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Full text of "Graphic methods for presenting facts"

GRAPHIC METTOS 

FOR 

I^RESENTiNG FACTS 





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t ■%ILLARD C. BRINTON 



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WORKS MANAGEMENT LIBRARY 



GRAPHIC METHODS 



FOR 



PRESENTING FACTS 



BY 



WILLARD C. BRINTON 




NEW YORK 
THE ENGINEERING MAGAZINE COMPANY 

1914 



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COPYKIGHT, 1914 

By The Engineering Magazine Company 



TO MY MOTHER 



PREFACE 



IN the preparation of this book there has been a constant effort to present the 
subject to suit the point of view of the business man, the social worker, and the 
legislator. Mathematics have been entirely eliminated. Technical terms are used 
practically not at all. Since the readers whom it is most desired to reach are those 
who have never had any statistical training, consistent effort has been made to keep 
the whole book on such a plane that it may be found readable and useful by anyone 
dealing with the complex facts of business or government. Though written primarily 
for the non-technical man, it is hoped that this book may, nevertheless, prove con- 
venient to the engineer, the biologist, and the statistician. 

A definite effort has been made to produce a work which can serve as a hand book 
for anyone who may have occasional charts to prepare for reports, for magazine 
illustration, or for advertising. Unfortunately, there are extremely few draftsmen 
who know how to plot a curve or prepare any kind of a chart from data presented to 
them in the form of tabulated figures. Most draftsmen can plot a curve if they are 
given the data and an example showing the general type of chart desired. The execu- 
tive who desires a chart is usually too busy to stand by a draftsman and explain 
in detail just how the chart should be prepared as concerns those all important 
details of proportion, scale, width of line, etc. It is believed that the owner of this 
book wiU find it feasible to run through the various chapters and pages until he finds 
a chart most nearly like that which he desires to have made from his own data. 
A sample chart placed before any draftsman of average ability should give the drafts- 
man practically all the instruction needed for the preparation of a similar chart from 
other data. 

Much careful labor has been expended in so arranging the book that a busy 
reader may get the gist of the matter by looking at the illustrations and reading only 
the titles and the sub-titles. The main title under each illustration is intended to 
show exactly what the chart represents, just as if it were used in some publication re- 
lating to the particular subject matter of the chart. The sub-titles relate to method 
and give criticism of each chart as a whole. Though the text gives much more de- 
tailed information concerning method than can possibly be put into any sub-titles, the 
reader who examines only the illustrations and the titles, without any reference to 
the text, will undoubtedly get a major portion of the vital material in the book. It is 
believed that an average reader may go through the illustrations and the titles in 
about one hour. 

V 



VI GRAPHIC METHODS 

Many of the illustrations which have been borrowed for use in this book are 
criticized ad\'ersely. It is the hope that all such criticisms will be accepted as an 
honest attempt toward an advance in the art of showing data in graphic form. In 
fairness to the authors of those charts which are criticized, it must be said that there 
has been a very rapid advance in the art of graphic presentation within the last few 
years and that many of these men would not present the material to-day by the 
methods which may have been used some years ago in the preparation of certain 
charts shown here. Where charts are used and criticized adversely, the charts have 
been included only because it is felt that they show a practice which is rather common 
but is nevertheless of questionable desirability. 

Many of the suggestions for standard practice contained in this book should be 
taken as tentative only. The American Society of Mechanical Engineers has invited 
about fifteen of the chief American societies of national scope to co-operate by sending 
one member each to a Joint Committee on Standards for Graphic Presentation. 
Though this committee is not yet completely organized, and it will be some time before 
any report is available, the reader who desires further information regarding standard 
practice should be on the lookout for any reports which the joint committee may 
publish in the future. 

This volume may arouse in the minds of many readers a desire for more detailed 
information than can possibly be given here. The following books are suggested 
for the person who wishes to take up the study of statistics as related to the collection 
and interpretation of data without special reference to the methods of graphic pres- 
entation. The present work is necessarily limited to the consideration of graphic 
presentation, and those who wish to go further in the general subject of statistics 
should by all means consult books of the type exemplified by "The Elements of 
Statistical Method," by Willford I. King, The Macmillan Company, New York; 
"An Introduction to the Theory of Statistics," by G. Udny Yule, Grifiin and Com- 
pany, London; '"Elements of Statistics," by Arthur L. Bowley, Charles Scribner's 
Sons, New York; "Primer of Statistics," by W. Palin Elderton and Ethel M. Elderton, 
Adam and Charles Black, London; "Statistical Averages," by Franz Zizek, Henry 
Holt and Company, New York; "Statistical Methods with Special Reference to 
Biological Variation," by C. B. Davenport, John Wiley and Sons, New York. Any 
list of this sort is, of course, incomplete and these books are mentioned as only a few 
of those which may be found useful to supplement the study of the subject considered 
in this volume. 

Part of the matter here presented was given in lectures delivered at the Graduate 
School of Business Administration of Harvard University, the Amos Tuck School 
of Administration and Finance of Dartmouth College, the Northwestern University 
School of Commerce, and the College of Commerce and Administration of the Uni- 
versity of Chicago. Some of the material was presented before the American Society 
of Mechanical Engineers in New York. The advance presentation of matter in 
course of preparation for the press was made with the cordial assent and approval of 
the publishers of this work. 

I am greatly indebted to Mr. Edward Scott Swazey, Mr. Curtis Prout, and Miss 
Katherine Tyng, for valuable assistance and suggestions received during the prep- 
aration of this book. Chapter XV is largely based on an article prepared at the 



PREFACE Vll 

suggestion of the author by Mr. Pierpont V. Davis of New York City and pubUshed 
by Mr. Davis in Moody's Magazine. I wish also to express my thanks to numerous 
friends who have given excellent suggestions and criticisms during the time the 
manuscript was in preparation. 

If this book should receive any commendation, much of that commendation will 
be the result of good fortune in securing an unusually high grade of drafting skill on 
those charts which are original. 

The author cannot be responsible for the accuracy of the data presented in many of 
the charts shown. The illustrations have been selected partly on account of the 
educational value of the facts, but chiefly because of the methods used in presentation. 
Though great care has been exercised to make the titles complete, the elaboration 
of titles beyond their wording in the original source may have resulted in some in- 
accuracies. 

As far as the author is aware, there is no book published in any language covering 
the field which it has been attempted to cover here. If the presentation of the 
subject appears to be crude and incomplete, it is hoped that any critic will keep in 
mind that there is httle precedent for guidance in a territory so unexplored. 

It is impossible entirely to avoid errors in any book containing as much detail as 
results here from the numerous complex illustrations and the necessity of carefully 
worded language to give condensed information. Any corrections, criticisms or 
suggestions will be appreciated by the author. 

WiLLARD C. BrINTON 

New York, June, 1914 



CONTENTS 



PAGE 

Chapter I. Component Parts 1 

The need for graphic methods in presenting facts. The method of pres- 
entation as important as the data. PossibiKty for standard methods of 
presentation. Tabulated figures versus graphic methods. A total shown 
with its component parts. The horizontal bar. The circle and sectors. 
Subdivision of components. Separate bars totalling 100 per cent. Charts 
giving numerous subdivisions. Organization charts. Routing charts 
for manufacturing plants and offices. 

Chapter II. Simple Comparisons 20 

Errors due to comparing by areas or by volumes instead of by one 
dimension only. The use of graphic methods in geography books. The data 
should be shown on the face of each chart if possible. Good and bad 
methods of including the data. "Eye-catchers" to attract the attention 
of the reader. Criticisms of methods commonly used. Certain bars 
made especially prominent. Increases and decreases. Lines connecting 
different bars. Examples of various good methods. 

Chapter III. Simple Comparisons Involving Time 36 

Impossibility of accurate interpretation when circles of different size are 
compared. Errors when pictures of the human figure in different size are 
compared. Methods which are popular and accurate as well. Examples of 
bad practice in arrangement and the same data correctly represented. 
Vertical bars giving the general effect of a simple curve. Curve plotting. 

Chapter IV. Time Charts 53 

Horizontal bars drawn to a scale of time. Complex time charts by which 
the relations of numerous horizontal bars may be studied. Time charts 
showing bars combined with a curve expressing totals. Curves to study 
whether time schedules are maintained. Rank charts to portray the rank of 
different individuals at various times. Rank charts showing actual rela- 
tive rank at any time and also changes in rank at various times. Train- 
dispatching charts. Time-distance curves. 

ix ■ 



GRAPHIC METHODS 



Chapter V. Curve Plotting 69 

The desirability of using only well-known methods of presentation. 
Curves permit a more rapid and more accurate interpretation than possible 
by other methods. Studies of the causes of crests and valleys of curves. 
Curves especially needed for complex data. The use of curves in advertising. 
Polar co-ordinates objectionable for presenting statistical data. Examples 
of good practice in curve plotting. 

Chapter VI. Curve Plotting Continued 84 

Independent and dependent variables. Confusion caused if the inde- 
pendent variable is not used for the horizontal scale. Examples showing 
correct arrangement of scales. Curves to advertise newspaper circulation. 
Curve charts combining much complex information. The use of two sets of 
co-ordinate ruling for the vertical scale. Moving averages. Smoothing 
curves. Index numbers. Weighted averages. Curve studies of national 
prosperity. . . 

Chapter VII. Comparison of Curves 107 

Similarity and contrast of curves plotted in the same field. The zero 
of the vertical scale should be shown on the chart. Advantages of plotting 
curves for different years one above the other for comparison. Contrast 
in shape of curves plotted in separate fields. Advantage from shading the 
space under a curve. Numerous dissimilar but related curves on the same 
sheet. Errors resulting if curves not having the same zero line are compared. 
A total curve plotted from several other curves. Inverse relations, one curve 
trending downward when another trends upward. Study of correlation 
by plotting a curve from the data of two other curves. The angle of a curve 
on ordinary rectangular co-ordinates tells nothing about the percentage rate 
of growth. Disadvantages of the arithmetical scale ruling for curve 
plotting. Advantages obtained by plotting curves on logarithmically ruled 
paper. 

Chapter VIII. Component Parts Shown by Curves 138 

Use of vertical bars with components totalling 100 per cent. Shaded 
area under a curve when the height of the total field represents 100 per 
cent. The use of several areas in a curve field which totals 100 per cent, 
in height. A contrasting method of showing all curves plotted separately 
but from the same zero line. Universal co-ordinate paper for convenience 
in curve plotting. Total curves with component areas so that any point on 
a curve totals 100 per cent for the height of the areas beneath. 

Chapter IX. Cumulative or Mass Curves 149 

Factory production schedules and actual outputs plotted on a cumulative 
basis. Curves for income and expense on a cumulative basis. Various uses 
for cumulative curves. Cumulative curves with lines drawn to show rate 



CONTENTS XI 



of change. A grand total cumulative curve plotted from several other 
cumulative curves. Cumulative curves for the determination of storage 
requirements for water supplies. 

Chapter X. Frequency Curves. Correlation 164 

The arrangement of objects so that their position shows a crude frequency 
curve. Vertical bars to represent frequency. Frequency curves. The 
"mode." Frequency curves much easier to interpret than charts using 
bars or areas. Cumulative frequency curves. The use of cumulative 
frequency curves for business problems. Cumulative frequency curves 
preferably plotted on a "more than" basis instead of on a "less than" 
basis. Necessity for making the independent variable the horizontal 
scale. Wage comparisons for industrial work. Studies of the percentage of 
clerical work and percentage of revenue from orders of various sizes. Pin 
boards to record costs of doing work on orders of different size. Theoretical 
curves for percentage of clerical work and percentage of revenue from 
orders of different size. The Lorenz curve. Correlation curves. "Shot- 
gun" diagrams. Plotting curves to represent numerous points. Shaded 
areas to represent numerous dots. Correlation charts for two independent 
variables. Isometrically ruled paper for chart work. 

Chapter XI. Map Presentations 208 

Map presentation of prime importance. Shading of different areas. The 
Ben Day method of mechanical shading. Lines of equality. Profiles. 
Maps with circles or dots representing quantities. Shaded areas with a 
key to represent quantity. Miscellaneous methods. Map charts showing 
traffic. Map models with built up strips to show quantities. 

Chapter XII. Maps and Pins 227 

Map tacks projecting above the map. Map pins pushed in till the heads 
touch the map. Photographing pin maps. Mounting maps for use with 
map pins. Wall maps for use with pins. Map cabinet systems. Pin maps 
for advertising work. Pins bearing identifying numbers. Spot maps to a 
scale with each dot representing some large quantity. Routing systems. 
Various types of pins and beads available. Bead maps and their great 
advantages. 

Chapter XIII. Curves for the Executive 254 

Peak-top curves versus flat tops. Methods for combining curves with 
figure^ recording the data. Cards for plotting curves for operating records. 
Advantages of the card method for instantaneous comparison of different 
curves. Typical operating curves for a manufacturing business. Typical 
records for a selling organization. Arrangement of the card system for exten- 
sion with increase of business. Moving average curves for operating re- 
cords. Record cards for preserving all information regarding each curve. 



Xll GRAPHIC METHODS 



Chapter XIV. Records for the Executive 288 

Need for complete records in curve form relating to all main features 
of a business. Curve-card filing methods. Blueprints from the curve 
cards allow a cross-index of all important operating curves. A complete rec- 
ord department for a business. Methods for keeping records as used by 
various large corporations. The need for education in the interpretation of 
curves. Curves in conference meetings by using a reflecting lantern and 
the curve-record cards without lantern slides. Curves on swinging-leaf dis- 
play fixtures. 

Chapter XV. Corporation Financial Reports 307 

The annual report of corporations not usually put in form to permit 
intelligent comparison by the stockholders. Records of previous years 
not usually given. The number of stockholders constantly increasing. 
Best policy is to give complete and clear information. Recent examples 
showing bad practice. Curves for the United States Steel Corporation as 
a suggestion for the type of chart to be included in a corporation annual 
report. Charts should be a feature of the annual report of every large 
corporation. 

Chapter XVI. General Methods 321 

Methods for collecting and tabulating data. Punched-card sorting 
and tabulating machines. Use of tabulating machines for manufacturing 
records and for analyses of selling results. The slide rule as a great con- 
venience. The use and abuse of significant figures. Photographic copying 
of charts. Use of the reducing glass. Preparation of copy for the engraver. 
The Ben Day process. Charts for two independent variables. Card-board 
models. Solid models. The desirability of curves and charts in political 
campaigns. The projecting lantern with charts for campaign purposes. 
Methods for presenting election returns to large numbers of people. Charts 
in parades. 

Chapter XVII. A Few Cautions 344 

The importance of clear and accurate titles. Symbols which are easily 
remembered. No necessity for plotting curves vertically. Errors resulting 
in interpretation of curves if the zero of the vertical scale is not shown on 
the chart. The selection of scales for curve plotting. Different impressions 
from curves from the same data but with various scales. Optical illusions 
which may afl^ect graphic work. A checking list for final inspection of 
graphic presentations. Need for standard rules of grammar for the graphic 
language. A few suggested rules for graphic presentation. Great ad- 
vantages may result if graphic methods are more widely used for portray- 
ing quantitive facts. 



GRAPHIC METHODS 

FOR 
PRESENTING FACTS 



^^ 



GRAPHIC METHODS FOR 
PRESENTING FACTS 



Chapter I 
COMPONENT PARTS 

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 happens 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 readily enough to overcome the 
opposition. It is often with impotent exasperation that a person 
having the knowledge sees some fallacious conclusion accepted, or 
some wrong policy adopted, just because known facts cannot be mar- 
shalled and presented in such manner as to be effective. 

Millions of dollars yearly are spent in the collection of data, with 
the fond expectation that the data will automatically cause the cor- 
rection of the conditions studied. Though accurate data and real 
facts are valuable, when it comes to getting results the manner of 
presentation is ordinarily more important than the facts themselves. 
The foundation of an edifice is of vast importance. Still, it is not the 

1 



2 



GRAPHIC METHODS 



foundation but the structure built upon the foundation which gives 
the result for which the whole work was planned. As the cathedral 
is to its foundation so is an effective presentation of facts to the data. 

We daily see facts presented in the hope of creating interest and 
action for some really worthy piece of work to benefit the people as 
a whole. In many of these cases the attitude of the person presenting 
the matter seems to be that the facts will speak for themselves and that 
they need little or no assistance. Ordinarily, facts do not speak for 
themselves. "When they do speak for themselves, the wrong conclu- 
sions are often drawn from them. Unless the facts are presented in a 
clear and interesting manner, they are about as effective as a phono- 
graph record with the phonograph missing. 

If it were more generally realized how much depends upon the 
method of presenting facts, as compared with the facts themselves, 
there would be a great increase in the use of the graphic methods of 
presentation. Unlimited numbers of reports, magazines, and news- 
papers are now giving us reams of quantitative facts. If the facts 
were put in graphic form, not only would there be a great saving in 
the time of the readers but there would be infinite gain to society, 
because more facts could be absorbed and with less danger of mis- 
interpretation. Graphic methods usually require no more space than is 
needed if the facts are presented in the form of words. In many 
cases, the graphic method requires less space than is required for words 
and there is, besides, the great advantage that with graphic methods 
facts are presented so that the reader may make deductions of his 
own, while when words are used the reader must usually accept the 
ready-made conclusions handed to him. 

In many presentations it is not a question of saving time to the 
reader but a question of placing the arguments in such form that re- 
sults may surely be obtained. For matters affecting public welfare, 
it is hard to estimate the benefits which may accrue if a little care be 
used in presenting data so that they will be convincing to the reader. 
If the average citizen, and especially the business man, knew how to 
uiterpret charts and curves, it would be feasible to convey to him in 
effective form those facts relating to broad public improvements, 
public-service operation, and national, State, or municipal manage- 
ment, which might affect the whole fabric of our civilization. Archi- 
medes wanted only a fulcrum for his lever and he would move the 
world. If the world is ever moved it will probably be by facts properly 



COMPONENT PARTS 3 

presented. The method of presentation is the fulcrum without which 
facts, as a lever, are useless. 

The preparation and interpretation of simple charts and curves 
should be taught in the public schools as a part of arithmetic. The 
work of kindergarten nature now done in the lower grades of the 
public schools could very readily be extended so that the pupils would 
be making charts and curves without realizing that the work (or play) 
had any relation to mathematics. Text-books for geography are al- 
ready making effective use of charts. In the public schools of Newark 
and of Trenton, New Jersey, grammar-school pupils are preparing 
charts and plotting curves relating to records which show the present 
condition and recent development of their home city. The principles of 
charting and curve plotting are not at all complex, and it is surprising 
that many business men dodge the simplest charts as though they 
involved higher mathematics or contained some sort of black magic. 

If an editor should print bad English he would lose his position. 
Many editors are using and printing bad methods of graphic presenta- 
tion, but they hold their jobs just the same. The trouble at present 
is that there are no standards by which graphic presentations can be 
prepared in accordance with definite rules so that their interpretation 
by the reader may be both rapid and accurate. It is certain that 
there will evolve for methods of graphic presentation a few useful 
and definite rules which will correspond with the rules of grammar 
for the spoken and written language. The rules of grammar for the 
English language are numerous as well as complex, and there are about 
as many exceptions as there are rules. Yet we all try to follow the rules 
in spite of their intricacies. The principles for a grammar of graphic 
presentation are so simple that a remarkably small number of rules 
would be sufficient to give a universal language. It is interesting to 
note, also, that there are possibilities of the graphic presentation be- 
coming an international language, like music, which is now written 
by such standard methods that sheet music may be played in any 
country. 

With oral and written language and with tabulated figures also the 
reader sometimes draws conclusions regarding the relative importance 
of different things from the comparative length of time or amount of 
space used in presentation. Graphic methods overcome this difficulty 
by showing quantitative facts in true proportions which give instantly 
the correct interpretation. In tabulations like that on page 4 it is only 



4 GRAPHIC METHODS 

the highly skilled reader who can refrain from regarding the five differ- 
ent items listed as of somewhere nearly equal numerical importance, 
simply because the five different items are given exactly the same space 
and prominence when written down on the page. 

Percentage op Each Race in the Population of the World 

Yellow 45 

White 41 

Black 11 

Brown 2 

Red 1 

It requires mental concentration in interpreting even these simple 
figures to get the correct impression of the very large percentage of 
the two chief races and the numerical insignificance of the one last 
named. If these data were shown in a simple horizontal bar, somewhat 
like that seen in Fig. 1, the relative proportions of the different races 



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Scale l«=»Cent. 

— 5 Cents 



Fig. I. Disposition of a s-cent Fare Paid to the Boston Elevated Railroad in the Year 

Ending September 30, 1909 

The horizontal bar gives an especially good method for showing component parts 



COMPONENT PARTS 



would instantly be seen without any mental effort on the part of the 
reader. 

Fig. 1 is a very satisfactory form of chart to bring out the component 
parts of any group total. The horizontal bar need be made only wide 
enough to show the various kinds of shading necessary to give a good 
contrast. Engineering dimension lines above each block in the bar are 
of great advantage 50% 

for convenient read- 
ing. The dimension 

lines permit of group- y<^rVh--''- ^'^<>';"--^-i'>'v-^;v /-^i^'^VivSo:^'^ 

ing in such a manner /'*^^•••X^";^^^'^;:i•>^i^^f^•^ 

that several of the 
detail blocks could 
be included in vari- 
ous sets of dimension 
lines to show such 
items as total fixed 
charges, total operat- 
ing expenses, etc. 

In this type of 
chart the actual 
figures representing 
the value of the com- 
ponents should be 
given for the use of 
any reader who may 
wish to draw his own 
conclusions or to 
make new combina- 
tions of figures dif- 
ferent from those shown in the chart. As a general thing it is always 
desirable to have full data given on any chart. Fig. 1 gives all the data 
without in any way detracting from the ease of reading the chart itself. 

It would be desirable to have a large number of the illustrations 
in this book printed in color. Charts which are made in color can read- 
ily bring out points which are not easily portrayed when only black ink 
is used. The reader should keep in mind for his own work that he 
should use colors in making those charts where colors are economically 
possible. For the purpose of this book, color printing is prohibitive 




Disposition of the Gross Revenue of the Bell Tele- 
phone System for the Year 191 1 

This chart was taken from the annual report to the stockholders of the 
American Telephone and Telegraph Company for the year ending 
December 31, 1911 

The circle with sectors is not as desirable an arrangement as the hori- 
zontal bar shown in Fig. 1 



6 



GRAPHIC METHODS 



on account of the cost. In printed reports, in magazine articles, and 
in magazine advertising, color printing is not at the present time com- 
monly available. The illustrations of this book will accordingly show 
what can be done in printing complex charts with only one color of ink, 

under the same conditions 
that would be found in the 
preparation of material for 
magazine articles, printed 
reports, and ordinary pro- 
spectus or other advertis- 
ing matter. 

Fig. 2 is a form of chart 
used probably more widely 
than any other form to 
show component parts. The 
circle with sectors is not a 
desirable form of presenta- 
tion, however, because it 
does not have nearly such 
flexibility as the method 
shown in Fig. 1. The sector 
method does not permit of 
convenient arrangement of 
names for the different 




Fig. 3- 



The Survey 

Disposition of a Family Income of from 
$900 to $1000 

This cut shows an attempt to put figures in popular form. 
The eye is likely to judge by the size of the pictures rathei' 
than by the angles of the sectors 



components. Note that the direction of the lettering must be reversed 
as the eye proceeds around the circle. In this case, "Interest and 
Dividends" reads upward while "Materials, Rents, Traveling Ex- 
penses, etc." reads downward. Another disadvantage of the sector 
method is the impossibility of placing figures in such manner that they 
can be easily compared or added. The horizontal-bar method permits 
of placing figures so as to keep the decimal points in line, thus making 
it possible to add the whole column of figures relating to the various 
components. 

The sector method is probably so widely known through presentation 
in exhibits, illustrations for popular magazines, etc., that it is more 
generally understood than any other niethod now in use. The more 
easy reading of the wedge or sector chart is, however, largely due to 
habit. If the horizontal-bar method of Fig. 1 were used as frequently 
as the sector method, it would be found in every way more desirable 



COMPONENT PARTS 



UOSTTHROUOH RADIATION, LEAKAGE OF STEAM ETC 



LOST THROUGH UNCON5UMEO FUEL IN ASH 



i.G5TJN THE FORM QF UNCONSUMEI? FUEL IN THE 
CfNDEfIS AND SPARKS 



LOST (N OASES DISCHARGED FROM STACK 



LOST IN VAPORIZING MOISTURE IN COAL 



lOO 3 



L. 50 




than the sector method and would, in a very short time, become so well 
known that it would be read much more quickly and accurately than 
the method involving sectors. 

