of the planning and drawing should
impress upon the student the necessity for observ-
ing closely and carefully every factor with which
he deals. He cannot afford to overlook even
the smallest detail as every detail must be accurate
if the completed chart is to be accurate. This
attention to minor details fixes the mind upon
the correctness of the figures; on the accuracy
of the scale units; on the spacing of figures and
lines; on the spelling of words; on the correct
designation and spacing and length of the bars,
and so on. Looking for possible defects or
errors develops the critical faculties. In the
course of practice all these separate but important
details soon fix a habit of mind and that which at
first may be hard work sooner or later becomes
almost mechanical attention. Working with
tools that require accuracy in their use the
chartographer soon learns from mistakes he must
correct that it does not pay to make mistakes —
that it is a loss of time and energy and materials
— and he comes consciously to apply himself so
as to avoid their repetition in order not to be
compelled to do the work over again. Out of this
experience he learns eflSciency in the concen-
tration of his energies and in their application to
his specific task. Chartography is thus an
invaluable mental training. It lends accuracy to
Primary Principles of Chartography 159
constructive thinking; it leads to the further study
, of statistics and of the underlying forces back of
them, and by these and similar steps the pro-
gressive student develops his thinking caj)abilities.
QUESTIONS FOR SELF-EXAMINATION
1. What is meant by planning the chart? How does it
differ from plotting the chart?
2. Diacuss the importance of selecting the right method.
5. What are the essentials of good chartography?
4. How is the size of the chart planned?
5 How is a reduction in size of the original determined?
6. Of what assistance is the reducing glass?
7. What are "French curves"?
8. Describe the more important phases of checking up
the completed chart.
9. Summarize briefly the more important of the funda-
mental principles of chartography.
10. Of what value is chartography in training the mind?
This book is DUE on the Rist date stamped below
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JAN 4 1937,^ipf^
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