In Fig. 4 a double scale is used by which the same data can be 
interpreted from two different standpoints. On the left the scale is 
given in millions of tons, and on 
the right in millions of dollars. 
The reader can interpret the chart 
from whichever standpoint he 
prefers. Though this chart is ar- 
ranged vertically instead of hori- 
zontally, it really makes little 
difference which way the bars are 
placed. As a general thing, the 
horizontal arrangement lends itself 
more readily to the use of type so 
that the reader may read type 
statements without having to turn 
the book. 

In Fig. 5 the whole population 
of the United States is divided first 
into native white, foreign white, 
and colored, then each of these 
groups is subdivided according to 
place of birth. This is an excellent 
type of chart to use if subdivi- 
sions in the component parts of 
any unit have to be shown. If the 
scale to which the chart is drawn 
is specified, it is possible for the 
reader to measure, with an ordi- 
nary ruler or with an engineer's 
scale, the exact percentage size of 
each of the different components. 



OTtLlZED BY BOILER 



I 



CONStJMeO IN STARTING flBES^ 

K^PlNa^NGlNE HOT WHILE STavdiNG^ 

AND LEFT IN FIRE aOJ^ aTCNDOI^ RUN^ESTimATEd) 



Adapted from Data, Chicago 

Fig. 4. Utilization and Accompanying 
Wastes of One Year's Coal Supply for 
Locomotives on Railroads of the 
United States 

The double scale permits reading this chart in tons 
or in dollars 



If the chart is made on co-ordinate paper with ruled squares, the 
reader can obtain the size of each component direct from the co-ordinate 
lines. The trouble, however, with using co-ordinate paper for charts 
of this sort is that the components are likely to begin and end at points 
not falling upon the co-ordinate lines, thus making it necessary to count 



8 



GRAPHIC METHODS 




fractions of a division at both beginning and end of the component 
to be measured. The best thing in charts of this kind is to use unruled 
paper, and specify the scale. The reader, if he wants the exact data, can 
take his measurements with a ruler. The engineer's scale has its sub- 
divisions in decimals and hence is the most convenient scale for chart 
work. An engineer's scale should be part of the equipment of every 
person who has charts to make. 

Another method of showing the relative size of the divisions and sub- 
divisions of a unit or group is shown 
in Fig. 6. In this case we have the 
total population of the United States 
split into its component groups accord- 
ing to the condition in regard to mar- 
riage. The subdivision bars, given be- 
low the total bars, show the conjugal 
condition in each of the main groups 
which enter into the total population. 
Each of these main-group bars is cross- 
hatched to show the conjugal condition 
within the group. The combined length 
of the four bottom bars is equal to the 
length of the total-population bar 
shown at the top. These same data 
could have been presented by the 
method shown in Fig. 5. It will be 
noted, however, that in Fig. 6 all the 
figures have been included, and are 
available for reference purposes with- 
out detracting from the utility of the chart itself. The lettering was 
done by hand and shows the possibilities for neatness resulting from 
hand work when a skilled draftsman is employed. In many ways the 
method of Fig. 5 is preferable, but it is probably true that Fig. 6 
would be more readily understood by the average untrained reader. 

Where there are a large number of items to be compared and the 
components of each item are given, the method of Fig. 7 is a very 
convenient one. The Census Atlas for the 1900 Census contained 
manjr pages of charts of this type for its comparisons of different States. 
By placing bars for all the States on one page, the total for the country 
is shown as 100 per cent in the vertical direction. No vertical scale 



I I I I i=f Scale fo inch equals 5 perceni 

United Slates Statistical Atlas for the Census of 1900 

Fig. 5. Elements of the Population 
of the United States in 1900 

Here the components of the total population 
are shown in their relative sizes on the 
vertical scale. Each component is also 
divided into different subdivisions whose 
percentage size may be read from the 
horizontal scale. This is an admirable 
method of presentation if components 
must be subdivided 



COMPONENT PARTS 



TtoTAU Population, .76.303.367 



Native White 
Nativc^Varents 



. . .40,949,362 



Native^wmitc 
foreign '^parents ' 



POREION WHITE 10,213.817 g S.znev'B' 




NeORO .e.B34,094 



^ 



Fig. 6. Conjugal Condition of the Population of the United States in 1900 

The tour lower bars show components of the total population represented by the upper bar. The combined 
length of the four lower bars equals the length of the upper bar 

is used, all the bars being made of equal width. In this particular 
case (Fig. 7) we have a total split into its components and again sub- 
divided so as to show the prevalence of a second factor which is in- 
cluded in the first. Thus, we see the proportion of illiterates in each 
of the main groups of population for each State. All of the States 
are shown on the same basis, since all are depicted by bars of the same 
length representing 100 per cent. It is not easy to make a clear black- 
and-white drawing if one kind of cross-hatching must be placed on 
top of another kind. Fig. 7 shows that it is possible, however, to 
superimpose two kinds of cross-hatching and get a drawing that 
is fairly clear. The facts in this chart would have been brought out 
better if colors had been used for the main divisions of population. 
Ruled cross-hatching in black to represent the percentages of iUit- 



New YorK 




West Virginia 



Mississippi 




Fig. 7. Males of Voting Age in certain States, in 1900, by Color and Nativity and 

by Illiteracy 

A method for two successive divisions into components is shown here. The proportion of illiterates in each 
groHp is brought out by the horizontal ruling 



erates would show clearly through 
the colored mk used for the main 
divisions. 

Though it would have been 
possible to portray the data given 
in Fig. 7 in the form of the square 
shown in Fig. 5, the square would 
take up so much room on the page 
that the method would be prohib- 
itive if all the States had to be 
shown on one page for comparison. 
With the method of Fig. 7, it is 
possible to place on one page all 
the forty -eight States so that com- 
parison between States can be 
made instantly and accurately. 

Fig. 8 shows another method of 
analyzing to 100 per cent in each 
of two directions. The method of 
Fig. 5 could be used for these data, 
but would not be as easy to under- 
stand as the method of Fie 8 
Fig. 5 would require most careful 
cross-hatching to bring out the ver- 
tical subdivisions for each of the 
different States. By using the 
method of Fig. 8, each State can 
be shown distinctly even if it is 
only the width of a line, as in the 
case of Nevada or Wyoming. The 
wide space between the different 
bars showing the States adds tre- 
mendously to the clearness of the 
diagram. The vertical scale for 
the width of bars is made accord- 
ing to the number of electoral 
votes from each of the States. 
New York has more electoral votes 
than any other State, and is there- 

10 



TArj- taia. 



TAfJ t900. 



BffYAN I90B. 



so CO 7o\a^ 90 looyi 



MASS. u>w////////////4 ^-mWfs^^^-^^^^ 
5D. e 

Calif tf^^^ 




Tenn. IV^/^/w////jVs^^^^^^^^^^t^.■'J^?^tg<x«>?^-:^'^y>■■w;w<X.'g^ 



Tex y/wAv\^V'j<j.y^<^»«'.j»^«Htf^a^Bj»^! 

La 

Miss 

SC 



) PARTtI S 



DOTTED LINC DIVIDES© 
CENTAGE' to the left, BRYAN 
HEAVY LINES PIVIDE @ PAR' 
FROM THE LEFT, TAFT, ROOSI 
RE.P. PR 

V//M}:m \^mm^ mmm 



y.'<H!-!S,11 



kyy///yyy/y^\\m^\\< ■^^a^^f^^^mm^ 



,-^.v^vvsa^<.MM'-rj 



■L»jj.-A^-.-.».''.>L"^s;'-w;;q 



■-t^L-^^ K^.'^ *H it A." ■■ ^.RAg 



zszzssssi^s^mi^szzs 



^S^^^SS 



IN 1908, TAFT PER— 
TO THE RIGHT. 
IE.5 IN I9I£.' BEGINrllNS 
WILSON. 

DEM. 



Fig. 8. 



Prof. Intng Fisher In the New York Times 



The Vote for President in 1908 
and in 1912 by States 

Compare this with Fig. 5 where the vertical scale 
IS continuous, without the gaps necessary here 
in order to distinguish different States 



COMPONENT PARTS 



11 



Relations Between Annual Cost of Motor Trucks 
And Characteristics of Service. 



fore given greater width than any other State in proportion to the 
greater size of its electoral vote. The horizontal division has been 
made according to the percentage number of votes for each of the 
main political parties. Two different elections are shown by using 
solid lines and dotted lines. The chart proves that the Democratic 
vote of 1913 was essentially the same as the Democratic vote in 1908, 

and that a Demo- 
crat was elected 
President in 1912 
largely because 
there were three 
candidates in 1912 
and only two in 1908. 
This is an admirable 
piece of presentation 
even though the 
lettering and draft- 
ing are not Cjuite as 
good as they might 
have been if more 
care had been used, 
though probably al- 
lowance must be 



a) Character o( work; , 

Size aod type of truck 

Nature of ioads 

Number of cars.r 

Distance per day 

Number of stoos per day- 
DayB In Bervlce 



;b) Roads and climate: 

Road surface 

Grades 

Other street traffic 
Climate 



c) System of operating: 

Routing 

Loading sod unloading. . 

OverloRalog 

OvernDeedlQ a 

Ganire faclllUea 

Care of cars 



tbdlrectly as ibft Iteui afferts •distance 
Indirectly as,rbls llem affect^ distapce 



Massachusetts Institute of Technology — Vehicle Research 



Fig, 9. The Factors Entering into the Annual Cost of made for the limit a- 
^. . , V Motor Trucking Service ^.^^^ ^^ ^^^^ 

Ihe scheme of this convenient form of tabulation is somewhat similar ^ _ i -i 

to that of Fig. 5. Here, however, the components are only named prCSSWOrk in daily 
without denoting their relative size or importance ... 

newspaper prmtmg. 
When studying a number of varied components, and the relations 
of each to every other one, a chart like Fig. 9 is frequently of great 
assistance. This chart shows that certain components are affected by 
features which may not affect other components. We have here the 
total cost of motor trucking, studied according to the components of 
the cost and also according to the conditions which produce those 
component costs. We may consider either the service conditions or 
the cost components. We have 100 per cent in the horizontal direc- 
tion and 100 per cent also in the vertical direction. The total of the 
components in either direction is 100 per cent, but the actual size of 
each is not given because the size is not known or because it may 
vary from time to time. 



12 



GRAPHIC METHODS 




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COMPONENT PARTS 



13 




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14 



GRAPHIC METHODS 













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4 



COMPONENT PARTS 



15 



STOCkHOLDCRS 



BOARD OF DIRECTORS 



SCCOND VICE PRESI 
DENT AND SECRETARY 



PRESIDENT 



[5"5"5~Q''5"^ 



TREASURER 



1 ASSISTANT TnCASUflCn 



BOOKKEEPERS 



ACCOUNTING 



FIRST VICE-PRESIDENT 
AND GENERAL MANAGER 



ISHimna 
dkpahtmeni 



ComT 

OCPAKTMCNT 

CHItr CLKWK 



cHUr clewkI 



ACCOOHTANTS 



dB^bcb [55Bd^ 65^5^ 



ocnchal supenintcnocnt 

<MAKINO) 



BALES OCPAHTMENT 
MANAQEfl 



CLINKS TIME KEEPERI 



APUEiiTrsiNG I bbbbiid) t5i5u^5& 



DEPARTMENT 



SALESMEN BflANCH HOUSES 



CONSTRUCTION AND> 
MCCHANtCAL 
DEPARTMENTS 



MTTCNM MAKINd 



mountino 

[assemblino; 



I I fORCMENJ I I I FOREMEN [~J r^fREMcij"! Q^^"^^"] F^'^^'CIl 

Ytt rrru T T Tfrfi T T T TrrfrtTrr 

cbchcbcb db d: di cb □□ a □□□□□□□□□ □ 



WORKMEri 



Si/slcm 



Fig. 13. Organization Chart of a large Company Manufactiiring Stoves 

A complete organization chart should always include the stockholders and the Board of Directors as shown 

here 

A diagram like that of Fig. 10 may be of considerable assistance 
if a very complex relation of components has to be shown. In Fig. 9, 
the components have only one subdivision. In Fig. 10, however, 
we have fuel cost subdivided as many as five different times. Though 
the method of Fig. 10 could easily be used for the data of Fig. 9, that 
of Fig. 9 has its advantages in that it makes printing cheaper and 
is therefore desirable whenever it can be used. Fig. 9 can be prepared 
on a typewriter or can be set up by any printer, while Fig. 10 requires 
the making of a drawing. 

In Fig. 11 the ramifications of the influence of the J. P. Morgan 
Company and various large banking concerns are shown. This chart, 
taken from the Pujo Monej^ Report, was drawn originally in several 
different colors of ink. Though the windmill effect of the chart is 
rather disagreeable to the eye, the chart nevertheless shows the ap- 
plication of the graphic method to such complex situations as it is 
almost impossible to portray with language alone. 

Organization charts are not nearly so widely used as they should 
be. As organization charts are an excellent example of the division 
of a total into its components, a number of examples are given here 
in the hope that the presentation of organization charts in convenient 
form will lead to their more widespread use. 



16 GRAPHIC METHODS 

It has been well stated that an organization chart closely resembles 
a genealogical tree. 

iVuthority reaches down through the several branches of an organization like 
descent of blood, and, if properly planned, it will be as irregular for a factor in an 
organization to be in doubt as to the person in authority over him as for the child 
to deny the parentage of his father. Such a chart should be drawn for every or- 
ganization, even more especially for those organizations which are short-handed ex- 
panding businesses in which one man holds the authority of several positions. It should 
be graphically shown what positions are onlj^ temporarily filled, so that when new men 
are engaged they will fit into the scheme with functions planned. Then there will 
be no irritation, no feeling on the part of some that their authority has been usurped. 

If such a chart is made there will be fewer cases of conflict or of short-circuiting 
of orders. Every command from the general that is given directly to the private 
over the head of the captain weakens the authority of the captain over the private 
and weakens the authority of the general over the captain. A military organization 
is so planned that each man knows from whom to take orders, but business proceeds 
too much on personal authority. An organization chart will help to prevent this. 

Of course, no two businesses can have identical organizations. The skeleton 
may be the same, however, and just as the proper study of the functions of the human 
body begins with the skeleton, so the study of organization should begin with those 
simple outlines which appear, in the main, in all completely and successfully organ- 
ized businesses. Very few enterprises are organized properly. Very few have an 
organization that can be charted at all. That is one reason why there is such in- 
efficiency in industry. 

As a general thing it is better to have an organization chart begin 
with the stockholders and then show the board of directors as inter- 
mediate between the stockholders and the president. In reality, a 
typical organization chart represents the shape of an hour glass or a 
double funnel, with the large number of stockholders on one side and 
the large number of employees on the other. The board of directors, 
the president, and the officers of the company are at the narrow part, 
with the president as the intermediary through which all transactions 
take place between the large number of stockholders and the large 
number of emploj^ees. 

The routing of work through the many processes and departments 
of a large plant is a subject of such great importance that charts are 
frequently desired for the study of such routing. Fig. 14 is a fairlv 
good example of this class of chart. In a complete chart, the depart- 
ments would of course be designated for easy reference, by names, 
numbers, or letters. Colored ink could be used to keep one class of 
work distinct from another. Colored inks would help tremendously 



COMPONENT PARTS 



17 




The Enn'necring Magazine 



Fig. 14. Graphic Representation of Processes and Routing in a Representative Plant 

Names of departments and operations are omitted by request of the proprietors of the establishment in 

which this chart was made 



18 



GRAPHIC METHODS 



i-r' 







COMPONENT PARTS 19 

in simplifying Fig. 14, but are not available here because of the pro- 
hibitive expense of color printing. Colored drawing inks can be ob- 
tained at almost any stationery store. A bottle of each color should 
be a part of the equipment of any person who is regularly doing chart 
work. Note in Fig. 1-4 the small curves drawn where one route line 
crosses another line. By means of small curves like these it is very 
easy to keep the lines separate and to show- clearly that the lines 
crossing each other are entirely independent. 

Orders and other printed forms sent through a large organization 
must follow a routing entirely distinct from that actually followed 
bj' the heavy materials. The routing of printed forms in a large 
business is, in itself, a matter worthy of most careful study to get a 
true understanding of their complex movements. A clear idea of 
office system is almost impossible unless the data are charted. Fig. 15 
may give some suggestions for a chart to show the movement of printed 
forms through an industrial plant. Here again printing by colored 
inks such as would be used on the original drawing would be of great 
service in making the chart easy to understand and easy to follow from 
department to department. 

If a building contains many stories the routing diagram for mate- 
rials and also the routing diagram for printed forms can be made 
conveniently by a rough perspective drawing showing the different 
floors as planes one above the other. Colored ink lines on the 
perspective chart will show clearlj' the movement of materials through 
the manufacturing building, and will indicate the elevator movements 
for material in a manner not possible if the departments are repre- 
sented all in one plane on the ordinary sheet of paper. Perspective 
charts of floors, one above the other, are so simply made that their 
advantage should not be overlooked when preparing routing charts 
for plants having multi-story buildings. 



Chapter II 
SIMPLE COMPARISONS 

ONE of a business man's chief assets is his abihty to show things 
to others in their true proportions. He is continually making 
contrasts, and holding up for comparison different propositions 
which come up in his daily affairs. The graphic method lends itself 
admirably to use in making comparisons. It is surprising 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. 
Fig. 16 is a cut taken from the report of the Metropolitan Sewage 
Commission. Most people know so little about bacteria that it would 
mean nothing to them to say that the Harlem River contains 15,600 
bacteria per cubic centimeter of water. When, however, such a com- 
parison is made as is shown in Fig. 16, even the most casual glance 
would convince anyone that the Harlem River is not the most ideal 

Bacteria per Cubic Centimeter of Water 






ISO 


I,600 


I5,600 


Atlantic 


Lower 


marlem 


Ocean 


New York 
Bay 


River 



Fig. i6. Bacteria in the Waters of New York Harbor 

This illustration is taken from the -eport of the Metropolitan Sewage 
Commission. The representation as though seen through a micro- 
scope is decidedly effective 

place. The figures for the bacteria count are given with 
the chart so that all the data are available to anyone who may wish 
to study the facts from a scientific standpoint. 

The drawing of Fig. 17 is of the cartoon type, effective for wall 
exhibitions or for use in the more popular magazines. This particular 

20 



SIMPLE COMPARISONS 



21 




Fig. 17. 



The Independent 

Five Forms of Our National 
Waste 

A cartoon type of chart like this will reach a 
popular audience. Accuracy of statement 
should not, however, be sacrificed as it has 
been here, in that there is no way of correctly 
comparing the money bags 



diagram contains nothing by which accurate comparison may be made. 

No figures are given, and it is impossible to tell whether the different 

money bags should be compared on 
the basis of diameter, area, or volume. 
x\lmost the only conclusion which 
can be drawn from such a diagram 
is one regarding the relative rank of 
the different expenditures. The re- 
liability of even that is likely to be 
questioned because of the evident 
lack of accuracy in this kind of chart. 
Nevertheless the cartoonist style 
should not be broadly condemned, 
for it has tremendous possibilities. 
It is possible to combine the car- 
toonist's wonderful power of arous- 
ing interest with methods of present- 
ing facts which will give a numerical interpretation that cannot be 

misunderstood. There is a great oppor- 
tunity waiting for the man who can 

combine cartoon methods with accuracy 

of numerical statement. 

Fig. 18 gives a statement which the 

illustration does not support. In the 

first place, the dates of the two years 

compared are not given. In the second 

place, it is impossible for the reader to 

tell whether the diagram is drawn on the 

basis of one dimension, two dimensions, 

or three dimensions. It would be a hope- 
less task to fit the area of the smaller 

washing machine into the area of the 

larger washing machine. Methods like 

this cannot be too severely condemned. 
Commercial geography, as it is now 

widely taught in the public schools by 

listing the various imports and exports of 

countries and the products of different 

cities, fails to give a clear idea of the 




Guod Houstkccping 

Fig. 18. Illustration Intended to 
Show that the Sale of Wash- 
ing Machines has Increased 
Sevenfold in the Past Three 
Years 

In comparing the two pictures it is not 
likely that the reader will obtain a 
ratio of seven to one. There is no 
way for the reader to tell on what basis 
the drawing was prepared, whether by 
height, area or volume. The title of 
this chart is also poor in that it does 
not name the two years for which the 
comparison is made 



22 



GRAPHIC METHODS 



11,483.000 Bales of iOO lb 


India 




S,082,000 


Egypt Russia 




1,506.000 


800,000 




B 














China, 775,000 




Brazil 810,000 



Tarr and McMurray' s New Geographies 

Fig. 19. The Six Leading Cotton-producing Coun- 
tries in 1910 

This arrangement is a bad one to place before school children. 
The eye cannot fit one square into another on an area basis so 
as to get the correct ratio 



relative importance of the materials listed. It frequently happens that 
the second or third item on a list may have only one-tenth the impor- 
tance of the first item. Because the three names are given one after 
the other, the pupil is quite likely to consider the three items of equal 
United Stale, importauce, just as three 

persons may be of differ- 
ent height, yet of about 
the same importance. 
The graphic method judi- 
ciously applied to school 
geography and to general 
commercial geography 
would make a tremen- 
dous difference in the 
student's grasp of the 
subject. 

Fig. 19 is a typical example taken from a geography book in which 
the attempt was made to use the graphic method. The introduction 
of the picture of the bale of cotton in Fig. 19 is justifiable. There is, 
however, no justification for placing the picture inside of one of the series 
of squares. The picture detracts from the size of the square. Graphic 
comparisons, wherever possible, should be made in one dimension 
only. In such a case as this, one-dimension presentation is perfectly 

feasible by the use of bars 
of different lengths. The 
pupil would find it an al- 
most hopeless task to fit 
one side of the block for 
Brazil into one side of the 
block for the United States 
and then square the result- 
ing ratio in order to learn 
that the United States pro- 



O 2SO0 $000 7500 JOOOO 

I I n I I 1 I I I I I I I I I I I I 



T/ie World- -^- 

United States ,..._. 

India 

Es'ypr 

China 

Asiatic Jfussia. , 



Fig. 20. 



The world's produc- 
tion of cotton, in igoj, in 
millions of pounds. 

Dodge's Advanced Geography 

The World's Production of Cotton in 1905 
in Millions of Pounds 

The above illustration together with the title is shown exactly 
as given in a recent geography book. Charts like this 
greatly assist the pupil in getting the correct relative im- 
portance of the different things studied. Note the scale duceS rOU^hlv thirtv times 
at the top of the chart ' & J ' J 

as much cotton as Brazil. 
Bars in one dimension only would show the comparison accuratelv. 
Under any circumstances, the use of the squares of Fig. 19 with the 
center line through the centers of the squares gives an extremely poor 
arrangement. 



SIMPLE COMPARISONS 



23 



VAtira OF PBODtTCTS FOB PBINCIPAL CITIES: 1909. 



CITIES 

NEW YORK 

CHICAGO 

PHILADELPHIA 

ST. LOUIS 

CLEVELAND 

DETROIT 

PITTSBURG 

BOSTON 

BUFFALO 

MILWAUKEE 

NEWARK 

CINCINNATI 

BALTIMORE 

MINNEAPOLIS 

KAWSAS CITV. KANS. 

SAN FRANCISCO 

JERSEY CITV 

IND1ANAPOLI3 

PROVIDENCE 

nOCNESTER 

LOUISVILLE 

SOUTH OMAHA 

VOUNOSTbWN 

LAWRENCE 

NEW ORLEANS 

WORCESTER 

BAVONNE 

AKRON 

PERTH AMBOY 

LYNN 

PATERSON 

LOS ANGELES 

BRIDGEPORT 

FALL RIVER 

PEORIA. 

TOLEDO 

OMAHA 

DAYTON 

LOWELL 

VONKERS 

ST. PAUL 

KAN8AS CrTY. MO. 

NEW BEDFORD 

DENVER 

READING 

NEW HAVEN 

SEATTLE 

WATERBUnV 



HUNDREDS OF MILLIONS 




Fig. 21. Value of Manufactured Products of Principal Cities of the United States 

in 1909 

This chart, taken from a Census office report, would have been greatly improved if the actual figures had 
been placed at the left of the bars in the manner shown in Fig. 27 

It is stated by the author of the book in which Fig. 19 is used 
that tests have shown that children grasp relative quantities better 
when separate squares are used than when the information is shown 
by lines or bars. If this is the case, it is probably due to the fact 
that the squares appear more prominently to the eye than do the bars, 
and it would seem that the best kind of presentation might be made 
by using much wider bars so that the bars would be easily seen. Bars 
can be made as wide as some of the squares seen in Fig. 19 and, if it 
seems best, thie bars could be made in outline rather than in solid 



24 



GRAPHIC METHODS 



black. Wide bars would give a striking visual effect and yet they 
would vary in one dimension only, so that relative proportions could 
be easily judged. Wide bars would probably have all the advantages 
and none of the disadvantages of the methods of either Fig. 19 or 
Fig. 20. Instead of showing the data of Fig. 19 by either bars or 
squares, another method would show pictures of bales in rows of dif- 
ferent lengths, on the general scheme of Fig. 41. The rows would be 
the same as the broad horizontal bars, but their numerical interpreta- 
tion would be less abstract. 



IS NEWBURGH SATISFIED WITH THIS 
SNAU SCHOOL EXPENDITURE? 



SCHOOL COST PER PUPIL 



NovRDclvlkl 
HL\fcrnon I 
Jluburn I 

damBStiiwn I 
Newburfji 1 
Walcrlown I 



^■■■■•46 75 
^^H •4271 

laa •4-0.27 

^m I39.8S 

■ <36.1S 

■ •35.4-1 
I '34-.89 



61.74- 
S4-.87 



^H^B^^^B 'SO. 22 

Cities 25000 to 35,000 People 
^Figures based on average daily attendance) 



Fig. 20 gives a diagram taken 
from another geography book. 
This is a much better form of 
presentation than used in Fig. 19. 
It could, however, be improved by 
giving the figures for each country 
in connection with its own. bar. 

Fig, 21 shows the horizontal- 
bar method applied to a larger 
number of items and proves the 
great utility of this method when 
several different items must be 
shown in their proper rank. In 
this case, however, the figures 
should have been given for the 
convenient use of any one who 
might wish to make ratios or to 
quote the actual value of products 

for any one of the cities. It is exasperating to run across a diagram 
of this kind which contains valuable information in such form that 
it cannot be carried away or quoted for use elsewhere. 

In Fig. 22 an attempt has been made to show in the graphic 
presentation the figures from which each horizontal bar was drawn. 
The method of placing the figures at the right of the bar is, however, 
unsafe. The eye is likely to make a comparison, not from the ends 
of the bars themselves, but from the right-hand end of the figures. 
Since the figures are of about constant length, visual ratios are in- 
accurate when made by comparing a short bar plus the constant 
length of figures with a long bar plus the constant length of figures. 
If the shortest bar in Fig. 22 were about the same length as the space 



Devanmera of Surveys and Exhibits, Russell Sage Foundation 

Fig. 22. Comparison of School Cost per 
Pupil in Cities of 25,000 to 35,000 
People in New York State 

This illustration was ptiotograplied down from a 
wall exhibit to adapt it to a printed report. The 
use of the iigures at the right-hand end of the 
bars is bad practice. The eye is apt to make 
the comparison from the last figures rather than 
from the ends of the bars 



SIMPLE COMPARISONS 



25 




UniTea iMngaom 



1 7, 576. 



United States 



5,05B 



Germany 



required for the figures, it would be possible to make a visual error 
of 100 per cent in the comparison. If the figures had been placed at 
the left of the bars, they would have been in a neat column and not 

at all likely to affect the ac- 
curacy of the visual com- 
parison. 

The chart, Fig. 22, was 
taken from a report devoted 
entirely to the city of New- 
burgh. On this account, 
it would have been much 
better if the word "New- 
burgh" had been printed in 
heavy -faced type so that it 
would stand out from the 
other cities in the list. 
Where the use of colored 
ink is possible, it is fre- 
quently desirable to make 
the item under foremost 
consideration stand out 
prominently by giving it a 
brilliant color such as red 



Norway 



France 



Br Colonies 



values given in Tlnousanas 
of Tons 



Italy 
It.azol 



Jap an 

IS) 

Ne therlands 

ED SB 

Fig. 23. Comparison of the Registered Shipping 
of the Principal Countries of the World 

The picture at the top of the chart assists in attracting the 
attention of the reader. After the attention is gained, the 
bars set forth the comparison more accurately than it 
could be given by any pictures of ships of different sizes 

Fig. 23 is an attempt to give a popular touch similar to that at- 
tempted in Fig. 19 by the bale of cotton. As a general thing, it is 
possible to attract attention by some such scheme as the steamship 
used in Fig. 23 and then, after the attention is attracted, to give the 
comparison by methods which are entirely correct and also familiar 
to the average observer. In Fig. 23 the figures are given for the data 
from which the bars are drawn. The values, however, were so large 
that it was necessary to leave off the last three ciphers and state that 
the values given are in "thousands of tons." Though the dropping 
of ciphers is very common, it is a practice likely to lead to serious 
error and should not be encouraged. Even with the ciphers omitted, 
the values could not possibly have been given inside the bar if more 
countries had been included in the list, or if the scale had been any 
smaller than that shown here. To place above each bar the title for 
that bar is not good practice. In general, it is desirable to have a 



26 



GRAPHIC METHODS 



title for each bar at the left, then the figures, then the bar. With such 
an arrangement, one title will be below another, easily perceived by the 
eye, and the figures will all be in one column with the decimal points 

in a straight line. ^_^T^. "^"^'^ states . .^93 ^■■^^h^^HH^ 
Figures running ^ - ^ I — - ^ mexico si ^m 

. . V ' ^ ^ ^ SPAIN etPORTUGAL, 52 ■■ 

into millions can be ^" j ^ ■■■ — ^ -japan 4z ^ 

•1 1 i> 1 \ ^ \ -^ CHILE 4Z H| THOUSANDS of Tons 

easily read from long ^^ p^ Australia. .34 ■ 

columns if sufiicient ^^_^g ^^"^ ['/[['^m 
white paper is left 

between figures in ^'^- ^4- Production of Copper in Different Countries 
. J^ for One Year 

Xne VerTlCai arrang,e- This chart is a redrawing of Fig. 25. The title here should state the year, 
nient and if each '^"^ ^^^^ ^'^^ °'^'' S^^'^^ ''^ the book from which Fig. 25 was taken 

group of three figures in the horizontal arrangement is widely set off 
by means of a comma. For graphic work, the groups of three figures 
should, in general, be more widely set apart than they are ordinarily. 
Fig. 24 shows the arrangement with the figures at the left of the 
bars. Here again, however, the ciphers have been omitted when it 
would probably have been just as clear if they had been included and 
set off by means of a comma and a wide space. The drawing for the 

<;- -, pigs of copper 

\ .Jri5; shown at the left 

\ .„:,'////// of the illustration 

V '^''"'^^^ gives an idea of 

\ ...„„M// what can be done 

O '^'^^--'^^^^'^ by hand drawing 

\ .,..yyy//// m order to at- 

\ . -^.'^y//// S ^ tract attention to 

\ .„^y////// ^5 ^ S S » s » the chart itself is 
V.:.^.^.^ ^ ^ S 3 S S S intended to illu- 

Unifed States Mexico Spain & Jaoan Chile Australia Germanv Canada 

^°''"8"' minate. In this 

493,476 01,000 54,188 44,310 4S.043 34,339 34,298 28,733 

PIHHps' Chamher of Commerce Atlas CaSC thc IcttCring 

Fig. 25. A Year's Production of Copper in Tons also has been done 

This illustration was copied from a prominent book on international trade. bv hand and is a 
Accurate interpretation of the chart is impossible. Graphic work of 
this sort is dangerous because it may be misleading gOod example of 

what a skilled 
draftsman may do without any great expenditure of time. The solid 
black bars of Fig. 24 come out in much better contrast than the gray 
bars of Fig. 23. 



SIMPLE COMPARISONS 



27 




I-Vderaled Malay 
States 
68,856 



BoliWa 



Fig. 25 shows a chart of the same data from which Fig. 24 was 
drawn. It is readily seen that it would be impossible for the average 
reader to tell whether this chart was drawn on the basis of height or 
the basis of area. The pigs of copper are not of the same size in the 
different piles, and it is evident that a pictured pig of copper is not 
intended to be the unit. If Fig. 25 is drawn on an area basis, it is al- 
most impossible for the eye to fit the area for the right-hand pile into 
the area of the left-hand pile. This chart is a typical example of 
thousands of illustrations used by the popular magazines and even 
by some of the more pretentious reference books. 

Fig. 26 is an even greater 
atrocity than Fig. 25. In Fig. 
26, the observer is entirely un- 
able to tell whether comparison 
is made in one, two, or three 
dimensions and he has an addi- 
tional puzzle because of the large 
amount of perspective shown 
for the top of the pigs of tin. 
It would be surprising if one man 
in a thousand could guess any- 
thing near the ratio intended to be expressed between the largest and 
smallest pigs shown. In general, graphic work of this kind is much 
worse than the use of figures alone. There are times when an ab- 
sence of knowledge is better than incorrect knowledge. 

Fig. 27 is a good example of what can be done as a standard arrange- 
ment for simple comparisons. On the left there is a symbol to attract 
the eye and interest the observer. 
Note that a dollar mark is shown 
on top of the picture of the bale 
of cotton in one case and the sheaf 
of wheat in the other, to indicate 
that the value of the crop is con- 
sidered rather than the number of 
units. After the pictures, which 
may be thought of as "ej^e catch- 
ers," we have the figures, and then 



Dutch E, Austra- United Siam 
Indies lia Kingdom 

29,937 15,807 12,755 5,05* 3,000 

Pfiilips' Chamber of Comm^ce Alias 

Fig. 26. A Year's Production of Tin in Tons 

This illustration, taken from the same source as Fig. 
io, is even more confusing. The perspective of 
the tops of the pigs of tin is such that there is 
no nay of telling whether \-isual comparison 
should be made by height, area or volume 




COTTON % 820,320,000 



WHEAT $561,051,000 



Fig. 27. Value of Cotton and of Wheat 
Produced in the United States in 1910 

Here is a suggestion for a standard arrangement for 
horizontal-bar comparisons. The illastrations 
at the left make the presentation popular in 
form, .vet actual figures for the data are given 
at the left-hand end of the bars 



the bars plotted to scale for quick comparison by the reader. This 
cut could have been improved slightly if the spaces between the sep- 



28 



GRAPHIC METHODS 



arate groups of three figures had been made somewhat larger and if 
the black bars had been made about one and one-half times as wide 
as shown here. 

TOTAL POPULATION 



MILLIONS 



MARF?IED 
WIDOWED 
DIVORCED 



m 



NATIVE WHITE OF NATIVE PARENTS 



MARRIED 
WIDOWED 
DIVORCED 






NATIVE WHITE OF FOREIGN PARENTS 



SINGLE 
MARRIED 
WiOOWEp 
DIVORCED 


3 




i 




i 












■ 





FOREIGN WTUTE 



SINGLE 
MARRIED 
WIDOWED 
DIVORCED 



SINGLE 
MARRIED 

WIDOWED 
DIVORCED 



FT 



NEGRO 



United States Statistical Atlas, 1900 Census 



Fig. 28. Status of the Population of the United States in 1900, in Regard to Marriage 

This chart would have been improved if the figures had been given at the left end of the bars. Note that 
the four lower groups of bars are a cross-index of the information given in the upper group 

Another application of the bar method is seen in Fig. 28. Each 
of the four lower groups of population is a subdivision of the total 
population shown in the upper group. The same data may be 
seen portrayed in a different way in Fig. 6. The arrangement of 
Fig. 6 is more desirable, in that the size of the components is more 
readily grasped when all are shown in the same horizontal bar. In 
Fig. 28 the eye does not readily make the addition necessary to fit 
together the four items "Single," "Married," "Widowed," and 
"Divorced" as percentages of the total 100 per cent in each group. 

The drawing in Fig. 29 is a portion of an illustration intended 
to show how far different kinds of trucks could travel for an expend- 



SIMPLE COMPARISONS 



29 





■T ; 




D 



> 

o 






B ^ 



cl 



-{2 5 



«, 



o o 
3'i3 



':g ^J 



O 
u 



2S 



d 

Vh 
0) 

is 



*" a 

4J O 

^^ 

O (U 
■^ S 



>> 

^ 



w o 

s t. 



H 






-a 



iture of one dollar. The placing 
of these trucks on different levels 
is somewhat confusing, but it was 
done in order that one truck would 
not have to be shown back of an- 
other. Note the bars behind each 
truck, to give the component parts 
of the total expenditure split into 
different kinds of charges. This 
chart is grossly misleading because 
the point where the race started 
is not shown. It appears, for in- 
stance, that for one dollar ex- 
pended a five-ton gasoline truck 
will run about twice as far as a 
five-ton horse truck. This con- 
clusion is entirely unwarranted, 
and would not be reached by any 
reader if the chart had been so 
drawn that the zero point or 
starting point for the race had 
been shown to scale at the left 
end of the chart. 

The black bars used in Fig. 30 
to show contagious diseases indi- 
cate an excellent method for differ- 
entiating items shown in graphic 
comparison. In the Boston health- 
report illustration from which this 
cut was adapted, the infectious 
diseases were shown in red. By 
making most of the bars in outline 
only, it was possible in Fig. 30 to 
use solid black to get the contrast 
obtained in the original report by 
means of red ink. 

It is frequently necessary to 
show increases and decreases on 
the same chart so that they may 



30 



GRAPHIC METHODS 




=llilpiiiSl .ltsi|i!f lif. 



liJ|i|||ii|llHll|^l|i^i-||l 



^^ Defttht from InfectlouB Dlteaata. 
< I De&thB from other Olmgw, 

^n«uaZ Report of the HeaUh Depanmcnr, City of Boston, 1910 

Fig. 30. Comparative View of Twenty- 
five of the Principal Causes of Death 
in Boston During 191 o 

In the Boston report, the infectious diseases were 
represented by red bars. Here attention is called 
to the infectious diseases by using solid black 
bars in contrast with bars shown only in outline 

zero line. The figures can be 
placed on the left-hand margin 
of the chart, immediately between 
the title for each bar and the end 
of the bar, in a manner similar to 
that shown in Fig. 27. Since the 
zero line must be near the center 
of the chart, rather than at the 
left-hand edge, when the right- 
and-left arrangement is used, it 



be in contrast. In Fig. 31 an ex- 
ample of the contrast of increases 
and decreases is given, increases be- 
ing shown to the right of the zero 
line and decreases shown to the left 
of the zero line. This right-and- 
left arrangement of increases and 
decreases is fairly well known and 
is so convenient that it should be 
more widely used. The actual 
figures from which each of the hori- 
zontal bars is drawn can be shown 
on the chart even if the horizontal 
bars are drawn to the left of the 

REPAIRS flllD REtimALS OF LOCOflOTIVES 
PERTOHTRflCTfyE FORCE. 

Average of S Yearj Ending /9/0 Compared 
w/ih 4-yearj Ending /905. 

ewEkriROMJ. 



EfmARK 
IV. 

crj.isrp. 

CJ!./.&P 

cmty. 

CJ-fi. 

cBsa. 

flXi-JF 



yycsTERri Roms. 



% 20 /s io s o s io is -^ 

"RailToad Operating Costs." .SiiJTcrn ct Son. New York 

Fig. 31. Increase is Here Shown to the 
Right of the Zero Line and Decrease to 
the Left of the Zero Line. A Heavier 
Zero Line and Arrows Pointing Right 
and Left from it Would Improve This 
Chart 



SIMPLE COMPARISONS 



31 



would be well to have a broad line for the zero line, so that the 
eye may at once perceive that zero is not at the left-hand edge of the 
chart. It would have been better if the zero line in Fig. 31 were some- 
what broader. Another help to the reader could be given by placing 
an arrow pointing to the right with the word "increase" and an ar- 
row pointing to the left with the word "decrease." 



Triuisfoimcrs 

Transmission Line 

Translormcis 

lintiiry Ccuvcitcis 
Contact Line 



SINGLE 
PHi^SE 



SINGLE 
PHASE 

WITHOUT 
*NSFORMERS 



Power Deli\ered 
to Locomotives 




Journal Aincr. Soc. Mechanical Engineers 



Fig. 32. Comparative Losses Between the Power House and Locomotives with Differ- 
ent Systems of Electric Traction 

The comparison of the losses in the different power systems is very clearly shown in this illustration, which 
was taken from a paper by George VVestinghouse 

Broad bars can be used either vertically or horizontally. The hori- 
zontal arrangement is usually the more convenient, as it lends itself 
more readilj' to the use of type and horizontal lettering for the titles, 
data, etc., of each bar, without forcing the reader to turn the book 
at right angles. In Fig. 32, however, the lettering can perhaps be 
more conveniently grasped by the reader with the bars placed ver- 
tically instead of horizontally. 

Note the lines connecting different bars to show how the com- 
ponents compare in size therein. These lines assist greatly in giving 
a clear and rapid interpretation of the chart. 

Fig. 33 is an admirable example of what the graphic method can 
do to boil down complex facts for quick interpretation by the reader. 
In this case the schools of each of the forty-eight United States were 



TEN TESTS OF EFFICIENCY 



I. WASHINGTON 
Z MA55ACHU5n'T5 
5 NEW VORK 

4 CALIFORNIA 

5 COMNECriCUT 
b OHIO 

7 NtW JERSEY 
S ILLINOIS 

9 COLORADO 
10 INDIANA 
I I RHODE 16LAN0 
12 VEJ?MONT 



CHIL- 5CH0OU tofPENSE 
DREN IN PLANT PER 
SCHOOL CHILD 



iCMOOL- 

DAY5 

PER 

CHILD 



SCHOOL 
YEAR 



f" • ]l 



V/////M 



V/////A 



AT- 
TEND- 
ANCE 



EXPEND 
ITURE. 
AND 

WEALTH 



DAILY 
COST 



HIGH 
SCHOOLS 



5AL- 
ARItS 



\: I I 



II .11 r 



\V/////A\ 



\V//////AV/////Ay/////A\y/////A\ 



\V/////A\ 



\V/////A\ 



W/////AV/////AL 



\ V/////A 



V/////A\ 



V/////AV/AAA\ 



\V/////A\ 



W/A/A. \v/y//A\ 



WyyA/AVA/Z/AT 



WAAAA 



W/AAA\ 



w • •• .11 



\VAA/A\ 



\^AAAX 



13 NEW MAMRSHIRE [ 
(4 UTAH 
IS OREGON 
IG MONT>i,NA 

17 MICHIGAN 

18 N DAKOTA 

19 IDAHO 

20 Minnesota 

l\ \Q\hltK 
IZ MAINE 



WA//AA^AAAAVAAA\\ 



V/AAAVAA/Ay/AA/AVAAAAXAAAAVA/AA\ 



WAAAW 



\VAAA\m£;;ZWAAAAVAAyA 




d5PENNSYLVAMiA wmmvA/Ammmy/yAAAVA A/A\ m 
tA KANSAS v/////Ammmmmv///AAv/////AVA/m 



\y//////AV//A//AV/Am 



£S NEEPA5KA 
Z<a 5 DAKOTA 
n NE-VADA 
28 WliCON&lKI 
£9 WYOMING 
'i^ ARIZONA 

31 OKLAHOMA 

32 MISSOURI 
35 W. VIRGINIA 

34 FLORIDA 

35 DELAWARE 

36 MAPYLAND 

37 TENNE-SStE 

38 TEXAS 

59 LOUISIANA 

40 NEW MEXICO 

41 VIRGINIA 

42 KEMTUCKY 
4i ARKANSAS 

44 GEORGIA 

45 M1'S5I«\PP\ 
iA NXAROLINA 
4? 6- CAROLINA 
48 ALABAMA 




Fig. 33. Rank of States in Each of Ten Educational Features, 1910. White Indicates 
that the State Ranks in the Highest 12 of the 48, Light Shading that it Ranks 
in Second 12, Dark Shading that it Ranks in Third 12, and Black that it Ranks in 
Lowest 12 

The above illustration is a photograph of one page of a pamphlet issued by the Division of Education of 
the Russell Sage Foundation, regarding the public schools of the United States. This type of chart is 
capable of wide application in other fields 

32 



SIMPLE COMPARISONS 



33 



considered from each of ten different view points. The different 
States were then arranged in grades one, two, three, or four, according 
to the efficiency of their schools from each of the ten different points 
of view from which they were considered. The best grade under 
each heading is shown by means of a white rectangle, the second grade 
by light cross-hatching, the 
third grade by dark cross- 
hatching, and the fourth 
and worst by solid black. 
States are shown in the 
complete chart in their com- 
parative rank. The State 
with the best schools is 
shown at the top of the 
chart and the State with 
the worst schools is shown 
at the bottom of the chart. 
On the chart as a whole, 
one can see at a glance just 
how the schools of any State 
rank with those in the 
other States, and wherein 
the greatest defects occur. 
The chart of Fig. 33 was 
in a thirty-page illustrated 
pamphlet sent broadcast 
over the United States by 
the Russell Sage Founda- 
tion to members of various 
legislatures, school boards. 



ADMINISTRATION ) -____ 


^^/administration 


BUBL'CA- 
TIDK 


PROOF BEADING V 


OLDMILITARVBECOBD^ ^ 


DISTRIBUTION Vr^ 


^^,^MAIL'^^ RECORD 


ORDERS yV 


MAIL ''.RECORD )-Aj 


-;:::^C0RRE5P0NDENC[ 




■I L.LISKD HCH X \ 


LtAMiNiHG 




WI5CEL- EFriCieNDR[COR05>A\W 


^^Etl5T[D MEN'S 


ENLISTED MEN'S J^-^ 


RECRUITING ) % 


R0LL5 y^ 


^/ OFFICERS 


APP COM ''. PERS ) Z 


MILITARY ACADEMY K'^y^ 


^^W^R[GIM[N]AL RECORD 


RETURNS V/^ / 




^y ARCHIVES 


REGIMENTAL- RECORDS V/ / 


ARCHIVES yfy'^ 


/ TAnniMr 


TENTH 
fjTRFFT 




MiLlIAR*RlUtRDtARDb_y / 


SEVENTEENTH ST. )/ \ 



Fig. 34. Organization of the United States 
Adjutant General's Office Compared with 
Organization Proposed by President Taft's 
Commission on Economy and Efficiency 

This method of connecting blocks with lines to show the dis- 
position of departments can be used in many types of 
chart presentation 



etc. This pamphlet has 
resulted in the appropriation of some millions of dollars for the 
improvement of public schools. The arrangement of the pamphlet 
itself is worthy of note in that each left-hand page is a chart, while 
each right-hand page, facing the chart, is devoted to a brief explana- 
tion of the conclusions which can be made from a study of the chart. 
This arrangement of alternate pages of chart matter and printed matter 
is tremendously effective and is well worth copying. 

It is frequently necessary to contrast one grouping of components 



34 



GRAPHIC METHODS 



with another grouping of components. In Fig. 34 we have a chart 
Nvliich may give a vahiable suggestion to anyone who is considering 
the rearrangement of departments in any large organization. The 
present arrangement and the proposed arrangement are each clearly 
indicated, with connecting lines to show instantly the disposition of 
each of the old departments. 



Steps under prcicri 
s>9iem 



Rteetvtjs. 
. Drait^ riieniorun 

duiii. 
. Tra 



vers. 



iruiisiM 
Receives. 
li\uiiiiiies 
DrufO 
'I niiismiij. 




Explanation. 



es and 



poll 



Ills 

12. Deliverii. 

1J. Evjiiiines. 

lA. 'I'niiisinils 

I&. Delivers 

I'i E\aiiiines 

IV. Indorses, 

le. Delivers. 

19. Approves. 

20. Delivers. 

21. Iridurse.s. 

22. Delivers, 
2:{. Exuioiiies. 



25 Dral'ls order 
20. Types order. 

27 * Records uct ion 
28. .K.\,iiiiine.-<. 

:9. iiiit iiiis. 



Slfjis UTider 
proposed system 



1 Kt- 



f I V I* 

ciii.'tiiii'flr.ifis 

2 (J-.i) Kirvicw- 
imkI iiiitiiilN. 

:! CiUI Til I-.. us 
in "..lit" I>o.\. 



I (:i::i lielivirv. 
.^(311 SiKlis. 



Fig. 35. Routing of a Letter Through the Adjutant 
General's Office Requesting the Discharge from the 
Army of an Enlisted Man in Recruitmg Service, 
Contrasted with the Routing Proposed by President 
Taft's Commission on Economy and Efficiency 

By referring to the horizontal scale and to the vertical scale the steps 
can be studied either by departments or by operations 

In Fig. 35 is given a convenient method to show the routing of 
papers through a large office, together with the operations through 
which these papers must pass. Across the top of the chart is a scale 
of departments. The circles drawn immediately below the space for 



SIMPLE COMPARISONS 35 

any department on the upper scale show that the papers receive some 
action in that particular department. At the right is a scale showing 
the nature of the work done in each of the departments. The chart 
is drawn on the basis of the intersection of vertical lines downward 
from the names of departments and horizontal lines through the 
names of the operations given at the right. Arrows joining the various 
circles then give the routing of the papers through the whole of the 
journey. The comparison of the existing routine with the proposed 
routine can be seen by considering the solid lines and the dotted lines 
and by comparing the two distinct columns or lists at the right. Thirty- 
nine operations may be counted in the present arrangement against 
five operations in the proposed arrangement. Though the drafting 
and the detail arrangement of this chart could be improved, the gen- 
eral scheme is nevertheless worthy of attention. 



Chapter III 



SIMPLE COMPARISONS INVOLVING TIME 



THOUGH in making comparisons, the horizontal bar divided into 
blocks is superior to the circle divided into sectors, the circle 
and sector arrangement is not inaccurate when only the com- 
ponent parts of any unit are to be shown. In the case of Fig. 36, how- 
ever, the comparison is between two circles, the divisions into com- 
ponent sectors being only an incidental 
feature. In this diagram, copied direct from '®°° 

the Statistical Atlas of the 1900 Census, it 
is practically impossible to tell how much 
larger the foreign-born population was in 
1900 than it was in 1850, 

' 1S50 

for it is necessary to com- 
pare the two circles on an 
area basis. To the average 
person this is an almost 
impossible task, because it 
is not feasible to fit one 
circle inside of the other 
visually as two horizontal 
bars may be fitted. If the 
circle for 1900 were esti- 
mated as twice the diameter 
of the circle for 1850, it 
would mean that the for- 
eign-born population in 
1900 was four times as great 
as that in 1850. If, how- 
ever, the ratio were some- 
thing less simple than this, 

interpretation of the chart would be difficult even by the processes 
of mental arithmetic. If the ratio between the diameters were, 

36 . 




w:i\m Irish ■ 

1 Germans 




F^a'^l British 
K\\^.\\\'i Canadians 



^^^^-''^ Scandinavians 
^g<^ Slavs 
l\\\?\\V Italians 
fvi^Sv^ All Others 

Uniied States Statistical Atlas, Census of 1900 

Fig. 36. Foreign-bom Population of the United 
States in 1850 Compared with that in 1900, 
also the Proportion of the Different Nation- 
alities in the Two Years Compared 

The method of presentation by means of a circle with sectors 
is not inaccurate when only component parts are to be 
shown. Here, however, we have two different circles com- 
pared on the basis of total area. The reader cannot com- 
pare the areas visually so as to get the correct ratio meas- 
ure of the increase in total number of foreign-born popula- 
tion. Horizontal bars are much preferable to circles when 
comparisons are to be made 



COMPARISONS INVOLVING TIME 



37 



1910 



1890 



1900 






for example, one and a half, the average reader would be completely 
nonplussed, as he would not trouble to go through the mental arith- 
metic of multiplying one and a half by one and a half. In general, the 

comparison of two circles 
of different size should 
be strictly avoided. 

Many excellent works 
on statistics approve the 
comparison of circles of 
different size, and state 
that the circles should 
always be drawn to rep- 
resent the facts on an 
area basis rather than on 
a diameter basis. The 
rule, however, is not al- 
ways followed and the 
reader has no way of telling whether the circles compared have been 
drawn on a diameter basis or on an area basis, unless the actual 
figures for the data are given so that the dimensions may be verified. 



1,647 2,244 3,302 

Figures in iviiilions of Dollars 

Fig. 37. Total Yearly Value for the United States 
of Combined Imports and Exports by Land and 
by Sea 

In this illustration the data have been represented by circles 
drawn on a diameter basis. The right-hand circle appears 
more prominent than the data would justify. Circles com- 
pared on a diameter basis mislead the reader by causing him 
to over-estimate the ratios. Compare Fig. 38 



In Fig. 37 the figures 
are given, and the circles 
have been drawn on a 
diameter basis. It will be 
noted that the figures for 
1910 are roughly twice 
those for 1890. The circle, 
however, has roughly four 
times the area of the circle 
for 1890 and, according- 
ly, seems to have much 
more than twice the im- 
portance. In Fig. 38, the 
same data have been 
shown on an area basis 



1890 



1900 



1910 






Ij647 2,244 3,302 

Figures in Millions of Dollars 

Fig. 38. Total Yearly Value for the United States 
of Combined Imports and Exports by Land 
and by Sea 

Here the data of Fig. 37 have been shown by means of circles 
drawn on an area basis, as recommended by many authorities 
on statistical work. The right-hand circle, however, shows up 
less prominently than the figures would justify. Circles com- 
pared on an area basis mislead the reader by causing him to 
underestimate the ratios. Circles of different size should never 
be compared. Horizontal bars have all the advantages of 
circles with none of the disadvantages 



as most of the authorities on statistical 
work recommend. If the figures were not given, the reader would be 
forced to fit the left-hand circle into the right-hand circle on an area 
basis, or else make a ratio between the diameters and then square the 
ratio. Either process is almost impossible to accomplish and there is 



38 



GRAPHIC METHODS 



o 
o 

I 

0) 

CO 




MINISTRY 



LAW MEDICINE EDUCATION BUSINESS PUBLIC SERVICE 



o 
o 

T 

0) 
00 





MINISTRY 



LAW 



MEDICINE EDUCATION BUSINESS PUBLIC SERVICE 



Independent 

Fig. 39. Proportion of College Graduates in Different Professions in 1696-1700 and 

in 1 896- 1 900 

Charts of this kind with men represented in different sizes are usually so drai^Ti that the data are represented 
by the height of the man. Such charts are misleading because the area of the pictured man increases more 
rapidly than his height. Considering the years 1696-1700, the pictured minister has about two and one- 
half times the height of the man representing public service. The minister looks over-important because 
he has an area of more than six times that of the man drawn to represent public service. This kind of 
graphic work has little real value 

no necessity of inflicting such cruelty on a reader. Though the circles 
in Fig. 37, drawn on a diameter basis, exaggerate the ratios, the circles 
in Fig. 38, plotted on an area basis, make the reader underestimate 
the ratio. Comparison between circles of different size should be 
absolutely avoided. It is inexcusable when we have available simple 
methods of charting so good and so convenient from every point of 
view as the horizontal bar. 

In Fig. 37 and in Fig. 38, it would have been better if the year 
had been given under each circle, with the figures for quantity placed 
above the circles, so as to follow the standard arrangement of havinc 



COMPARISONS INVOLVING TIME 



39 



1911 



1809 





H.59 1,000 
One Mile 



32,837,000 
One MJle 



dates placed always at the base of 
the chart. 

Another difficulty in the com- 
parison of areas is shown in Fig. 
39. No figures have been given 
and the helpless reader must com- 
pare by means of the pictures 
alone. By measurement, it will be 
seen that the minister in 1700 has 
over three times the height of the 
minister in 1900. Since the man 
in each case is shown in his natural 
proportions, the picture of the 
minister in 1700 has over nine 
times the area of the picture for 
1900. Whether the ratio should 
be roughly three or roughly nine, 
we cannot tell. 

Another example of the same 
kind of difficulty appears in Fig. 40, 
but here the figures are given and 
we can check up the author to see 
whether he has drawn the 1911 man on the basis of height or on the 
basis of area. The 1911 man, on account of his far greater area, looks 
to be rather more than two and a quarter times as important as the 
man of 1899. Though this type of graphic work is quite common, it 
should be avoided, for its visual inaccuracy is serious enough to cause 
distrust of the whole graphic method. In considering Fig. 40, the point 

333333311 

14.591,000 



Worid's Work 

Fig. 40. Passengers Carried on the Rail- 
roads of the United States in 1899 
and in 191 1 Compared 

This illustration has all the bad features mentioned 
for Fig. 39. Here the numerical data are given 
and we can prove for ourselves that the two 
pictured men are compared on the basis of 
height. Because of the disproportionate area, 
the right-hand picture gives the reader a false 
and exaggerated impression of growth. See 
Fig. 41 



1899 



ONE MILE 




1911 



32,837,000 
ONE MILE 




Fig. 41. Number of Passengers Carried on the Railroads of the United States in 1899 

and in 191 1 Compared 

Here is a chart drawn from the same data as Fig. 40. It was not a larger passenger, but more passengers, 
that the railroads carried. The ratio expressing increase in business can be clearly and accurately seen 
from this method of portraying the facts 



40 



GRAPHIC METHODS 




250.440,000,000 Tons 



WoTld's Work 



Fig. 42. 



Comparison of the Total Amount of Freight Service on the Raikoads of 
the United States in 1899 and in 191 1 

It would have improved this illustration if the two locomotives had been shown one exactly above the other 
facing to the left. The additional cars representing the increase in 1911 would then be seen as though 
added to the rear of the train 

to be brought out is not that the railroads carried a larger passenger 
in 1911, but that they carried more passengers. 

If it is necessary to have a popular method, we can at least be 
accurate by portraying the data in the form of Fig. 41, not as in Fig. 
40. Copy for an illustration of this sort is very simply made by taking 
proofs from a cut of one man and then pasting these proofs on a long 
strip of paper until a row of the correct length is obtained. The whole 
arrangement can then be photographed down to produce the effect 
shown in Fig. 41. To avoid fractional men at the end of a row, it is 
usually easy to express the ratio with a sufficient number of men in 
each row or bar to get numerical correctness. Note that in Fig. 41 
the whole arrangement is similar to that of Fig. 24 or Fig. 27 in Chapter 
II, the actual data being given at the left of the row or bar. It would 
have been better if the men in Fig. 41 had been faced to the left in- 
stead of to the right. The additional men in the row for 1911 would 
then appear to have joined the rear of the line rather than to have come 
in at the front of the line. ^ 











1901 


I 




















jgr 




-^^ 




1 


tt 


a — rL 


:■■■ 


n A 


n r, 


t. ) cy nT 


Hi-e?K 



1912 



-ptr 



" " '> rr 



Wtt^^j^^3 



World's Work 

Fig. 43. Comparison in Size of Trainload on the Chicago, Buriington & Quincy Rail- 
road in 1901 and in 1912 

Here one locomotive is above the other but both face in the wrong direction. Figures for the data are not 
given and the reader cannot tell whether the two lengths compared should include the locomotives or 
only the cars. Clearness could have been assured if the cars had been shown for comparison in solid 
black, with the locomotives included for pictorial effect, but only in outline 



COMPARISONS INVOLVING TIME 



41 



In Fig. 42 the idea is brought out that the raihoads are now han- 
dhng more freight. The drawing, however, should be reversed so as to 
have the two locomotives one above the other facing to the left, with 
the additional cars at the right-hand end. It would also be better 
if the dates for the two years and the figures representing tons had 
been placed at the extreme left in the manner shown in Fig. 41. 

In Fig. 43, the two locomotives are placed neck and neck, but 
the whole chart reads backwards in that it reads to the left instead 
of to the right. Turn the page over and hold it up to the light. Through 
the back of the paper, the arrangement of the cars appears from left 
to right as it should. 



lavo 



I880 



1890 



I900 




5.7 




242 = too >; 

3S 






^^^B^^WWB^WHHUHIHll 





PRODUCTION 
I EXPORT 

UPPER riGURES 

MILLIONS OF BALES 
LOWER FIGURES 

MILLIONS OF DOLLARS 



7.3 
308 = t00y„ 
4.9 , 




HiftiHiHIiliilfflilliffliliHHffliiililiiil =^^==^=^^^^^^^^^=^ 




Fig. 44. Yearly Cotton Production and Export of the United States. The Figures 
with the Arrows Show the Number of Millions of Bales and also the Value in 
Millions of Dollars 

If horizontal bars are used to represent years, the earliest year should be shown at the top as seen here 

No data are given in Fig. 43, and it is impossible to tell whether 
the comparison between 1901 and 1912 should be based on the ratios 
of the whole length, including engines, or whether it should be based 
on the lengths for cars only. A ratio without the engines would be 
much larger than with engines. This chart is accordingly unreliable. 
The difficulty in regard to engines being included in the drawing 
could be entirely overcome if the freight cars were made in solid black, 
with the engines shown in outline only, so that the eye could judge 
the ratio between the solid black bars representing freight cars without 
including the outline drawings of the engines. 

Often in charting information like that given in Fig. 44, vertical 
bars instead of horizontal bars are used. However, the figures given 
in Fig. 44 in conjunction with the bars make it desirable that the bars 
should here be horizontal in order that the figures may be read easily. 



42 



GRAPHIC METHODS 



1912 


$990 






1911 


$1,100 j 






1910 


$1,380 






1909 


$1,700 






1908 


$1,880 



THE RISE OF THE LOW-PRICED CAR 
SHOWING HOW THE AVERAGE VALUE OF EXPORTED 
AMERICAN AUTOMOBILES HAS DROPPED IN FIVE 
YEARS 

World's Wort 

Fig. 45. The Illustration and the Titles 
are Shown Above Exactly as Origi- 
nally Printed 

The reader is misled if he does not notice that the 
earliest year has been shown at the bottom 
instead of at the top. The wording of the two 
titles, when taken in conjunction with the chart, 
really adds to the general confusion 



AVERAGE VALUE OF AMERICAN AUTO EXPORTS The arrangement of dimension 

marks with an arrow-head at each 
end is a convenient scheme worthy 
of wide use. Note that the per- 
centage figures in the illustration 
clearly refer to the value of the 
cotton rather than to the number 
of bales. The figures representing 
time, in this case years, read down- 
ward as they should do in every 
case in which horizontal bars are 
used to represent facts at different 
periods of time. If the horizontal 
bars are arranged with the earliest 
date at the top, any reader who 
wishes to do so may read the chart 
as a curve from the left-hand edge 
of the page and the dates will then appear in correct order from left 
to right. 

In Fig. 45 the latest date has been placed at the top of the chart. 
This causes an impression absolutely the reverse of what it was in- 
tended to bring out 
by the drawing. Any 
one glancing at this 
chart is likely to 
suppose that the 
earlier year is indi- 
cated at the top and 
probably would not 
notice that the 
draftsman in this 
case, for some unjus- 
tifiable reason, has 
reversed the correct 
arrangement. 









PASSENGER 


AND FREIGHT REVENUES 














(Average for U. S.) 










PER MILE OF ROAD 


Average 








Ratio of 










Receipts 


Average 


Average 


Average 
Haul 


Operating 






No. of 


No. ot 


per 


Receipts 


Journey 


Eypenses to 


Date 


Net 


Paaaeagera 


Tons 


Passenger 


per Ton 




per Ton, 


Operating 




Operating 


Carried 


Carried 


per Mile, 


per Mile, 


Passenger, 


Miles, 


Revenues, 




Revenue 


1 Uile 


1 Hile 


Cents 


Cents 


Miles 




Per cent 


I90«' 


83 171 


130 073 


974 654 


1.937 


.754 


32,86 


143. 83 


69.75 


1*7 


3 6% 


123 259 


I 052 119 


2.014 


.759 


31.72 


131,71 


67.53 


iao6 


3 548 


114 529 


982 401 


2.003 


.748 


31. 64 


132,33 


66.08 


iins 


3189 


109 949 


861396 


1.962 


.766 


32,21 


130,60 


66.78 


HI 14 


2 998 


104 198 


829 476 


2,006 


.780 


30,64 


133,23 


67.79 


HH 


3 133 


103 291 


855 442 


2.006 


.763 


30,10 


132,80 


66.16 


1902 


3 048 


99 314 


793 351 


1.986 


.757 


30.30 


131.04 


64.66 


m\ 


2 854 


89 721 


760 414 


2.013 


.750 


28,58 


135.03 


64.86 


m» 


2 729 


83 290 


735 352 


2.003 


729 


27,80 


130.87 


64.65 


\m'i 


2 435 


77 821 


659 565 


1.978 


.724 


27.89 


131.04 


65.24 


imt 


2 325 


72 462 


617 810 


1.973 


.753 


26.70 


132.09 


65.58 



Courtesy of ''Data," Chicago 

Fig. 46. Average Raihroad Revenues from Passengers and 
from Freight in the United States 

Here again the earliest year has been shown at the bottom instead of at 
the top. In tabulations of this sort there is less danger of erroneous 
reading if the earliest year is shown at the top. Years are usually 
grouped in fives, including in one group years ending from one to 
five inclusive, and in the next group years ending from six to ten 
inclusive 



In Fig. 46 also, 

the latest year has been placed at the top of the column instead of at 
the bottom of the column. Though some precedent could probably 
be found for such an arrangement, the arrangement nevertheless seems 



COMPARISONS INVOLVING TIME 



43 



VALUE, AMERICAN EXPORTS 


1906 


$4,409,136 






1911 


$21,636,661 




1912 


$28,300,139 


VALUE, 


IMPORTS FROM ABROAD 


1906 


$4,910,208 


1911 $2,446,248 

1912 $2,000,000 

A MARVEL OF EXPORT TRADE 



an unfortunate one which should 
not be copied. Note that in Fig. 46 
the figures have been arranged in 
groups of four with a blank space 
to assist the eye in reading across 
the page. In general, it is cus- 
tomary to have such figures not 
in groups of four but in groups of 
five, the groups including years 
ending in 1 to 5 inclusive and 6 to 
10 inclusive. 

A rapid reader seeing Fig. 47 is 
likely to get a much exaggerated 
idea of the increase in the Amer- 
ican exports of automobiles. The 
arrangement of the three hori- 
zontal bars for the three years is 
such that the reader is justified in 
assuming that the years are con- 
secutive. He is not likely to 
notice that the upper bar repre- 
sents the year 1906 and that four 
years are omitted between 1906 and the consecutive years 1911 and 
1912. Since there is nothing to indicate that years have been left 

out after 1906, the reader seeing 



SHOWING THE AMAZING INCREASE IN OUR EXPORTS 
OF MOTOR CARS, AND THE STEADY DECREASE IN OUR 
IMPORTS, IN THE LAST SEVEN YEARS 

World's Work 

Fig. 47. This Illustration was Originally 
Printed with Fig. 45 on the Same 
Page of a Magazine, yet in Fig. 45 
the Earliest Year was Shown at the 
Bottom While Here the Earliest Year 
is Properly Shown at the Top 

There is, however, danger, in this illustration, that 
the reader may assume that the three bars rep- 
resent consecutive years without noticing the 
jump from 1906 to 1911. Compare Fig, -iS 



1906 



Value, American Exports 

'4,409,136 H 



1911 
1912 



21,63e,661 
28,300,139 



Value, Imports from Abroad 



1906 

1911 
1912 



4,910,208 

2,446,248 
2,000,000 



Fig. 48. The Contrast of American Ex- 
ports and Imports of Automobiles 

The data of Fig. 47 have here been redrawn. The 
values have been shown at the left of the bars, 
where they give the neatest and most convenient 
arrangement. Note that the bar for 1906 is 
somewhat separated from the bar for 1911, so 
as to indicate to the reader that the three bars 
do not represent consecutive years 



the figure 1912 is apt to assume 
that the two earlier years are 1911 
and 1910. 

Fig. 48 is a redrawing of Fig. 
47 with a change in scale to indi- 
cate to the reader that the earlier 
year shown for comparison must 
not be read as one of three con- 
secutive years. Though the space 
left between the bars for 1906 and 
1911 would not be sufficient for 
the four omitted years, if the 
whole chart were drawn to scale, 
the space is nevertheless large 



44 



GRAPHIC METHODS 



enough to serve as a safeguard to the reader. A slight break could 
indicate in this manner a gap of any large number of years which it 
would not be feasible to denote by allowing space according to scale. 
In Fig. 48 the years and the figures for the chart are properly shown 
to the left much as they are shown in Fig. 24 and in Fig. 27. 



1912 







BU. 

SB 


BU. 




1312 



1311 1912 1911 1912 



A'tw York Times AnnalUt 



Fig. 49. The Size and the Value of the Com Crop of the United States in 191 1 Com- 
pared with that of 1912 

The object of the chart is to show that, though there were more bushels of com in 1912, the producer re- 
ceived less total money than in 1911. 

The left-hand illustration is incorrectly made as it shows the earlier year to the right. In the central 
illustration this error has been corrected and the years are named at the base instead of at the top. 
The arrangement still fails, however, to bring out the message clearly. 

From the right-hand presentation it can be seen instantly that the number of bushels has increased while 
the total money received has actually decreased. The right-hand presentation is arranged in accord- 
ance with the working of the average person's mind 'and it gains in clearness accordingly 

The left-hand group in Fig. 49 was used as an illustration in a 
business magazine. The purpose of the chart was to show that in 
1912 the farmers of the country raised more bushels of corn than in 
1911 but received less total money in return. Note that the earlier 
year is placed at the right instead of at the left, and that the dates 
are given at the top rather than at the bottom. The middle group 
of bars corrects the error, but the information is still not as clearly 
brought out as it should be. The best way to bring out this informa- 
tion is to show that the number of bushels has increased while the 
number of dollars has decreased, and this is not clear from the middle 
drawing. In the right-hand presentation it is clearly seen that the 
bushels went up though the total value came down. The right-hand 
drawing follows the working of the average person's mind and it gains 
in clearness accordingly. 

As a general rule dates should always be arranged to read from 
left to right, and columns of figures should be arranged with the col- 
umn for the earher date at the left. A common exception is made, 
however, in the case of financial reports when it is desired to show 
the most recent year next to the various type-headings relating to 



COMPARISONS INVOLVING TIME 45 

« 

earnings, expenses, etc., as in Fig. 50. In the case of financial reports 
it is always the latest year which is of chief interest, and for this reason 
the arrangement of Fig. 50 seems permissible in order that the figures 
and the account names may be side by side. The problem in Fig. 49 
is so entirely different from that in Fig. 50, that the method of Fig. 50 
cannot be held as a precedent to justify the reversed arrangement 
of dates shown at the left of Fig. 49. The fact that one needs an 
umbrella on a rainy day is not sufficient reason for carrying an um- 
brella at all times. 

* • • 

UNION BAG AND PAPER COMPANY— Reports for 
the year ended Jan. 31 : 

1913. 1912. 1911. 1910. 

Net earnings $554,251 $1,017,835 $1,038,112 $1,055,400 

Depr. and ext. fd. 122,585 122,205 120,987 149,925 

Balance 431,000 895,570 917,125 905,470 

Skg. fd. & bd. red. 134,925 114,095 110,745 107!o05 

Balance 296,741 781,475 806,380 797,870 

Interest 253,748 202,480 197,135 204,611 

Balance for divs.. 42,993 578,995 009,245 593,259 

Preferred dividend .330,<X)0 440,0iX) 440,000 440,000 

Deficit 287,0'}7 •138,995 •109,245 *153,259 

Prev. surp 1,921,788 2,020,471 1,851,226 1. 097,968 

Bond disc. & exp. 70,945 237,677 

Profit and loss sur.l, 563,836 1,921,788 2,020,471 1,851,220 

* • • 

New York Times Annalist 

Fig. 50. Brief Financial Statement Regarding the 

Union Bag and Paper Company ' 

In condensed statements of this sort there seems to be good 
reason for placing next to the headings at the left the column 
of figures for the latest fiscal year, since this information 
is of most vital interest to the reader. Columns for other 
years are then printed to the right for comparative pur- 
poses. The earliest year is shown at the extreme right 

Though this reversed arrangement of years seems permissible 
for the purpose of printed reports as here used, there is 
no justification for the use of the reversed arrangement in 
chart work. As a general rule material given by years 
should be shown with the earliest year at the left 

Fig. 51 is an illustration photographed down from a large drawing 
used in a wall exhibit. It is a fair example showing what can be done 
to arouse interest by the judicious embellishment of charts, especially 
of those for wall exhibits intended to reach a miscellaneous audience 
having an average of rather limited education. Note the smoke- 
stacks in Fig. 51. The smoke-stack at the left is the same height as 
the bar for the year 1906-07, and the taller smoke-stack at the right 
the same height as the bar for 1912-13. As this drawing was made 
for a wall exhibit to show the co-operation of manufacturing companies 
with the college, the pictorial embellishment seems quite justifiable 
and useful to attract attention to this particular exhibit. A pictorial 



46 



GRAPHIC METHODS 



effect also relieves monotony in a large exhibition which may have 
hundreds or even thousands of different charts and other wall exhibits. 
Fig. 52 was shown in conjunction with Fig. 51 with the idea of 
pointing out that the number of students in the University of Cin- 
cinnati had increased just as (according to Fig. 51) the number of 
firms co-operating in the engineering work of the University had 

increased in the same time. 

The bars in Fig. 51 and 
Fig. 52 are placed vertically, 
each bar representing a year. 
This vertical arrangement of 
bars permits reading the chart 
as if a curve had been made 
by drawing a line through the 
tops of all the bars. Curves 
are the common language of 
engineers and statisticians. 
In order that the bars may 
be read as curves, it is desir- 



THE NUMBER OF FIRMS 
: CO-OPESATIMG WITH THE 

ENGINEERING COLLEGE 

OF THE 

UNIVERSITY or CINCIHNATI 

HAS INCREASED 289 y. 



mm llll 




American Reaiew of Reviews 



Big. 51. The Increasing Number of Business 
Firms Co-operating with the Engineering 
College of the University of Cinciimati 

^\'hen the bars represent years or other divisions of time, 
a vertical arrangement of the bars is usually more 
desirable than the horizontal arrangement seen in Fig. 
44. With the vertical arrangement a line may be 
imagined joining the tops of the bars so as to give a 
"curve". 

Note, in this illustration of a wall chart, the popular touch 
given by the pictures of manufacturing plants with 
smoke-stacks of the same height as the first and the 
last vertical bars 



able to have the bars placed 
in a vertical position, if they 
represent divisions of time, 
rather than entirely distinct 
subjects such as the separate 
cities compared as to the 
value of their output of manu- 
factured products, in the chart 
reproduced in Fig. 21. 
Lettering like that shown in Fig. 51 or Fig. 52 is conveniently 
made by using the gummed black-paper letters and figures which can 
be obtained in many good stationery stores. A thin pencil line as a 
guide at the bottom of the letters, and some judgment used in spacing, 
will assist greatly in getting a neat result from the gummed letters. 
Large bars like those shown in Fig. 51 and Fig. 52 can be made by 
cutting out strips of black paper and pasting them onto white card- 
board. Such work, however, must be very carefully done or the bars 
will curl on the edges and give an unpleasant effect. It is generally 
better to use India ink in making the bars if a good result is to be 
assured. The liquid drawing ink sold at most stationery stores is 



COMPARISONS INVOLVING TIME 



47 



INCREASE IN STUDENTS IN] 
CO-OPERATIVE COURSE 
ENGINEERING COLLEGE 

INCREASE 1913 OVER ..1907 I 

lassv. 



available in many different colors. Some grades of the drawing ink 
are water-proof after drj'ing. On elaborate charts the water-proof 
cjuality should always be used to make certain that a few rain drops, 
or handling with moist hands, will not ruin the finished w^ork. 

In the discussion of Fig. 51 and Fig. 52 it was mentioned that a 
line could be drawn through the tops of the vertical bars to give a 
curve. If the curve were actually drawn, the bars themselves would 
be omitted. In Fig. 53, instead of using bars, 
we have lines which may be considered as curves 
for each of the several items compared. In this 
case it would be impossible to use bars for each 
of the items shown because the bars would cover 
each other. The bars are entirely omitted and 
lines are simply drawn from the 100 per cent 
point in 1897 to the various points for different 
items in 1907. It is certain that the prices (that 
of pine lumber, for instance, shown by the upper 
curve) did not have the uniform rate of increase 
which the straight hue from 1897 to 1907 would 
indicate. We are considering here, however, the 
changes over the period as a whole, and we can 
for simplicity draw a straight line and neglect 
all the fluctuations of intervening years. The 
general scheme of Fig. 53 is convenient, as the 
neglect of detail brings the main information out 
clearly. Fig. 53 has, unfortunately, been drawn 




in a misleading manner in that the reader is 



likely to interpret the cm-ves as if zero were 
shown at the bottom of the chart. The general 
rule in charts of this kind is that zero should be 
shown as the bottom line, or, if not shown at the 
bottom, that the omission of zero should be 
clearly indicated. As Fig. 53 is shown on a per- 
centage basis, the 100 per cent line should be 
clearly indicated by drawing a broad line on the 
chart for the line opposite the figure 100 in the 
scale. It would have been better, perhaps, to have plotted the data 
so that zero would replace the figure 100. On a scale so made, pine 
lumber would go up 83 per cent, while railroad rates would be shown 



American Review of Revieu-s 

Fig. 52. The Increasing 
Number of Students in 
the Co-operative 
Course of the En- 
gineering College of 
the University of Cin- 
ciruiati 

This illustration was originally 
used as a companion piece 
to the chart of Fig. 51. For 
a popular exhibit the use of 
vertical bars brings out in- 
formation quite clearly. 
Though curves (such as are 
shown in later chapters) are 
superior to vertical bars, it 
is imfortunately true that 
most people do not know 
how to read even the sim- 
plest curves correctly. 

Note the lettering at the upper 
portion of the chart. Letter- 
ing of this kind may be had 
by using separate gummed 
letters such as may be pur- 
chased ready for use 



48 



GRAPHIC METHODS 



as decreasing 4 per cent. The scale would read upward from the 
zero line for increases, and downward from the zero line for decreases. 
By changing the scale and using a broad zero line, misinterpretation 
of the chart would be entirely prevented. 

Fig. 54 is somewhat similar to Fig. 53 in that intervening years 
are neglected, and that lines drawn from left to right of the chart 
indicate the total movement rather than short-time fluctuations. 
Fig. 54 would be better if the lines around the outside of the drawing 
had been omitted. In general, lines of this kind around the outside 
of a chart are likely to be confusing. In this case, the double lines 
at the bottom of the chart draw too much attention to the bottom 

and may cause a wrong interpre- 
tation of the chart. As charts of 
this type are usually made so as 
to have the bottom at zero, the 
reader of Fig. 54 may get an en- 
tirely erroneous idea of the actual 
increase in the rates of wages. This 
chart of Fig. 54 should have been 
drawn with % inch more room at 
the bottom so that the scale would 
begin at zero rather than at $1.00. 
A glance at the chart as it is shown 
here might convey to any but a 
careful reader that the wages of 
trackmen had more than doubled, 
within the period of ten years 
covered by the records thus graph- 
ically presented, though the ac- 
tual wage increase was only from 
about $1.12 to $1.50. Though Fig. 
54 contains a good suggestion for 
presenting data in popular form, 
it is in itself misleading because it 
does not have its base line at zero. 
Fig. 55 is a commendable piece of work for popular presentation, 
as for instance in a magazine. Note the use of dimension marks in 
two independent horizontal rows so that the upper row indicates the 
material from which the ships are made while the lower row shows the 




Reprodvced by Permission from Droege's " Freight Terminals and 
Trains", copyright, 1913, by the McGraw-Hill Book 
Company 

Fig. 53. Changes after Ten Years in Costs 
of Railroad Materials and in Freight 
Rates for a Large Railroad System 

A simple chart of this kind is often advantageous, 
as it neglects all temporary fluctuations and 
shows only the important changes over a period 
of time considered as a whole. The line for 100 
on the scale should have been made a broad line 
to indicate the basis of comparison. A wavy 
line should have been put at the bottom of the 
chart to show that the scale does not begin at zero 



COMPARISONS INVOLVING TIME 



49 



method of propulsion. Dimension lines used in this way are an ex- 
tremely valuable adjunct to chart work and should be used much more 
commonly than they are at present. 
Tendencies for the future are 
frequently very accurately pre- 
dicted by drawing a smooth curve 
through known points and then 
continuing this curve for future 
years in the manner shown by the 
broad line in Fig. 55. The trend 
of this curve indicates that by 
1925, we are likely to have ships 
about 1,200 feet long. Though 
the method of prediction by ex- 
tending a curve into the future is 
very valuable, care must always be 
used to apply the method with 



judgment. If in Fig. 55 a curve 



had been drawn from the data up 
to the year 1860 and extended 
from that point to show the prob- 
able length of vessels in succeeding 
years, the curve would have indi- 
cated a likelihood of 1,200-foot 
ships by 1870. We can see in the 
light of history that such a predic- 
tion would have been most errone- 
ous. It would have assumed the 
continuance of side-wheel steamers 
and would have been based chiefly 
on the length of the Great East- 
ern alone. The Great Eastern 
was too far in advance of the age and was in reality an engineering 
failure. Hence, we see the error which would result from basing a 
prediction curve on too limited an amount of data. 

Periodic photographs of any kind of construction work are one 
of the most striking forms of graphic presentation. Many large 
contractors and machine manufacturers now make a practice of 
having photographs taken of each job at least once each week. The 




THE RISING WAGE SCALE 

SHOWING THAT THE PAY OF RAILROAD EMPLOYEES 
HAS INCREASED FROM 30 TO 50 PER CENT. IN TWELVE 
YEARS. NOTE THAT THE GENERAL OFFICE CLERKS 
NOW RECEIVE LESS THAN THE TRAINMEN. 

World's Work 

Fig. 54. Wage-Scale Increase 

This illustration is so drawn that wages appear to 
have increased much more rapidly than is 
proved by the actual data given in the chart it- 
self. The chart should have been extended to 
show the zero line of the vertical scale so as to 
assist the reader in getting a correct interpre- 
tation 



50 GRAPHIC METHODS 

photographs are carefully dated and filed for reference in case there 
should be any dispute later regarding the progress of the work and 
payment therefor. If a large card giving the date of the work is placed 
in front of the camera so that the date is photographed directly into 
the picture, the date is somewhat more easily proved than it would 
be otherwise. Putting the date card in front of the camera with the 
date upon the card gives a chance for any passer-by to check the hon- 
esty of the date on the picture, much as the "amount purchased" 
card at the front of a cash register checks the honesty of the clerk. 

Progress photographs like those described above are particularly 
effective for use in advertising. A series of three or four pictures 
placed one below another, with the dates carefully stated on each, 
give the best possible demonstration of the rapidity with which con- 
struction work has been completed by the advertiser. A broad use 
for these progress photographs is found in the preparation of reports, 
catalogues, magazine advertising, etc. Thus a manufacturing plant, 
for instance, can be pictured in a series of photographs taken some 
years apart showing buildings which have been added to provide for 
increase in the business. In the case of machinery, a series of photo- 
graphs taken in different years are of value to show the increase in 
the size of the machines built or the successive improvements made 
in the design. 

Moving-picture machines have opened up a whole field of possi- 
bilities in the rapid conveying of accurate information. Many com- 
panies are now using moving-picture films to show the technical 
operations involved in making up their manufactured product, or to 
show views in different parts of a factory. Moving-picture cameras 
have been used also in a very striking way by Mr. Frank B. Gilbreth 
as an adjunct to methods of time and motion study. By placing in 
the camera field with the worker a clock with a large dial and a sweep- 
ing second hand, an automatic and permanent record may be secured 
both of the worker's movements and the corresponding elapsed time. 
The statistics thus graphically recorded are immeasurably more 
accurate and more conclusive than any that could be secured in any 
other way. Possibilities for the use of moving-picture machines in 
educational work in schools are only beginning to be grasped by a 
few of the world leaders in thought. When the moving-picture ma- 
chine becomes a feature of every school room the results will be as- 
tounding. 



COMPARISONS INVOLVING TIME 



51 



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Fig. 55. The Growth in the Length of Ocean Liners 



WoTlfs Work 



This is an excellent piece of presentation for reaching an average non-technical class of readers. A smooth 
curve line has been drawn through the ends of the pictured ships so as to approximate most closely the 
general law which seems to govern progress in ship building. The smooth curve has been extended into 
the future as a prediction of the length of the ships which will probably be built during the next ten years. 

Note the excellent use of dimension-line arrows at the base of the chart showing the materials used in ship 
building and the methods of driving ships at different periods in history 



Bars to represent different intervals of time as in Fig. 51 and 
Fig. 52 maj^ be compared to the progress photographs mentioned 
above. Though the bars and progress photographs are valuable, 
they may be said to give information only in spots. A moving-picture 
machine shows pictures so rapidly that the pictures blend into a con- 
tinuous narrative in the eye and the brain of the observer. What the 
moving picture is to separate progress photographs, the curve is to 
detached bars representing time. In just so much as the moving 
picture is superior to separate pictures shown by lantern slides, in 
just that much is a curve superior 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. The use of curves will be covered in later chap- 
ters. 



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52 



Chapter IV 
TIME CHARTS 

THE liorizontal-bar method used in Chapter I to show the com- 
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various conditions at diflPerent hours, days, and other sub- 
divisions of time. Fig. 57 illustrates a convenient scheme to assist 
the arrangement of vacations for concerns having many employees, in 
which it is necessary to plan the vacations so that there shall always 





O O 

VAOATIOKS FOR THE YEAR 1912 


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Fig. 57. Chart for Assigning Vacation Periods in a Large Office 

Vacations have here been planned so that not more than two men are away at any one time 

53 



54 



GRAPHIC METHODS 





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Fig 

The 



, 58. Chart Illustrating Bonus Work in a Factory where Bonus Work was Intro- 
duced Too Rapidly at First 

curve at the bottom shows the total number of workers earning a bonus each day. On November ii 

all the workers earned a bonus 



be a. good man available to take charge of responsible Avork. A chart 
of this kind can be made quickly if co-ordinate paper is used, the hori- 
zontal lines being drawn in with lead pencil. Vacations are shifted 
around until an arrangement is found that is satisfactory to the man- 
ager and also to the various employees. After a final schedule has 
been decided upon, the time given each employee can be made suffi- 
ciently conspicuous by going over the lead-pencil marks with crayon 
or ink. A chart of this nature posted on the bulletin board of an 
office would serve as a convenient means of giving information to 
the employees as to their respective vacation periods. 

Fig. 56 (page 52) illustrates a method regularly used by Mr. H. L. 
Gantt to indicate conditions in a manufacturing plant. This particular 
chart was drawn to show progress made in training the employees 
of a worsted mill under scientific management. Trained employees 



TIME CHARTS 55 

may earn a bonus by completing a certain quantity of work each 
day. It will be seen at a glance that the chart becomes blacker at the 
I'ight hand, thus showing that two-months training had greatly in- 
creased the output of the employees.. If a chart like this is made 
with different colored pencils, the facts can be grasped more quickly 
than when only one color is used. 

Fig. 58, at the right-hand end, shows that the workers were earning 
a bonus practically every day, and it also shows clearlj^ that some- 
thing was wrong during the middle part of October. The workers 
failed to earn a bonus at that time for the reason that the bonus work 
was introduced so rapidly that they did not get adequate instruction. 
The manager of a plant would realize such a situation at once if he 
had this kind of a chart before him. 

At the bottom of Fig. 58 a curve is plotted to give the number 
of operators who earned a bonus every day. The horizontal scale for 
this curve is exactly the same as for the bar chart above, except that 
in the curve a day is represented by a line rather than by a space. 
In plotting curves, it is customary to represent time by lines rather 
than by spaces, and this curve is plotted in accordance with good 
practice. The scale at the left-hand edge of the lower part of the 
chart represents the number of workers who made the bonus. In 
order to plot the curve, one simply counts in the upper section of the 
chart the number of black blocks which are filled in for the particular 
day. Thus, for October 10, we see that there are seven black blocks. 
The point on the curve is then placed in the lower portion of the chart 
at the intersection of the horizontal line representing the number 
of workers earning a bonus and of the vertical line representing the 
day, October 10. The curve gives a convenient method of deter- 
mining the total number of operators who are earning a bonus. When 
it is desired to know only the number of employees earning bonus 
each day, the curve shows the matter more clearly than do the black 
blocks in the upper portion of the chart. The horizontal bars give 
the story for each worker, the curve gives the total for all the workers. 

A chart like that shown in Fig. 59 would ordinarily be made on 
a long sheet of co-ordinate paper so that the co-ordinate ruling could 
be used for the vertical lines, indicating time. Co-ordinate paper in 
several different rulings can be purchased in rolls so that the desired 
ruling can often be had in continuous lengths. Sometimes, however, 
the desired ruling can be obtained only in flat sheets of limited size 



56 



GRAPHIC METHODS 




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TIME CHARTS 57 

and it is then necessary to make a long sheet by pasting together 
several of the separate sheets. The original study from which Fig. 59 
was prepared was made upon a built-up sheet seventeen inches wide 
and eight feet long, so that a full month of lighter operation could be 
shown on the one chart. ,' 

In a large working chart, such as is shown in Fig. 59, very little 
ruling is required except for the lines limiting the width of the hori- 
zontal bar representing each lighter. In the original chart, drawing 
inks of different colors were used to indicate the four different condi- 
tions — working north and working south, and idle north and idle 
south. Black was used to indicate towing. Solid red showed idle 
time in the north, and a red made up of red-ink strokes with white 
spaces showed idle time in the south. Thus all idle time may be 
indicated by red, the method of application determining whether the 
delay is at the north or at the south end of the trip. Working time 
may similarly be indicated by solid green and by green strokes with 
white spaces. 

It is desirable in all chart work to have certain conventions by 
which colors would be understood to have certain definite meanings. 
Thus, following railroad practice, red could generally be used in chart 
work to indicate dangerous or unfavorable conditions, and green to 
indicate commended features or favorable conditions. Where neither 
commendation nor adverse criticism is intended, colors such as blue, 
yellow, brown, etc., could be used. 

In Fig. 59, an ordinary atomizer filled with writing ink was used 
to fill in gray areas representing night hours. If a little care is used 
in regulating the spray, a good uniform and light shade of gray is 
obtained, on top of which colored crayons will show out clearly, as, 
for instance, in Fig. 59 where Lighter No. 7 is represented as working 
on the night of September 23. To prevent the ink spreading over 
the chart, a strip of cardboard should be laid carefully on each edge 
of the surface which it is desired to ink in by means of the spray. 

In making up charts like that shown in Fig. 59, the data are usu- 
ally recorded on the chart day by day as reports come in. This in- 
volves a large amount of handling of the chart, and the chart is likely 
to be much smeared by the time the last reports are entered. If col- 
ored crayons with the color embodied in paraffin are used, very brilliant 
colors can be obtained, yet rubbing with the hands will not smear 
the colored areas. Unless a non-smearing crayon is used, it is better 



58 



GRAPHIC METHODS 




■■ Idle W^ Towing Carfloat ^^ towns lighter ^g running ught HBtaking Water ^^Coauns 

Fig. 60. Operations of Three Tug-boats in New York for Twenty-four Hours. The 
Boat Represented by the Lower Bar is in Service for a Twelve-Hour Shift Only 

A working chart of this kind would usually be made on a long strip of co-ordinate paper. The illustration 
was drawn entirely by hand to show the possibilities of hand cross-hatching for bringing out information 
ordinarily shown in several colors 

to make up colored charts by using different colors of drawing ink. 
The ordinary crayons smear so badly that a chart made with them 
is sometimes unrecognizable before it is finished. 

Fig. 60 is a further elaboration of the method used in Fig. 59. 
The actual chart from which this illustration was made was drawn 
on co-ordinate paper ruled in tenths of an inch. Each of these tenth- 
of-an-inch spaces was made to represent ten-minutes time, so that a 
much larger scale was obtained than in Fig. 60. As the tug-boat 
captains regularly kept log-books in which their work was recorded 
to a five-minute interval the chart was made to the same interval 
by splitting the ten-minute squares to represent five-minute intervals. 
With a scale of this size it was feasible to use colored crayons, even 
though some of the divisions of time were very short. 

Fig. 60 was drawn by hand and shows the possibilities in preparing 
an illustration of this kind when only one color of printing ink is 
available. 

The chart from which Fig. 60 is taken was made to determine how 
much idle time there was in the operation of three tug-boats, and to 
ascertain whether the boats could be so run as to reduce the amount 
of idle time and give better service. The black in Fig. 60 shows the 
idle time vividly. By looking from bar to bar, it is possible to study 
all the work of the three tug-boats and to determine whether, if the 
work were differently assigned, there would be less waiting between 
jobs. Frequently the tug-boats had to tow two or more lighters or 
two or more car-floats, simultaneously, as will be seen from the extra 



TIME CHARTS 59 

bars placed below the main bar for each tug. The number of lighters 
and car-floats towed simultaneously is clearly shown in the chart, as 
well as the time at which each was picked up, and the time at which 
each was delivered by the tug. In the case of car-floats, a frequent 
break will be noticed at the end of the towing, one-half the width of 
the horizontal bar being marked with black. This convention was 
adopted to show that the idle time was occasioned by the necessity 
of waiting to obtain an unoccupied float bridge into which the car- 
float could be shifted. Though the tug-boat was standing idle it was 
not feasible for the dispatcher to take the tug away from the par- 
ticular car-float to which it was attached, for the tug would be neces- 
sary to place the car-float in the float bridge as soon as the float bridge 
became free. 

Charting of information frequently brings out points which would 
be entirely overlooked if charts were not made. The tug-boat chart 
from which Fig. 60 was taken at once calls attention to the time re- 
quired for the tugs to obtain water. As the service of tugs was valued 
at about $9.00 per hour, the time spent in taking water was a serious 
loss. As soon as the chart showed the extent of this loss, it was com- 
paratively simple to remedy the situation by providing different 
methods of getting boiler-feed water. 

A time chart like Fig. 60 can often be used advantageously in 
conjunction with other time charts covering the same period of time. 
Thus, in studying tug-boats, the information on a chart for lighter 
operation such as is shown in Fig. 59, and on charts for the operation 
of car-floats or of float bridges, may be valuable. All the various 
kinds of equipment with which the tug-boats may be employed could 
be considered in the study, if it is to be determined whether or not 
the most effective use is being made of the tug-boats. If all the charts 
used in the study are drawn to the same horizontal scale, the charts 
can be placed immediately above each other so that the operations 
of all related equipment for every hour of the day and night can be 
instantly seen during the whole of a test period, of, say, a week or a 
month. 

The charts thus far considered in this chapter have shown time 
in the horizontal direction only. In Fig. 61 we have time shown by 
days in the horizontal direction and by hours in the vertical direction. 
This type of chart is extremely valuable in determining whether or 
not schedules are maintained uniformly over any period of time. 



CO GRAPHIC METHODS 

By using different colors of ink a chart of this kind can be made so 
as to show all related operations without the drawing becoming too 
complex to read. Fig. 61 has purposely been made simpler than the 
ordinary chart of this kind to overcome the handicap of being limited 
to only one color of ink in the reproduction. 

Charts in the form of Fig. 61 are valuable in that they show on 
one sheet all the operations occurring during a given period of time — 
in this case, twenty-four hours. Some conditions, such as the blizzard 
of January 7, affect all the dehveries to the different railroads. Study 
of the chart brings out in contrast conditions which are beyond the 
control of man and conditions which are the result of carelessness 
or poor management, which usually crop up first in connection with 
one railroad, then in connection with another, without being so gen- 
eral as to affect all of the curves, as did the blizzard of January 7. 

Fig. 62 shows the possibility of simplification when so many dif- 
ferent horizontal curves must be shown that easy reading is impossible. 
The simplification is made in Fig. 62 by showing only one railroad 
on each sheet. All the figures for one railroad are shown in curves,* 
placed one above the other. Ordinarily curves like those in Fig. 62 
will be nearly parallel, for the time interval required to complete 
each of the steps of work remains about the same day after day. What 
Fig. 62 brings out most of all is not so much the time interval between 
the different steps as the information as to whether each of the dif- 
ferent steps was started promptly on schedule. Any one operation 
started late must delay all the following operations. 

The paper on which Fig. 62 was drawn is in itself worthy of at- 
tention. This letter-sheet size of paper was carefully laid out so that 
a typewriter could be used for the lettering on the margins of the four 
sides of the sheet. The paper was purposely ruled in squares so that 
any of the common divisions of time might be shown. The possibilities 
in this direction are: 

The days of the month may be used on the short edge of the paper 
as in Fig. 62. 

Fifty-two weeks for one year can be shown by using the long edge 
of the paper. 

Three years by months can be plotted by using the thirty-six 
squares on the short side of the paper. 

One year by months can be shown by using every third line along 
the short edge of the paper. 



TIME CHARTS 



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Fig. 6i . Operation of Freight Car-Floats at a Railroad and Steamship Freight Terminal 

Here we have time represented by days in the horizontal direction and by hours in the vertical direction. 
The object of the chart is to record whether car-floats are loaded and dispatched at the same hour each 

Dotted lines show the time at which cars are pushed onto car-floats by locomotives. Solid line.s show 
the time at which car-floats are towed away by tug-boats. Curves for any one car-float destination are 
in pairs bearing the same letter. 

If the departure schedule is well maintained, all curve lines will be practically horizontal. Note that the 
blizzard of January 7 affected the locomotives less than the tug-boats 



62 



GEAPHIC METHODS 



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Fig. 62. Operation of Freight Car-Floats at a Railroad and Steamship Terminal 

In Fig. 61 several different railroad connections were shown on one large sheet. Here, in Fig. 62, but one 
railroad is represented on one sheet, with the idea of using as many sheets as there are railroad connec- 
tions. 

This illustration is photographed down from a sheet of 8^ 2-inch by 11-inch co-ordinate paper specially 
designed for use with a typewriter. The zinc cut for this illustration was made directly from the type- 
written original 



TIME CHARTS 63 

Percentages up to 100 per cent can be indicated by using fifty 
of the fifty-two squares on the long dimension of tlie paper. Tliis 
ruling gives a co-ordinate paper which is extremely convenient for 
general work. Other charts drawn on this same ruling of paper may 
be seen in Figs. 134, 130, 103, 156. 

Fig. 63 was adapted from a chart shown in the United States 
Statistical Atlas for the Census of 1900. The Atlas illustration was 
printed in color, while Fig. 63 is in black ink. The scheme of this 
chart is one which could be used widely, for it is an extremely con- 
venient method of showing a frequently changing rank for a large 
number of units. The blocks for the various States are numbered 
according to the rank of each State at the first year shown at the left. 
The rise or fall in rank of each State at each census can be seen at once 
by following the lines joining the numbered blocks. The actual nu- 
merical rank at each census is seen by reading horizontally to the rank 
number at the right-hand margin or to the numbers in the left-hand 
column of blocks. 

Sales managers publishing a house organ may find the method 
of Fig. 63 of great advantage in showing the status of each branch 
selling-house or the rank of each salesman. If every member of the 
selling organization is given a confidential number, the rank of each 
can be shown in the house organ sent out each month. Branch houses 
can be encouraged to compete with each other if their relative rank 
month after month is indicated on the chart. In the case of salesmen, 
if the numbers are kept confidential no one salesman can tell from the 
chart anything about any other salesman. He could, however, see 
very clearly that his own position in the sales force was getting better 
or worse, according to whether his relative-rank line pointed upward 
or downward. This comparison of selling units on a rank basis is in 
many respects fairer than any curve based on the value of sales. Good 
business conditions or bad business conditions afi^ecting all alike do 
not show up in charts like Fig. 63. What is shown is the real progress 
or lack of progress made by every man or branch selling house as 
compared with all the others. 

Printer's copy for a chart like Fig. 63 can very easily be made 
up if printed strips of the blocks shown in the chart are used. These, 
if desired, could be made from Fig. 63 itself. Simply photograph 
the chart, then take one vertical row of the blocks, as for the year 
1900, and have a line engraving made of them, eliminating the figures 



64 GRAPHIC METHODS 

for numbers which appear in the middle of each block. Print from 
the zinc plate a number of strips of blocks. With shears and a paste- 
pot, another vertical row of blocks may be added at the right-hand 
edge of the chart copy each month to provide "copy" for the plate 
to print the succeeding month's illustration. The identification could 
be lettered by hand inside of the vertical row of blocks for the latest 
month. It then takes only a short time to draw lines joining blocks 
having corresponding numbers. The built-up "copy" is then ready 
for the engraver to make a zinc plate. Zinc plates cost so little that 
there is almost negligible expense required for the new line cut needed 
each month. 

In Fig. 64 the general scheme of Fig. 63 is expanded so that the 
chart shows not only the rank, but also the comparative size of the 
units under consideration. This illustration shows also some inter- 
esting combinations of shading by means of which blocks of distinctly 
different appearance are obtained. Fig. 64 was photographed directly 
from a United States Government report. Otherwise, the years 
would not be shown here reading from right to left instead of from 
left to right. Though the right-to-left arrangement is unfortunate, 
the general scheme of Fig. 64 is excellent, as it gives a large amount 
of information in a small space. The convenience due to this method 
of double comparisons, either horizontal or vertical, gives it a decided 
advantage in clearness. 

Train charts like that shown in Fig. 65 are very commonly used 
by railroads, rapid-transit subways, etc. Fig. 65 would not look so 
complex if colored ink were available to show in contrast the express 
passenger trains, the work trains, etc. It is suggested that the reader 
observe the key at the top of Fig. 65 and then follow a few of the 
various trains from one end of the line to the other, taking into con- 
sideration the fact that this is a single-track railroad and that trains 
must pass at the turnouts which are available. To schedule a pas- 
senger train such as that leaving Tyrone at 12:25 p. m. is no simple 
proposition on such a crowded railroad as this. 

In rapid-transit work in large cities a time-distance chart in the 
general scheme of Fig. 65 is almost essential if methods of giving 
high-speed service to the people are to be studied. These time-distance 
charts can be made on so large a scale that two horizontal lines may 
be used to indicate the stations, with the lines spaced a distance apart 
to show to scale the actual length of each station platform. Time- 



TIME CHARTS 



65 



lero 




190O 

Rank 

^ New York 

2 Penn. 

3 Illinois 

4 Ohio 

5 Missouri 

6 Texas 

7 Mass. 

8 Indiana 

9 Michigan 

10 Iowa 

11 Georgia 

12 Kentucky 
!3 Wisconsin 

14 Tennessee 

15 N. Carolina 

16 New Jersey 

17 Virginia 
IS Alabaoaa 

19 Minnesota 

20 Mississippi 

21 California 

22 Kansas 

23 Louisiana 

24 S. Carolina 

25 Arkansas 

26 Maryland 

27 Nebraska 
2a W. Virginia 

29 Connecticut 

30 Maine 

31 Colorado 

32 Florida 

33 Washington 

34 Rhode Isl'nd 
3B Oregon 
36N.Hampah'e 
37 S. Dakota 
30 Oklahoma 

39 Indian Ter. 

40 Vermont 

41 N. Dakota 
42Dist.of C. 

43 Utah 

44 Montana 

45 N. Mexico 

46 Delaware 

47 Idaho 
4S Hawaii 

49 Arizona 

50 Wyoming 
Si Alaska 
52 Nevada 

Adapted from the United States Statistical Atlas 



Fig. 63. Rank of States and Territories in Population at Different Census Years 

from i860 to 1900 

Each State is represented by a block bearing an identifying number. The change in rank from census to 
census is indicated by the connecting lines. Actual rank at any census can be seen by referring horizon- 
tally to the figures at the right or to the figures at the left. 

A chart of this kind can be used for showing relative rank of salesmen or comparative sales of different 
branch sales-houses ■ 



66 



GRAPHIC METHODS 




TIME CHARTS 



67 











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68 GRAPHIC METHODS 

distance curves like those shown in Fig. 65 are then plotted, one for 
the rear end and another for the front end of each train. As the train 
remains constant in length throughout one whole journey it is obvious 
that the two curve lines must be a constant vertical distance apart 
throughout the length of the chart. At stations, subway trains must 
stop in such a way that the whole length of the train will be opposite 
the platform so that passengers may get in and out of every car. The 
trains follow each other very rapidly, and it is essential that sufficient 
room be left between two trains for safety. If two curves on a time- 
distance chart should touch each other, it would indicate a collision. 
The distance between different train curves on a chart gives informa- 
tion regarding the kind of signal and brake systems that must be used 
to give the desired degree of safety in operating the road. 



Chapter V 
CURVE PLOTTING 

INFORMATION may be charted in many different ways. Under 
present conditions, if six men were given a set of figures and asked 

to chart these figures, the six resulting charts would be widely 
divergent in method. Though variety in method of charting is some- 
times desirable in large reports where numerous illustrations must 
follow each other closely, or in wall exhibits where there must be a 
great number of charts in rapid sequence, it is better in general to use 
a variety of effects simply to attract attention, and to present the data 
themselves according to standard well-known methods. 

In Fig. 66 the attempt to give a spectacular scheme of presentation 
seems to have overshadowed everything else in the mind of the illus- 
trator. Though a striking architectural design has undoubtedly 
been obtained, the chart means nothing, for it is impossible of inter- 
pretation. No scale has been used in either the horizontal or the 
vertical direction, as can be seen by comparing the figures on the block 
for 1830 with the figures on the block for 1840. Even if some scale 
had been used in making up this chart, the general scheme is such 
that the reader would hopelessly flounder in trying to reach an accu- 
rate interpretation. 

Fig. 67 puts the data given in Fig. 66 in the form of horizontal 
bars. Note that the values which the bars represent are given inside 
of the bars, for reference purposes. In order to make the shape of 
each bar stand out distinctly, gray dots were used which permit the 
figures representing the values to be read through the shading. This 
is an interesting attempt, but it is not satisfactory as a general scheme. 
Though Fig. 67 gives the data much more clearly and far more accu- 
rately than Fig. 66, the method is not satisfactory because it is diffi- 
cult for the eye to follow the ends of the different bars in order to 
judge the increase made from decade to decade. The best method 

69 



70 



GRAPHIC METHODS 



134 



I830 



222 



I840 



318 



I850 



687 



I860 



829 



I870 



I504. 



!280 



164-7 



IS90 



2224- 



ISOO 



The Philadelphia Commercial Museum 

Fig. 66. Commerce of the United States since 
1830. The Sum of Annual Exports and 
Imports. Values are given in Millions of 
Dollars 

Such a chart as this is worse than none. There is no scale 
in either direction. The block for 1830 is drawn with a 
larger area than the block for 1840 which represents a 
larger quantity. Compare with Fig. 67 and Fig. 68 



CURVE PLOTTING 



71 



1630 t l34l 


1 




1B40 C 


S22 










reso C 


. ^IG 


"3 




1B60 C 




607 ■ 


Z3' 


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1690 r 






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rsoo [ 






.,, Z24<|- • .-wv^a-.W :;,,.,] 



Fig. 67. Values of Annual Exports and Imports 
of the United States. Figures are Given 
in Millions of Dollars 

This chart is drawn to scale from the data given in Fig. CO, 
to show tlie use of horizontal bars for work of this nature 



of the three is followed in Fig. 68, where the data from Fig. 67 are 
plotted in the form of a curve. The curve method brings out all 
the information in less space and in clearer form than does the block 

system in Fig. 66. •"' 

An understanding of 
how to plot curves and of 
how to read them should 
be part of the equipment of 
every business man, just 
as it is of every engineer, 
physician, biologist, and 
statistician. The general 
scheme of curve plotting 
is so simple that instruction 
in it should be given as part of the work in elementary arithmetic in all 
pubHc schools. Children over ten years of age can do plotting and 
can understand simple curves like that of Fig. 68. Curves are usually 
plotted on co-ordinate paper already ruled in squares, so that the person 
doing the plotting need not take 
the time necessary to rule the 
paper. For reports, for illustra- 
tions of magazine articles, or for 
advertising, it is ordinarily better 
to rule by hand a small area such 
as is shown in Fig. 68 so that the 
spacing of the ruling may suit ex- 
actly the data which it is desired 
to plot. 

In Fig. 68 we have data avail- 
able only by decades, from 1830 to 
1900 inclusive. Lines are drawn 
vertically for each decade. The 
scale need not run above 2,300, for 
the largest figure to plot is 2,244 
millions. A suitable scale is secured 
by using one line for each 200 millions. After the background ruling 
has been drawn, the figures at each census are laid off to scale, on 
the proper vertical lines to represent census years, and a dot is 
placed on each vertical line at that vertical distance which represents 



MlLUONS 
OF — 


N 


687 
829 

1S04 
1647 


2200 






























/ 


1 800 














/ 


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/ 










/ 






1200 
tooo 
800 

600 
400 










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1630 40 '50 '60 "70 '80 '90 1300 

Fig. 68. Value of Annual Exports and 
Imports of the United States. Fig- 
ures are Given in Millions of Dollars 

This curve is drawn from the same data as Figures 
66 and 67. The curve shows the changes 
from decade to decade more vividly than do 
the horizontal bars of Fig. 67 



72 GRAPHIC METHODS 

the data according to the scale chosen. Thus the figure 222 for the 
year 1840 would be indicated as a dot on the vertical line for 1840 
slightly above the place where the horizontal scale line for 200 crosses 
the chart. After the dots for decade years have been placed on the 
vertical lines, the dots are joined with a heavy line and a curve 
appears. 

The curve of Fig. 68 shows the changes from decade to decade 
much better than the bars of Fig. 67. It can be seen at once from 
the curve that the greatest gain in any decade was between 1870 
and 1880 when the increase was three and a half divisions on the ver- 
tical scale. The bars in Fig. 67 have no horizontal scale to measure by 
and the comparison between census years is accordingly more difficult. 

When plotting any curve the vertical scale should, if possible, be 
chosen so that the zero of the scale will appear on the chart. Other- 
wise, the reader may assume the bottom of the chart to be zero and 
so be grossly misled. Zero should always be indicated by a broad 
line much wider than the ordinary co-ordinate lines used for the 
background of the chart. 

In Fig. 68, it will be noticed that figures are given at the top of 
the chart to represent the value for each point plotted on the curve. 
The use of figures at the top of the chart in this manner is very de- 
sirable. The figures are in plain sight, so that anyone desiring to 
know the value of any point on the curve can look above the point 
to get the actual figure wanted, without having to read from the scale 
at the left-hand edge and then estimate roughly the value for any 
point which happens to fall in a space between two horizontal lines 
of the scale. Reading from the figures at the top of the chart permits 
any desired figure to be obtained more rapidly and much more accu- 
rately. In addition to this, the figures are recorded in such manner 
that they may be quoted for use elsewhere by anyone who may wish 
to make use of the data in a speech or in a written article in which 
the chart itself cannot be used. 

It would be a desirable thing if in all curve charts the figures for 
the horizontal scale were placed at the bottom of the chart rather than 
at the top. Many illustrations in this book, taken from pubhcations 
of excellent standing, show dates (such as years, months, etc.) at the 
top of the chart. If the horizontal scale were always placed at the 
bottom, the standard arrangement would be a convenience to the 
reader and would give the additional advantage that the top of the 



CURVE PLOTTING 



73 





















y 


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y 
























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y 














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SB 



chart would be free for a numerical statement such as is found at the 
top of Fig. 68. 

The scales of any curve chart should be so selected that the chart 
will not be exaggerated in either the horizontal or the vertical direc- 
tion. It is possible to cause a visual exaggeration of data by care- 
lessly or intentionally selecting a scale which unduly stretches the 
chart in either the horizontal or the vertical direction. Just as the 
English language can be used to exaggerate to the ear, so charts can 
exaggerate to the eye. 

A curve permits of finer "^Ssliisil 

interpretation than any 
other known method of 
presenting figures for anal- 
ysis. Fig. 69 gives some 
information which many 
persons might not fully 
grasp if only a column of 
figures were used to indicate 
the average yearly earnings 
of Princeton graduates. The 
fairly uniform slope of the 
curve for the first six years 
after graduation indicates 
that the men were receiving 
almost uniform raises in pay each year. It must be remembered that a 
straight-line curve simply indicates that the amounts of the increases 
year by year are uniform in numerical value. If a curve were started at 
the lower left-hand corner of the chart and drawn diagonally across each 
of the rectangles of the chart, it would be seen at once that there 
would be a straight line indicating an increase in salary of $500 per 
year. With such a straight line across the chart, the increase in salary 
for the first year would be $500. As compared with a zero beginning- 
wage there would be an increase of an infinite percentage at the end 
of the first year. The next year the increase would again be $500. 
Compared to the $500 salary, the increase would be 100 per cent. 
The third year the increase would be $500, and compared to a $1,000 
salary the increase would be only 50 per cent. A curve of uniform 
slope on any chart of rectangular co-ordinate lines indicates only that 
there has been a uniform increase or decrease in actual numbers, not 



Fig. 69. Average Income of 155 Princeton Grad- 
uates of the Class of 1901 for Ten Years After 
Graduation 

Note the effect of the 1907 panic on incomes in 1908 



74 



GRAPHIC METHODS 



values given in Millions of UollaJ^ 



•PRODUCTION 



a uniform rate of change on a percentage basis. A plotted line repre- 
senting a uniform rate of increase from year to year on a percentage 
basis may be seen in the curve given in Fig. 121. 

The untrained reader of 
curves will probably not be 
able to tell instantly what 
made the fiat portion of the 
curve in Fig. 69 during the 
year 1907 to 1908. One of 
the chief advantages of the 
curve method of presenting 
information is that a curve 
forces one to think. A 
little thought here will at 
once bring out the fact that 
the flattening of the curve 
was caused by the 1907 
panic. Though the panic 
started in October of the 
year 1907, the year 1907 
was really one of the most 
prosperous years the coun- 
try has ever known. It 
would be more fitting if the 
panic were called the 1908 
panic, since the main effect 
of the panic came in 1908 
rather than in the year 
1907. It can be seen that 
the Princeton men had 
their incomes reduced dur- 
ing the year 1908 so that 
the average fell below that 
of 1907. By looking along 



IMPORTS 



EXPORTS 



rmTi 



8- & 



Cotton Goods 

The Philadelphia Commercial Museum 

Fig. 70. Cotton Goods Production, Import and 
Export for the United States. Values are 
Given in Millions of Dollars 

The order of years here reading from right to left gives the 
first impression that production is decreasing. Compare 
this illustration with Fig. 71 



the curve it will be noticed 
that though there was a larger yearly increase in salary after 1909, 
salaries at the end of 1911 had not attained the point which it 
would seem they would naturally have reached if no panic had 
occurred at a time so shortly preceding this date. 



CURVE PLOTTING 



75 



Millions 

or 
Dollars 



In Fig. 70 vertical bars have been placed touching each other, 
with the earlier years at the right. The whole arrangement of the chart 
is extremely poor and also misleading. In Fig. 71 the data of Fig. 
70 have been replotted. The most striking thing about Fig. 71 is 
the falling off in the rate of increase of production in the decade 
between 1870 and 1880. The shape of the curve at once starts a train 
of thought in regard to tariff legislation and other conditions which 
may affect the manufacture of cotton goods. 

It will be noticed in Fig. 71 that we have four curves, while only 
three sets of bars were given in Fig. 70. It is evident that if we add 
production and imports and then deduct exports, we will have a fair 
indication of consumption if the amounts remaining in warehouses, 
etc. (which are probably a negligible percentage of the whole con- 
sumption) are excepted. Note that the import and export curves follow 
each other in general form, 
though the export curve 
fluctuates on a percentage 
basis much more rapidly 
than does the import curve. 
Remember that in the fluct- 
uations of two curves like 
these, the change from year 
to year must be judged 
from the zero base line 
rather than from the slope 
of the curves themselves. 
The drop in the export 
line from 1860 to 1870 was 
almost one-half, while the 
drop in the import line for 
the same period was much 
less than one-half, even 
though the import line 
does show the greater slope 
downward. 

In Fig. 72 we have an example of what not to do in charting. 
The main effect of the circles is to give one a headache without per- 
mitting any accurate comparison between the years. The eye does not 
easily see each circle as an area. The tendency is to see only rings 













/ 












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/ / 








/ 


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// 










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ltn£orts _ 





.-— - ■"^ 








exPSCt^-- 




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Fig. 71. 



Cotton Goods Production, Import and 
Export for the United States 

These curves are plotted frcm the data of Fig. 70, and show 
the information in much clearer form 



76 



GRAPHIC METHODS 



between the lines of the circles, 
rather than the whole area in- 
cluded inside of each circle line. 

Fig. 73 gives the data of Fig. 
72 in curve form. The heavy solid 
line curve shows the changes from 
decade to decade as they could 
never be interpreted from either 
the actual figures or the circles of 
Fig. 72. The tremendous increase 
in the world's commerce between 
1900 and 1910 is of very great 
interest, showing the effect which 
better means of communication 
have brought about as a result of 
the splendid increase in scientific 
and engineering knowledge. 

If one makes comparisons be- 
tween the circles of Fig. 72 on a 



Billiont) ot 
Donors 




The Philadelphia Commercial Mvsevm 

Fig. 72. Annual Commerce of the World, 
Imports and Exports Combined. 
Shown at Ten-year Periods, 1850- 
1910 

These circles, drawn on an area basis, are even more 
difficult to interpret than the circles of Fig. 38. 
The eye is likely to see the rings rather than the 
whole areas of the circles. Compare Fig. 73 



3£ 
20 

le 

IE 
6 

4 
O 
























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1850 1S60 1870 1680 1890 1900 1310 

The Philadelphia Commercial Museum 

Fig. 73. Annual Commerce of the World, 
Imports and Exports Combined. 
Shown at Ten-year Periods, 1850- 
1910 

The solid line is plotted according to the figures 
given in Fig. 72. The dotted line shows the 
erroneous impression which would be obtained 
by the reader if he should interpret Fig. 72 by 
the diameters instead of by the areas of the 
circles 

diameter basis rather than on the 
area basis to which the circles were 
drawn, one gets an interpretation 
like that indicated by the dotted 
line in Fig. 73. By comparing the 
dotted line with the solid curve 
the reader may see the extent of 
the error which arises if circles are 
compared on a diameter basis after 
being drawn on an area basis. 

Fig. 74 gives a good idea of the 
utility of the curve method for 
showing concisely a large quantity 
of data. If the figures for the price 
of cement had been expressed in 
dollars and shown in a long numer- 
ical column, there would be very 
few readers who would take the 



CURVE PLOTTING 



77 



trouble to follow the table of figures and notice tbe fluctuations from 
year to year. The curve, however, gives all the variations in price 
at a glance and shows in most striking manner the great reduction 
which occurred in the price of cement as manufacturing facilities im- 
proved and increased. A curve of this kind greatly stimulates thought, 
for one immediately wishes to know the cause of each of the peaks 
and of each of the valleys in the curve. One gets a vista of recurring 
periods of financial boom and of financial depression, and a glimpse 
of such factors as new developments in methods of manufacturing 
cement and the constantly increasing demand for the product. 

If the reading of curves were understood by the average educated 
person, it would be possible to use, in almost any kind of magazine, 
advertising illustrations on the order of that shown in Fig. 75. Since, 
however, curves are not 
widely understood at 
present, this type of 
advertising must now 
be limited chiefly to 
the technical journals 
read by engineers and 
others who understand 
curve interpretation. 
It is really a calamity 
that curves are not 
more widely under- 
stood. Ad vertising men 
are now frequently un- 
able to convince people of their argument simply because they have 
no language by means of which figures can be made interesting or 
even intelligible when expressed in an advertisement of hmited size. 
The author ventures to predict that it will be only a very few years 
until curves are so widely understood and used that they may be 
presented advantageously in any high-grade advertising pages. 

It would be almost impossible to give a clear idea of the flood 
indicated in Fig. 76 if only columns of figures were used. With the 
curve it can be seen clearly that the stream rose very rapidly and 
subsided rapidly, so that the stream was down almost to normal 
level within forty-eight hours after the beginning of the flood. This 
curve was probably plotted from flood-gauge readings taken once an 



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FTom Data 


Fi 1 s s 

Chicago 



Fig. 74. Prices of Cement, per Barrel, in Bulk, at the 
Mill, from 1880 to 1910 

Columns of printed figures or a series of vertical bars could not por- 
tray this information as vividly as it is brought out by the curve 
shown above 



GRAPHIC METHODS 



hour, or even more frequently. The curve, therefore, was plotted 
on much more numerous points than are indicated by the vertical 
lines of the horizontal scale. Frequent observations of the gauge 
height and the numerous points plotted on the curve in Fig. 76 ex- 
plain those fluctuations in the line of the curve which occur in the 
spaces between the vertical lines. Ordinarily a chart is sufficiently 
accurate if straight lines are drawn from point to point of the plotted 
data for a curve, without attempting to make a smooth, flowing line. 



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(jdnrul Kitcinc UtriLtc 



Fig. 75. Advertising Illustration used in a Technical Magazine, with a Heavy-type 
Statement Proclaiming that "3000 Central Stations in the United States need a 
High Grade Gasoline-Electric Generating Set" 

The black areas indicate the portion of the ^-t-hour power-house load for which the gasoline engine would 
be used 

The curve looks smooth in this illustration simply because the gauge 
readings were taken so frequently that the nearness of the many 
points made the lines joining them appear curvilinear rather than 
angular. Such a smooth curve would not have resulted if gauge read- 
ings had been taken only every six hours and the chart made by con- 
necting with straight lines the points plotted for the data obtained at 
these longer intervals. 

Another flood curve is shoAvn in Fig. 77. The speed with which 
the water ran off the territory drained can be judged by the shape 
of the curve. It is not. however, safe to compare the shapes of the 
curves in Fig. 76 and Fig. 77 without noticing that in Fig. 77 we have 
one day represented by a space approximately the same as the space 
used in Fig. 76 for only six hours. If the curve of Fig. 76 were plotted 
on the same horizontal scale as the curve of Fig. 77, the flood would 
appear to be much more severe and rapid than it appears from Fig. 76. 



CURVE PLOTTING 



79 



30 






















































01 








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Atob/7 /Voon Noon 

Sept.eth Sept.Tth. Sept.ath. 

Time in Hours 

Engineering Record 

Fig. 76. Curve Showing Duration of a Flood, September 16, 1909, 
in the Canadian River, New Mexico 

This curve was first plotted on a paper having co-ordinate lines close together. For 
ease of reading, the intermediate lines were omitted from the magazine illustration 

In general, it is unwise to compare the shapes of two curves unless 
they are plotted to the same scales, both horizontal and vertical. 

The curve of Fig. 77 is misleading because the scale does not begin 
at zero. Only the peak of the flood is shown, with no zero line from 

which to judge the 
extent by which the 
flood exceeded the 
normal flow of the 
river. If the co-ordi- 
nate lines were drawn 
so as to show the zero 
line, the base of the 
chart would be about 
^ inch lower than it 
appears in Fig. 77, and 
the whole curve would 
make a different im- 
pression. The omission 
of the zero line in charts 
of this kind is partic- 
error made by persons 




ZDOOO 24 25 26 27 28 29 JO jr I 2 

March. 1913 April 

Engineering Retard 

Fig. 77. Flood in the Hudson River at Mechanics- 
ville, N. Y., March, 1913 

Note the different scales at the right and the left by which the 
curve may be interpreted. This chart is misleading because the 
scales do not begin at zero 



ularly irritating, yet it is a very common 
drawing charts. 

Note that in Fig. 77 the curve can be read from two distinct scales, 
one scale on the left side of the chart, and a different scale on the 



80 



GRAPHIC METHODS 



CITIES 



right side of the chart. If only one scale is used, it should be placed 
at the left-hand side of the chart. In very large charts it is some- 
times desirable to repeat the scale at the right-hand side as well. 
Where two different units of measurement are used in the scales, 
the units should be carefully named so that there will be no danger 
of the reader's using the right-hand and the left-hand scales inter- 
changeably as though they represented the same unit. 

Charts like that shown in 
Fig. 78 are quite frequently 
used in public health reports. 
It is difficult to see how such 
an unsatisfactory type of 
chart ever came into general 
use, unless it was because 
there are twelve months in a 
year and twelve hours on the 
face of a clock. If the death 
rates for the different months 
of the year were plotted in a 
curve, using rectangular co- 
ordinates, the data would be 
just as easy to read and to 
understand as when shown by 
the radial scheme (polar co- 




United States Statistical Atlas of the 1900 Census 

Fig. 78. Death Rate from Consumption per 
1000 Inhabitants for Each Month of the 
Year in Cities of the United States 

This type of chart should be banished to the scrap heap. 
Charts on rectangular ruling are easier to draw and 
easier to understand 



ordinates) of Fig. 78. There 
would be the additional ad- 
vantage that the rectangular 
method would be more widely understood than the circular method 
of Fig. 78. 

Though a chart in the form of Fig. 79 might be justified in the 
Sunday supplement of a newspaper where an untrained audience must 
be reached, it is much better to use a curve in the form of Fig. 80 
Avhenever a trained audience is assured. The most interesting thing 
about Fig. 79 is the slanting line which gives an unusual optical illusion 
if observed under artificial hght, especially with a bare gas flame. 
The slanting line then appears blue, although it is printed black like 
the horizontal bars of the chart. 

The dotted line in Fig. 80 corresponds to the slanting line of Fig. 
79, and represents a progressive average of all the points on the curve 



CURVE PLOTTING 



81 



above. The dotted line, of course, coincides with the soKd line at the 
first point where there is only one point to consider in the average. 
Figures for the dotted line are obtained by averaging the figures for 
the first two years, then the first three years, then the first four years, 
etc., until the last point on the dotted line represents an average for 
all the points on the solid line. 

Fig. 80 is worthy of attention as a model of good practice which 
may be studied carefully by anyone just beginning to plot curves. 



1879- I95TONS 




PittsbuTgh and Lake Erie Railroad 

Fig. 79. Yearly Average of Revenue Tons per Train Mile on the Pittsbxirgh and Lake 
Erie Railroad. The Slanting Line Shows a Progressive Average 

If this illustration is observed with artificial light, an interesting optical illusion may be noticed in that the 

slanting line appears blue in color 
The use of horizontal bars here gives a chart less easy to interpret than the curve shown in Fig. 80 for these 

same data 



82 



GRAPHIC METHODS 



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Fig. 80. Yearly Average of Revenue Tons per Train Mile on the Pittsburgh and Lake 
Erie Railroad. The Slanting Line Shows a Progressive Average 

Here we have the data of Fig. 79 plotted in a curve which can be interpreted easily and accurately 
This chart may be considered a model of good practice in curve plotting. All of the work, including the 
lettering, has been done by hand, thus insuring better results than can usually be obtained from printing 

The following features of Fig. 80 are pointed out for the benefit of 
anyone who may have curves to plot: 

1. The zero line is a much broader line than the co-ordinate 
lines. 

2. Heavy lines are not used at the right- and left-hand edges, 
since the chart does not start or end at the beginning or end of 
time. 

3. All lettering is so made that it can be read horizontally or 
from the right-hand edge of the sheet. 

4. Years are given with four figures for every tenth year 
ending in zero. Other years are indicated with two figures so that 
they may be more quickly read. 



CURVE PLOTTING 83 

5. All letters and figures on this chart were made by hand, 
showing the perfection which may be attained by practice in 
lettering. 

6. The curve itself stands out clearly from the co-ordinate lines. 

7. Figures at various points along the curve indicate matters 
which are worthy of special notice. Foot notes are not given 
here, however, as they are only of highly technical interest. 

8. Figures for the values of points on the main curve are given 
at the top of the chart immediately above each corresponding 
point on the curve. Values may be read correctly from the upper 
figures rather than guessed at by estimating them roughly on the 
left-hand scale. 

9. The statement "Revenue Tons per Train Mile" at the upper 
left-hand corner is purposely printed diagonally so that it may 
serve as a heading for each of the two columns of figures, one at 
the left and the other at the top of the chart. The diagonal ar- 
rangement gives a neater effect than can be obtained otherwise. 

10. Though figures for the dotted curve could be shown at 
the top of the chart the dotted line is of only minor interest here. 
It is accordingly best to avoid the two columns of figures at the 
top in order that the figures for the main curve may stand out 
more prominently. 



Chapter VI 
CURVE PLOTTING CONTINUED 

THERE are so many different applications of curves and such 
varied yet convenient methods of plotting curves, that it seems 
worth while to take up some of these in detail, and point out 
certain advantages and disadvantages of different curve-plotting 
schemes. 

Practically all curves display relations existing between different 
sets of data which we may call "variables". One of the variables 
is used as a standard or measure by which to interpret the facts under 
consideration, and it may be called the "independent variable". The 
other variable, which is interpreted from the independent variable, is 
called the "dependent variable". For example, in a bacteriological 
examination of a pond at varying depths, distance below the surface 
would be the independent, and number of bacteria per cubic centimeter 
the dependent variable. In a seasonal gauging of a stream the dates of 
observation would be the independent and cubic feet per second of 
flow the dependent variable. Sometimes we consider more than two 
variables simultaneously, and we then have two or more independent 
variables from which to consider a dependent variable. 

It is difficult to make a general rule for determining in any case 
which is the independent variable and which is the dependent variable. 
The decision depends entirely on how any set of data is approached 
and on the habits of mind of tlie investigator. When time is one of 
the variables it is usually, but not always, the independent variable. 
If we consider values or quantities at different dates, as in Fig. 80, 
time is very obviously the independent variable. If, however, we are 
interested in the length of time required to do different operations, as 
in Fig. 85, Fig. 86, and Fig. 87, our data are expressed in length of 
time and time is the dependent variable. This example is an excep- 
tional case and it is named here only to show that, although time is 

84 



CURVE PLOTTING 85 

ordinarily the independent variable when it enters into curve plotting, 
nevertheless there may be occasions when time is the dependent 
variable, and charts should be plotted accordingly. It is important 
that the person drawing a chart should in each case distinguish be- 
tween the independent varial)le and the dependent variable, for this 
distinction affects the whole arrangement of the chart. 

It should be a strict rule for all kinds of curve plotting 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 information from the vertical scale. 
If there were no 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 from the hori- 
zontal scale, or the reverse. If charts are 
always plotted with the independent varia- 
ble as the horizontal scale, there need be no 
question in the reader's mind as to how he 
should interpret the chart. The rule for scale 
arrangement is not always followed, and a 
so' or/- piEfj-/!- few examples are shown here to indicate the 

(JImple" 3soTo 3Si) difficulty of interpretation which the reader 

„ „ ^ , , may have iust because a rather simple prin- 

MelTOpolUan Sewage Commission J J t 1 

of New York, HJ12 (;.jp]g of curvc plotting has been neglected. 
Fig. 8i. Number of Bac- ^^ p- gj ^j^^ j^^j^ ^j ^^^ ^ ^ ^ 

tena per Cubic Centi- 111 1 c 

meter of Hudson River been plotted downward from the top of the 

Water at New York at ^^art so that the reader may get the impres- 
Different Depths below . „ . . 1 xi-o. ,i- 

the Surface ^^*^^ 01 measurements taken at dmerent dis- 

tances below the surface of the water. In 
making the tests which are represented in Fig. 81, different depths 
below the surfaces were selected and the bacteria determined from 
the water samples taken at these depths. The depth is here the in- 
dependent variable, and bacteria per cubic centimeter the dependent 
variable. The decision as to which is the independent variable and 
which is the dependent variable rests entirely on how the problem is 
approached. Numerous samples could have been taken at different 
depths, and then a curve plotted to determine the depth at which 
certain numbers of bacteria per cubic centimeter were found. In 




80 GRAPHIC METHODS 

such a case, bacteria per cubic centimeter would be the independent 
variable and depth would be the dependent variable. This sort of 
problem may be attacked from either one standpoint or the other, 
and it is just a question of convenience as to which method is used 
and which variable is made the independent variable. Though the 
problem can be stated in such manner that either one variable or the 
other can be made the independent variable, after the statement 
has been made the chart should be consistently drawn so that the inde- 
pendent variable will be used as the horizontal scale and the dependent 
variable as the vertical scale. 

As Fig. 81 is shown it is necessary for the person interpreting the 
chart to select from the vertical scale some number of feet below 
the surface and then read the number of bacteria per cubic centi- 
meter by the horizontal distance to the right. It is only after some 
little puzzling that the reader will notice that the scales for the 
variables have been reversed and that the chart has been practically 
turned on its side. How this chart would appear if the horizontal 
scale were used for the independent variable may be judged by turning 
the book and looking at Fig. 81 from the left-hand side of the page. 
Though it is easy to see why the person making Fig. 81 happened to 
arrange the chart in the manner shown with the variables reversed, 
the gain due to showing depth below the surface in the vertical direc- 
tion does not make up for the possibility of misinterpretation which 
results because of the neglect to follow standard practice. 

In Fig. 82 we again have depth plotted downward from the top 
of the chart. As we wish to determine the velocity of the stream at 
different depths of water, depth is the independent variable and 
velocity is the dependent variable. The arrangement of Fig. 82 is 
not as objectionable as Fig. 81, for the upper half of the illustration 
sliows quite clearly in pictorial form that the subject under considera- 
tion is a stream having a channel shaped as shown, with widths and 
depths as indicated by the two scales. In the bottom portion of the 
diagram the scale of depths downward relates very definitely to the 
upper portion of the illustration so that the reader cannot easily go 
astray. Notice that the curves for the velocity of the water are each 
plotted on a separate vertical line which serves as zero line. The 
curves for velocity begin at various points depending upon the thick- 
ness of the ice, as will be seen from the upper portion of the chart. 
There is, of course, no velocity in that portion of the stream which 



CURVE PLOTTING 



87 



Distances in feet 
40 50 




CURVES OF EQUAL VELOCITY 



VERTICAL VELOCITY CURVES 
Note Numbers at to|5 of curves indicate measuring points 
Numbers at bottom of curves indicate mean velocity in the vertical 




Horizontal divisions represent one foot per second velocity 



Enginecriny Nev:s 



Fig. 82. The Velocity of Water in Different Portions of a Stream Flowing under Ice 

The horizontal scale at the top of the illustration shows points where velocity measurements were made 
through holes in the ice. Velocities at different depths are indicated by the curves in the lower half of 
the chart, each curve being plotted to the right of a vertical zero line which corresponds with some hole 
in the ice. Lines are drawn in the upper portion of the chart showing different points in the stream 
where velocities are the same 

is frozen. The velocity curves end abruptly at the bottom of the 
stream. It will be seen by reading velocities horizontally from the 
different zero lines from which the curves are plotted that the velocities 
are considerably greater in the center of the stream than they are 
near the banks or the bottom. This is natural, as the friction of the 
earth bottom and sides, as well as the friction of the ice at the top, 
causes the water to be retarded and the velocity lessened. In the upper 
portion of the illustration lines are drawn through all those points 
in the stream cross-section which have the same velocities. The lines 
are similar to the well-known isothermal lines on a weather map show- 



88 



GRAPHIC METHODS 



ing where the temperatures are the same. From these hnes it can be 
seen instantly that the highest velocity is at the center of the stream, 
as far away as possible from retarding influences. Velocities gradually 
grow less as the sides, the bottom, or the ice at the top are approached. 



4.00 .BO S,00 .50 6.00 

AELATIve VALUE IN DOLLARS 



'W 9.00 ■» '9.00 



T 

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Counesy of Data, Chicago 

Fig. 83. Relative Value of Different Coals as Compared to Anthracite Coal 

The price of anthracite coal is here the "independent variable" since it is the standard or measure by which 
the other variable is judged. The price of anthracite coal should have been made the horizontal scale 
of the chart. See Fig. 84 

Fig. 82 is an interesting piece of work and the method used in charting 
is justifiable, even though in this case, as in the preceding, the 
independent variable is plotted downward and the dependent variable 
is plotted horizontally. 



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234567S9 

Price of Anthracite Cool — Dollars 



11 



Fig. 84. Relative Value of Different Coals as Compared to Anthracite Coal 

With the arrangement shown here the curve lines for different coals appear in their correct position. Illinois 
coal is at the bottom instead of at the top. The heavy line here drawn for anthracite proves at a glance 
which fuels are better and which poorer than anthracite 



CURVE PLOTTING 89 

Fig. 83 is intended as a comparison between different kinds of 
coal from the standpoint of actual heating value. At the first glance 
at this chart the reader sees that the line for Illinois coal is above the 
other lines, and he is apt to draw the conclusion that Illinois coal is 
better than anthracite, coke, or Pocahontas coal. It is only after 
some puzzling over the chart that one notices that the whole chart 
has been drawn in reversed order. We are considering what the 
relative values of other coals may be if we know the value of anthracite 
coal. The whole scheme of reasoning begins with the "price of an- 
thracite coal." The "price of anthracite coal" is the independent 
variable and should be plotted horizontally, with the "relative value 
in dollars" plotted as the vertical scale. The reader may get a correct 
impression of the chart in Fig. 83 if he will turn over the page and 
read the chart by holding the page up to the light in such manner 
that the zeros of the two scales appear at the lower left-hand corner. 
When this is done, it will be seen that the relative value of Pocahontas 
coal exceeds each of the other fuels mentioned and that Illinois coal 
comes not at the top of the list, but at the bottom of the list in so far 
as fuel value is concerned. 

Fig. 84 has been drawn with the "price of anthracite coal" as the 
horizontal scale, where it belongs because it is the independent vari- 
able. The lines for different fuels now appear in their correct order, 
and the reader sees at a glance that Pocahontas coal has more fuel 
value than anthracite coal. Notice that a heavy line has been used 
for the curve line drawn for anthracite coal. As this line is the standard 
by which the values are compared, it seems best to give it prominence 
on the chart. The position of other curve lines above or below this 
line shows instantly whether the fuels are better or worse than anthra- 
cite in relative value. 

In Fig. 85 an effort has been made to show detail time-studies 
by the use of curves. There is an error here, however, in that the curve 
has been arranged in such manner that the independent variable is 
drawn vertically and the information desired as "time in seconds" 
must be read off from the horizontal scale. The reader wishes to 
know how many seconds are required for any one step or any series 
of steps in the whole work. The chart can be interpreted in the accus- 
tomed way if the page is turned over, and the diagram read by hold- 
ing the page in such manner that the zero on the scale of "time in 
seconds" appears at the lower left-hand corner of the chart when the 



90 



GRAPHIC METHODS 



page is held up toward a light. The curve for operator No. 1 then 
appears below the curve for operator No. 2 and the chart shows cor- 
rectly the relative merits of the two operators. Fig. 86 is a re- 
drawing of the data 
shown in Fig. 85. 
Here the curves for 
the two operators 
appear in their cor- 
rect relative position, 
and it is seen at once 
that operator No. 1 
is the more rapid 
worker, since he uses 
less time. With the 
independent v a r i - 
able made the hori- 
zontal scale, a chart 
can be interpreted 
quickly. If the de- 
pendent variable is 
used as the horizon- 
tal scale the reader is 
likely to draw a con- 
clusion the reverse of 
that the chart was 
intended to show. 





Operator No. . Operator NO. 2 




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IS £0 25 30 

Time in seconds 



Adapted from Sysiem 

Fig. 85. Record of a Detailed Time-Study of Two 
Operators Labeling Packages 

We are here studying the time for different operations. The names of 
the operations constitute the independent variable while time is 
the dependent variable. The chart reverses the proper arrangement 
of scales and causes the curve for operator No. 1 to appear improperly 
above the curve for operator No. 2. Compare Fig. 86 



Fig. 87 shows the data of Fig. 85 and Fig. 86 redrawn in the form 
of horizontal bars such as were seen in Chapter I and Chapter II. 
The relative times for the various operations are shown much more 
clearly by the horizontal bars than by the curves used in Fig. 85 and 
Fig. 86. The time in seconds required for each operation is given 
by detailed dimension lines above each section in the horizontal bar, 
and the comparative total time of the two different men can also be 
grasped instantly. The total time in seconds for the whole series 
of operations is shown by an over-all dimension line above each of 
the bars, and the reader, if he wishes, may make an accurate com- 
parison between operator No. 1 and operator No. 2 by using a numerical 
ratio. A chart of this kind can be very quickly made for ordinary 
office purposes if the horizontal bars are drawn on co-ordinate paper 



CURVE PLOTTING 



91 



and the different areas made to 
stand out in contrast by the use of 
colored crayons. The actual differ- 
ences between the two operators 
would show more clearly, operation 
by operation, if lines were used join- 
ing the ends of the components in 
the two bars in a manner similar to 
that seen in Fig. 32. The data of 
Fig. 85 do not lend themselves well 
to presentation in curve form. In 
Fig. 85 and in Fig. 86 the shape 
of the curves means nothing, since 
there is no numerical scale relating 
to the names of operations. Fig. 
87 shows a much more satisfactory 
method for portraying the data. 

In Fig. 88 we have an applica- 
tion of curves to advertising in pop- 
ular magazines. The curves de- 
pict the circulation of a newspaper, 



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Operations 

Fig. 86. Record of a Detailed Time- 
Study of Two Operators Labeling 
Packages 

Here the scales have been properlj' arranged and 
the two curves appear in their correct relative 
position on the chart. These data, however, 
are not well suited for curve presentation 
and they are more clearly brought out by the 
bar method used in Fig. 87 



Oper- 
ator 
No.E. 















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1 <^ . 


4-0 oocorKT 


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Fig. 87. Record of a Detailed Time-Study of Two Operators Labeling Packages 

By this method of presentation the reader may see clearly the relative length of time for different operations 
as well as the comparison of total time taken by the two workers. Dimension marks and figures show 
conveniently the actual number of seconds required. The different operations have here been given 
numbers instead of names. The scale to which the chart is drawn is named 



92 



GRAPHIC METHODS 



1915 



150.000 




ioooo 



60.000 
SOJOOO 



70000 

EXPLANATION OF CHART 

This chart shows the Cleveland Plain Dealer's circulation by 
months from February 1905 to June 1913. E^ch line up and down 
represents a month, each line across. a.thousand copies sold. Note 
how the top line indicating Sunday .£dlea, and the lower line indi- 
eating daily sales move steadily upward. Observe the steady, 
healthy, sturdy growth from the first month to the last — no sudden 
mushroom-like gains, no unexplained losses, but a consistently 
increasing total affected only by the changing seasons and the bus- 
iness health of the whole country. 

Cleveland Plain Dealer 

Fig. 88. The Use of Curves in an Advertisement to Show the Growth in Circulation 

of a Newspaper 

It is unfortunate that this illustration was not made so as to show the zero line of the vertical scale. In 
advertising work it usually pays to avoid anything which might seem like exaggeration. Omitting 
the zero line makes the growth seem more rapid than it would if the zero line were included in a chart 
drawn to scale. Though the drafting on this chart might have been better, the application of curves to 
advertising deserves commendation 

with the object of convincing advertising managers that this par- 
ticular newspaper is a desirable one in which to place advertisements 
because of the rapidly and steadily increasing circulation. It is sur- 
prising that circulation managers of newspapers have not more often 
used charts to show circulation, instead of the wordy typed state- 
ments so frequently seen claiming great growths in circulation over 
a period of months or years. Though Fig. 88 shows a commendable 
progressiveness on the part of this particular newspaper in adapting 
curves to circulation statements, it seems necessary to point out the 
fact that the chart may cause distrust in the minds of some readers. 
There is a chance that the man who has advertising to place may feel 



CURVE PLOTTING 



93 



that the chart has been drawn in too optimistic a manner because it 
does not show zero at the bottom of the scale. It would have given 
a much more conservative impression if the excellent record of circu- 
lation growth had been plotted in curves having the zero line shown 
at the bottom of the chart, so that the relative growth could be accu- 
rately judged visually. 

In Fig. 89 a large amount of information has been condensed into 
a small amount of space, yet the chart is fairly clear and easy of in- 
terpretation. Several ingenious combinations have been included as, 
for instance, the arrows that show the prevailing direction of the 
wind each day. The chart gives unusually complete information in 
a most convenient form for any ventilating engineer or power-plant 
manager who wishes to keep careful track of his cost of coal in different 
months of the year as dependent upon weather conditions. 



DAY OF MONTH 
g 10 II 12 13 14 15 16 17 18 19 



24 25 26 a? g6 80 30 al 




S R 3CRRCPCSSCPCC PCS: PC R R Fi PC PC S S Sn S Sf? C S R S 

Heating and Ventilating Magazine 

Fig. 89. Record of the Weather in New York City for December, 1912 

The heavy line indicates temperature in degrees Fahrenheit 
The light solid line shows wind velocity in miles per hour 

The dotted line depicts relative humidity in percentage from readings taken at 8 a.m. and 8 p.m. 
Arrows portray the prevailing direction of the wind 

Initials at the base of the chart show weather conditions as follows: S, clear; PC, partly cloudy; C, Cloudy; 
R, rain; Sn, snow 

Fig. 90 shows an example of double co-ordinate ruling on the 
same sheet of paper. The scheme of using double co-ordinates is 
not very well known even to engineers and it seems worthy of atten- 
tion here. The solid line plotted in the general form of a curve with 
a flat space for each month shows the total water consumption in 
millions of gallons per day. The total water consumption is read 
from the scale of the horizontal lines as for any curve plotted by 

The slanting lines are drawn after the total 



rectangular co-ordinates. 



94 GRAPHIC METHODS 

number of gallons used per day has been divided by the number of 
inhabitants in the district so as to obtain a figure for the average 
daily consumption of water per capita. As the population figure used 
depends upon census records it may be necessary to get the rate of 
growth in the population from records as much as ten years apart. 
In Fig. 90 it can be observed that the slanting lines showing the rate 
of growth of the city are straight lines, indicating probably that the 
census figures were used in the drawing of these lines because j-early 
figures could not be obtained. If yearly figures were obtainable the 
slanting lines could be extended vear bv vear until thev reached 
completely across the chart. The rate of growth in population deter- 
mines the angle of the slanting lines, the more rapid the growth the 
greater the angle of the lines. 

The slanting lines are located on the page so that a curve can l)e 
read from either the horizontal lines or from the slanting lines. The 
method of locating the slanting lines can be worked out by anyone 
who will experiment a little in making a chart of this type. When the 
population is known and the total consumption is known, it is only a 
matter of division to determine the consumption per capita. After the 
slanting lines are once placed upon the chart, the curve can be read 
either from the horizontal lines showing the total consumption or 
from the slanting lines showing gallons per capita. 

Taking the peak for February, 1912, we see that the total con- 
sumption averages during the month 142,000,000 gallons per day. 
Reading this same month from the slanting lines we obserA'e that the 
average consumption per capita daily was 127 gallons. Notice, that 
while the total consumption in gallons was much larger in February, 
1912, than in January, 1909, as seen by considering the horizontal 
lines, the consumption per capita in February, 1912, read from the 
slanting lines, was somewhat less than in January, 1909. 

If we consider the growth in the population of the city of Boston, 
it is permissible that the total water consumption in 1912 should be 
greater than in 1908. In spite of the large growth of the city from 
1908 to 1912, there has been a general decrease in the total quantity 
of water consumed. The decrease in total consumption is chiefly 
due to the metering of water to individual users, eliminating a large 
part of the Avater waste which formerly occurred because of careless- 
ness on the part of consumers. The actual percentages of the services 
which were metered in each one of the years considered may be seen 



CURVE PLOTTING 



95 




110^ 



J90& 



/ie-fropoJUarr Wortsr Djsirjct 
Dia^i-am Shoiv/rtf 
Average Dcnily Consumpfion of iVarisr 

M^xen & Whipple 
/9'J 



Jioy 



'»"» w-r ^"9 



/9/0 



/9'l 



/git. 



9" 



Counesy of Hazen & Whipple, New York 

Fig. go. Chart Showing by Months the Average Total Daily Water Consumption in 
Boston, and by Months the Average DaUy •per Capita Water Consumption. Also 
the Yearly Average of Daily Consumption Stated in Total and per Capita 

In this illustration the curves may be read from either of two different sets of co-ordinate rulings. I'sing 
the horizontal ruled lines, we may read from the curves the average total consumption per day. By 
reading from the slanting lines, the same curves may be interpreted as the average consumption per 
capita per day. The scheme of using two sets of co-ordinate rulings is a valuable one. The scale for 
"million gallons per day" should, however, have been shown only at the left, with the slanting line 
scale for "gallons per capita" placed in the right-hand margin for the sake of clearness 

by referring to the figures near the upper portion of the chart. Note 
that in 1908, 21 per cent of the services were metered, while in 1911, 
45 per cent were metered. The proportion of the services metered in 
1912 was not known at the time the chart was made and hence is 
not recorded. 

A httle study of Fig. 90 will show that there is a very striking 
similarity in the shape of the waves for different calendar years. Water 
consumption is high in the winter and again high in the summer months, 
with the lowest point each year usually found in November. The 
exact amount of resemblance of these waves to each other could be 
determined in an interesting manner if a separate curve were plotted 
for each year so that all the curves would be shown one above the 
other in the manner seen in Fig. 103. 



96 GRAPHIC METHODS 

Just how much the total consumption in water has been decreased, 
even though there was an increasing population, may be seen by re- 
ferring to the dotted line on the chart. This dotted line was plotted 
from points which represent the average for the whole of each year. 
Thus, the average in 1905 was about 122 million gallons per day and 
in 1911 about 113 million gallons per day. There is so great a fluc- 
tuation in the main curve from month to month that it would be diffi- 
cult to judge accurately whether the average consumption is going 
up or down if some such curve as the dotted line were not used. An 
average curve line run through a curve in the manner shown by the 
dotted line in Fig. 90 is of great assistance in drawing accurate con- 
clusions from curves which have much fluctuation. 

In Fig. 90, the dotted line, plotted through a point giving the 
average for each year, thoroughly eliminates all the fluctuations 
which would be so confusing to the reader if he had to study only the 
monthly curve. The dotted line shows conclusively by its slant that 
the total consumption from 1905 to 1908 inclusive went up just about 
as rapidly as the growth of the population would lead one to expect. 
After 1908, however, there was a tremendous drop in total consump- 
tion, even though the population kept on increasing. In 1912, the 
average total consumption per day went up somewhat above 1911, 
but yet it did not increase much more rapidly than the slanting line 
of the 'per capita scale might indicate as permissible. Fig. 90 could 
have been improved somewhat if the dotted line had been replaced 
by a broad black line which would bring the yearly-average curve 
vividly to the attention of the reader. The yearly-average curve 
really gives the most interesting conclusions which can be drawn 
from this chart and it is worthy of greater emphasis to the eye than 
is given to it in the chart. 

It would have been better if the scale for "millions of gallons per 
day" had been placed only at the left-hand edge of the chart in heavy 
lettering so the figures would stand out clearly. The scale for the 
slanting co-ordinate lines could then be placed at the end of each 
slanting line at the right-hand side of the chart. The scale for the 
slanting co-ordinate lines is too difficult to find in Fig. 90. 

An interesting study could be made from Fig. 90 by plotting a 
curve which would show each year the percentage of services which 
were not metered, instead of using the figures at the top of the chart 
which show the percentage of services which are metered. A curve 



CURVE PLOTTING 97 

for the percentages of services not metered should show some similarity 
in shape to the dotted line curve in Fig. 90, giving the yearly average 
of daily consumption. 

When any curve fluctuates greatly, the general trend of the curve 
can be most easily determined if the method of moving averages is 
used. If -data are plotted by months, a moving average is frequently 
made to include twelve months. As a succeeding month is included 
in the moving average, that calendar month of the preceding year is 
dropped out of the average so that the average always includes twelve 
months. The moving-average curve is a much smoother curve than 
a curve made from the monthly figures, and is accordingly more easily 
interpreted. The degree of smoothness of any moving-average curve 
depends chiefly on the number of points included in the moving av- 
erage as compared with the number of points in one complete wave 
or cycle in the data curve, and the moving-average curve is most 
smooth if the moving average includes the same number of points 
as are usually found in one complete wave or cycle of the fluctuating 
curve. 

Many curves plotted by weekly or monthly observations show a 
complete wave or cycle each year because of the effect of the seasons. 
With such a curve it is best to use for the moving average the number 
of points included in one year of the fluctuating curve. When, how- 
ever, we study curves relating to financial conditions in any country, 
we find that there are complex cycles which involve several years. 
With such a complex curve considerable care must be used to deter- 
mine the average length of one wave or cycle, so that the moving- 
average curve may be made as smooth as possible and most nearly 
represent the data being studied. 

In Fig. 91 the data when plotted by years give such a complex 
curve that it is not easy to determine just how rapidly exports have in- 
creased. To show the effect of different numbers of points included 
in a moving average, curves were drawn with moving averages for 
three years, five years, and ten years. Since the distance between 
peaks on the curve making one cycle of fluctuation averages more 
nearly ten years than three years or five years, the ten-year curve 
more closely approximates a smooth curve line than either of the 
other two curves. As a matter of fact, the intervals between peaks 
change somewhat so that it is difficult to select any one number of 
years as the correct number for use in making up the moving average. 



98 



GRAPHIC METHODS 




CURVE PLOTTING 99 

The heavy smooth curve was drawn finally by using the points which 
represent the averages of the decades and then sketching in, free 
hand, a line which gives a smooth curve and removes the waves found 
in the ten-year moving-average curve. Notice that the heavy smooth 
curve is so drawn through the ten-year curve as to give approximately 
equal areas on either side of the smooth curve between that curve 
and the curve for the ten-year moving average. The curve for the 
ten-year moving average evidently does not give a fair interpretation 
of yearly data, because the ten-year average curve shows a peak in 
the year 1886 while the data as plotted by years show a valley for that 
year. The peak in the ten-year moving-average curve in 1886 was 
caused by the number of years included in the moving average not 
being a true representation of the length of one full cycle. The length 
of the cycle changes from time to time, so that no one selected cycle 
length is satisfactory for the whole curve. The heavy curve sketched 
in by hand is the fairest approximation to show the trend of the fluc- 
tuating curve as a whole. 

In Fig. 91 the points on any smoothed curve are plotted midway 
horizontally in the range of years included in each moving average. 
It is on this account that the smoothed curves, though all plotted 
from the same data, do not seem to end at the same year at the right- 
hand side of the chart. Though it is good practice to plot smoothed 
curves in this manner with each point midway in the horizontal range 
of the points included in any moving average, there are times when 
it is not desirable to have the point on the moving-average curve fall 
behind the latest point on the data curve. For operating records in 
industrial work, the moving-average curve is convenient to show an 
average for the preceding twelve months or for any other length of 
time immediately preceding. With such curves it is usually best to 
have the last point of the moving-average curve plotted on the same 
vertical co-ordinate line as the last point of the data curve. 

Index numbers are used very commonly in the study of facts 
relating to the prices of commodities over a long period of time. When 
making comparisons by index numbers, conditions are selected which 
as nearly as possible represent the normal or typical conditions for the 
subject under consideration. The figures for other dates are then 
compared with the figures representing the normal conditions, by work- 
ing on a percentage basis so that the figures for the normal conditions 
are taken as unity or 100 per cent. Figures for the conditions to be 



100 



GRAPHIC METHODS 



compared with the normal are expressed in percentages, making the 
increases above normal in figures above 100 per cent and decreases 
below normal in figures below 100 per cent. Unfortunately, the reader 
not familiar with index numbers may not realize that a chart relating 
to index numbers should be read from the 100 per cent line rather 
than from the base of the chart. It is very common to find a chart 
relating to index numbers so drawn that the chart does not extend 
to the zero of the 
vertical scale. Such 
a chart may give a 
false impression of 
much more violent 
fluctuation than 
would be interpreted 
from a chart plotted 
on the usual co-or- 
dinate field and 
showing the zero of 
the vertical scale. 

Fig. 92 is taken 
from the United 
States Government 
Croj) Reporter, a 
magazine widely dis- 
tributed to farmers. 



/309 /S/O /9// /9/S 


'\\ %\\ \ % \'\ % \ \'\ \ \ \ 


i""/^a 1 1 1 1 1 1 L 1 ij r 


r.:: ^k^ /^ i' r i 


Cl--^----tt-- t\ -- - 


: /-U--i-- .1--- 


I-1--J-4--/- /........./.. 


1 jt Mn / I - ; - L 


IZ \r t lit I J -\ tV 


^rl':::!::::::::-:-:-!-.— --^--ut- 


C ii r w. 1. 



United StateslGovernmeJU Ctov Revorter 

Fig. 92. Fluctuation in the Price of Eggs in the United 
States as Compared with the Average of the Monthly 
Figures for the Preceding Four Years 

An untrained reader may not realize that this chart must be read from 
the line representing 100 per cent. Charts for index numbers, where 
the fluctuation is compared with 100 per cent, should have the 100 
per cent line made broad, and a wavy line should be used at the 
bottom of the chart unless the zero of the scale is shown. An alter- 
native arrangement is shown in Fig. 93 



It has been the hope of this magazine to give producers of agricultural 
products an opportunity to study the price records of previous years, so 
that they may, in so far as possible, sell at the time of the year when 
prices are the highest. It is much to be doubted whether the average 
reader of charts like that seen in Fig. 92 would realize that the 100 per 
cent line must be used as a basis for interpreting the chart. The 100 per 
cent line has not been made any heavier than the other lines on the 
sheet. A man who had been at all accustomed to reading charts 
having zero at the base of the chart would be apt to read Fig. 92 as 
though the bottom line were the zero from which the curve had been 
drawn. On such a basis, he might think that the price of eggs in 
January, 1912, was more than eight times the price in July, 1911. 
Such a conclusion would, of course, be entirely unwarranted by the 
actual figures. 



CURVE PLOTTING 



101 



Where charts for index numbers are made on the 100 per cent 
basis, it would seem best to have a broad Hne for the 100 per cent 
line. If there is not room to extend the co-ordinate field down to the 
zero of the vertical scale, the co-ordinate field may be shown broken 
off with a wavy line at the base indicating to the reader that the bot- 
tom of the chart is not a zero line, and that the chart must be read on 
the 100 per cent basis. 

Fig. 93 was drawn from the data of Fig. 92 as a suggestion for a 
type of chart which might be used where an untrained class of readers 
must be reached. By plotting increases above the zero line and de- 
creases below the 



PERCENT 



III 
i « 





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zero line, a chart 
is obtained which 
needs little space 
and which never- 
theless is on a large 
scale, giving a 
great amount of 
« 2o I I ly i I I I I I 1 1 I I 1 1 I 1 1 I I I 1 1 1 1 . 1 I I I l y i I 1 1 1 1 I i ^i iin detail so as to per- 

^ 3o J=--y- ^i^it accurate read- 

' "^ iTf ing of all the vari- 

ous points on the 
curve. There is 
very small chance 
for any untrained 
reader to misin- 
terpret a chart 
made by the gen- 
eral method used 
in Fig. 93. 

Fig. 94 is essentially a chart relating to index numbers. The 
vertical scale, instead of being shown with 100 per cent to represent 
unity, has zero placed opposite the line representing unity. The chart 
does not clearly point out that the curve drawn above the zero or 
unity line represents increases in revenues and not total revenues. 
A much greater fault with the chart, however, is found in the fact 
that the chart compares the operation of a railroad in different years 
by using the year 1908 as unity. 1908 was a panic year, with very 
serious business depression affecting railroads even more than some 



Fig. 93. Fluctuation in the Price of Eggs in the United 
States as Compared with the Average of the Monthly 
Figures for the Preceding Four Years 

The Government Crop Reporter is intended to be of service to farmers. 
Any charts included should be as clear as it is possible to make them. 
The illustration above is submitted only as a suggestion 



10l2 



GRAPHIC METHODS 



of the industrial companies. All the years following 1908 are likely 
to show a greatly increased volume of business in practically any field 
of commerce or industry. Because 1908 was selected as unity in Fig. 
94, the reader would be justified in feeling that the increased amount 

of revenue in the years 
following 1908 might 
have come solely from 
the improvement in 
general business condi- 
tions, without any as- 
sistance whatever from 
ability in managing the 
railroad. If the better- 
ment in the general 
prosperity of the coun- 
try were great enough, 
it might even be pos- 
sible to show in Fig. 94 
a large increase in oper- 
ating revenue due only 

Annual Report or the Wneeling and Lake Erie Railroad. 191i tO thc 'gCUCral imprOVC- 

Improvement in Economy of Operation of ment in business con- 
ditions and in spite of 
reduced efficiency in 
the operation of this 
individual railroad, con- 
sidered 'per se. It is 
not intended here to cast any reflections upon the managing ability 
on the railroad in question. The only object in mentioning the matter 
at all is to point out the fact that the use of the year 1908 as unity 
puts the road unnecessarily under suspicion of attempting to mislead 
the public. 

In any chart where index numbers are used the greatest care 
should be taken to select as unity a set of conditions thoroughly typical 
and representative. It is frequently best to take as unity the average 
of a series of years immediately preceding the years for which a study 
is to be made. The series of years averaged to represent unity should, 
if possible, be so selected that they will include one full cycle or wave 
of fluctuation. If one complete cycle involves too many years, then 




Fig. 94 
the Wheeling and Lake Erie Raibroad, 1908 to 1912 

It will be noticed from the upper left-hand corner of the chart that 
the j'ear 1908 is taken as unity. 1908 was a year of great business 
depression. As business conditions naturally improved in the 
years following 1908, there could be a legitimate question in the 
reader's mind whether the better showing of the railroad is due to 
better management or to the increase in the general prosperity 
of the covmtry 



CURVE PLOTTING 



103 



the years selected as unity should be taken in equal number on either 
side of a year which represents most nearly the normal condition. 

Fig. 95 is an illustration reduced in size from a large chart 10 by 14 
inches. The chart is of especial interest because it is one of a series 
of several hundred charts submitted to the board of arbitration in 
the concerted wage movement in the eastern territory by the Order 
of Railroad Conductors and Brotherhood of Railroad Trainmen in 
1913. These charts cover practically all phases of railroad operation 
and give in condensed form a tremendous quantity of information. 

RELATIVE RETAIL PRICES OF FOOD: SIMPLE AND WEIGHTED AVERAGES-UNITED STATES 























1890- 


1912 
























AVERAse PRICE TOR I890-ISS9" 100.0 


1890 ia»l 1B92 1893 1694 1895 1896 1897 1898 1899 1900 1901 19 


02 11 03 1904 1906 1906 190? 1908 1909 1910 1911 IS 


12 










1 1 i 

Simple 
Year Average 


1 

aelatlvtf 

Prlo«B 


























/ 


160 

140 
130 

120 










890 102.0 

891 103.6 
893 101.7 

893 104.0 

894 99.6 
89& 97.2 

896 94. 9 

897 96.4 
S98 99.4 

899 100.6 

900 102.9 

901 109.5 

902 116.9 

903 116.9 

904 118.5 

908 118.3 

906 122.4 

907 128.0 
906 132.& 

909 140.3 

910 148.6 

911 146.9 

912 157.9 


101. 
103. 
101. 
104. 

S9. 

97. 

96. 

96. 

99. 
100. 
103. 
108. 
114. 
114. 
116. 
116. 
120. 
125. 
130. 
137. 
144. 
143. 
154. 






























160 
140 
130 

lao 










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ILATIVE PRICES? 






no 




























1 1 1 1 1 1 1 








^StMPLE M{.tiAG£ OF THE RELATIVE PRICES Of 


ZreLATIVE prices weighted according to the AVERA6E CONSUMPTION 




15 PRINCIPAL ARTICLES OF FOOD, 


OF THE VARIOUS AfiTICLES OF FOOD IN WORKINCMEWS FAMILIES. 


F;m e-«au. of L»l..r St».t;»e;ci, U.S. D./...rm.«f ^ 


'■'■'■•' (-,,..,...■.,>-...■ . ...-. 



Counesy of F. J. WaTne, Washington, D. C. 

Fig. 95. Relative Retail Prices of Fifteen Principal Articles of Food in the United 
States, 1890 to 1912, by Simple Averages and by Weighted Averages. Average 
Prices for the Years 1890 to 1899, Inclusive, Were Taken as 100 Per Cent 

The solid line shows ordinary averages of the prices for each year considered. In order to get the data for 
the dotted line, estimates were carefully made of the average consumption in workingmen's families 
of each of the fifteen various articles of food. The food prices were then "weighted" in proportion to 
the quantities of each kind actually consumed and the averages shown by the dotted line were obtained. 
The prices of foods to the workmen did not increase as much as the simple averages shown by the solid 
line would indicate 

There is such a great quantity of data arranged in convenient form 
for reference, it seems Hkely that a person wishing to study railroad 
operation could obtain more insight into present-day railroad condi- 
tions by two-hours' study of this series of charts than he could pos- 



104 



GRAPHIC METHODS 







SNO± JO SNOmiW 


-tO «oot>-Q3ia^ertM" 


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IndtistHal Depressions, iv 0. H. HvU 

Fig. 96. A Study of Steel-Construction Work in the United States from 1896 to 1910 as Related to the Financial Condition of 

the Coimlry 


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CURVE PLOTTING 105 

sibly obtain by two months of reading the reports of transportation 
companies and the pages of railway journals, and of asking questions 
from railroad executives. 

A heavy line in Fig. 95 shows the relative average prices of fifteen 
articles of food used in workmen's families. Since the fifteen articles 
of food are not consumed in equal quantities, or in equal value, it was 
necessary to take into account the actual quantity or value used of 
each kind of food. This was done by the method usually designated 
by the name "weighted averages". It is obviously of less importance 
to the workingman if the price of salt should increase 500 per cent 
than if the price of bread or meat should increase 50 per cent. When 
the fifteen articles of food are considered by simple averages, all foods 
are considered as though used in equal quantities and a very great 
increase in the value of some one food would seriously affect the simple 
average even though that food is consumed in only small quantity. 
By weighted averages the actual price of any food is multiplied by 
the budget percentage figure showing the percentage of that food 
used. The products resulting from the multiplication are added for 
each year, and the totals or averages are compared on a percentage 
basis to give a corrected comparison by weighted averages of food 
prices in different years. The weighted averages represent more 
accurately than simple averages the increases in food prices as they 
really affect the pocketbook of the workingman. It will be seen at 
the right of Fig. 95 that the heavy line for simple averages is consider- 
ably higher than the dotted line representing the weighted averages. 
This shows the amount of error which would have resulted in this 
particular study if only simple averages had been used for comparison 
instead of weighted averages. Weighted averages are of very great 
importance in most studies relating to the cost of living, and they 
could be used in other work much more widely than at present if their 
importance and utility were more generally understood. It is un- 
fortunate that in Fig. 95 the term "relative prices" is used in the 
lower portion of the chart as the key for the dotted line. The simple 
averages show relative prices also and the term "relative prices" 
means practically nothing. The dotted line could more properly be 
referred to by the term "weighted averages" as used in the title at 
the top of the chart. 

Fig. 96 is an example of a type of chart which can be of great 
assistance to the chief executive of any corporation having a business 



106 GRAPHIC METHODS 

seriously affected by the ups and downs in financial conditions af- 
fecting the country as a whole. In this chart, a study has been made 
of supply and demand in the hope of getting some basis for prediction 
in regard to periods of financial depression. The various factors 
which might affect prosperity in steel construction work are assembled 
here on one chart so that the whole situation may be studied con- 
veniently and thoroughly. In a chart of this kind some estimates 
and approximations must be made because it is usually impossible 
to obtain accurate data to the extent desired. For work of this nature 
it will ordinarily be found that a little "horse-sense", used in making 
estimates for missing data, will permit the construction of a chart 
giving an astonishingly large number of suggestions useful in deter- 
mining the policy of a business, so that expansion and contraction 
may be in harmony with the basic financial conditions of the country. 



Chapter VII 
COMPARISON OF CURVES 

THERE are many men who from long experience have become 
so skillful that they can glance down a column of figures and 
obtain quickly a good idea as to the high points and the low 
points shown by the figures taken as a whole. When it comes to 
considering two or three columns of figures simultaneously to see 
whether there is a similarity in the fluctuations shown by the various 
sets of figures, the number of men who can intelligently grasp the 
facts presented are rather few. It is in just such problems as these; 
where a number of different sets of data must be compared, that curves 
have tremendous advantage over presentation by columns of figures. 
A man must be almost a genius to grasp quickly the facts contained 
in several parallel columns of figures, yet anyone of average intelligence 
can interpret correctly a chart which has been properly made for the 
presentation of curves. Though there are numerous convenient meth- 
ods which are useful in comparing curves, we can take up here only 
the few of those which are likely to be of most frequent use to the 
average reader. 

Fig. 97 brings out the facts of its subject matter with splendid 
clearness. There are relatively few men who could interpret quickly 
the data for this chart, if the data were shown to them only as two 
separate columns of figures. When a chart like that shown in Fig. 97 
is used, no mental effort is required to get at the gist of the matter, 
and the facts can be obtained much more rapidly than would ever 
be possible by observing columns of figures alone. 

A chart like that used in Fig. 97 can be prepared from tabulated 
figures by any ordinary draftsman in less than one hour of work. 
The cost of making a line cut is probably no more than the cost 
of setting the type if the data are to be shown by tabulated fig- 
ures. The space required for a chart like Fig. 97 is very little 

107 



108 



GRAPHIC METHODS 



No. of 
Calls 
1 l.OOO 



more than would be required for the tabulated figures, and if there 
is any serious limitation on space. Fig. 97 could be much re- 
duced in size without detracting from its clearness. 

Health-department 
reports are not usu- 
ally of interest to the 
layman. Yet health- 
department reports, 
well presented, may 
be of as much popular 
interest as a well- 



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Data of the New York Edison Company 

Fig. 97. Number of Telephone Messages Each Hour 
for One Day in a Business District in New York City 
as Compared with a Residence District 

Solid line, the "Broad" exchange — a tj'pical business exchange 
Dotted line, the "Riverside" exchange — a typical residence exchange 
Note the great number of business calls after mail has been opened in 

the morning and after return from lunch. In the residence district 

there is much morning shopping by telephone 



written magazme ar- 
ticle. Fig. 98 is taken 
from a commendable 
report by the health 
department of the 
city of Boston. In 
the report itself, dif- 
ferent colors of ink 
were used for the 
various curves, with 
the effect of empha- 
sizing the contrast. 



Though the colored inks assisted in catching the eye of the reader, 
the chart with curves designated by letters is usually sufficient for 
all practical purposes whenever the curves do not cross over each 
other in such manner as to be confusing. As mentioned elsewhere, 
a certain slope of a curve plotted on rectangular co-ordinate paper 
does not in itself indicate a greater or less amount of increase or de- 
crease than holds true for some other curve having a different slope. 
The slope of a curve plotted on paper with ordinary co-ordinate ruling 
depends largely on whether the data of the curve are in large figures, 
so as to bring the curve near the top of the chart, or in small figures, 
bringing the curve near the bottom of the chart. In Fig. 98 the fact 
that curve A slopes more than curve C is due to the fact that curve A 
is placed higher on the vertical scale of the chart than curve C. A 
little study will show that the reduction in mortality portrayed by 
curve A is much less on a percentage basis than that depicted by 
curve C, yet curve A has the steeper slope. The slope of these two 



COMPARISON OF CURVES 



109 



curves can best be compared if a pencil line is drawn in such manner 
that the peaks above the pencil line are approximately equal to the 
valleys below the pencil line for each curve. 

Fig. 99 contains some interesting information. Though the chart 
proves fairly well the close dependence of the price of cast-iron pipe 
upon the price of the pig iron from which it is made, the chart is never- 
theless misleading in that the first glance would indicate a much 
greater fluctuation in the price of pig iron than actually occurred. 



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From liic 1910 Annual Report of the Heatlh Department, City of Boston 

Fig. 98. Deaths in Boston of Children under Five Years of 
Age, under One Year, and from Five of the Principal 
Infectious Diseases, Expressed as a Percentage of the 
Total Mortality 

Curve A. Deaths of children under five years of age as a percentage of 

the total mortality 
Curve B. Deaths of children under one year as a percentage of the total 

mortality 
Curve C. Deaths from Diphtheria, Scarlet Fever, Measles, Typhoid Fever 

and Smallpox as a percentage of the total mortality 
Note that Curve A shows a much steeper slope than Curve C, yet Curve C 

drops in 1910 to less than half the figure for 1871. Curves plotted by 

rectangular co-ordinates should not be compared by the slope of the 

different curve lines 

The reader is apt to overlook the fact that the vertical scale of the 
chart does not extend below $11 per ton. He is quite likelj^ to 
think that the price of pig iron had all the rapid fluctuations which 
would be indicated by the changing vertical distances between the 
pig-iron curve and the bottom line of the chart itself. The amount 
of fluctuation would look much less if the chart extended to the zero 
line of the vertical scale. 



110 



GRAPHIC METHODS 



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There is probably a fallacy 
in Fig. 100 because of the rise 
in the general standard of liv- 
ing between 1901 and 1906. It 
is not fair to the 1901 Princeton 
men to expect that they would 
earn as much immediately after 
graduation as men who gradu- 
ated in a period of time several 
years later. In addition to this 
there is probably another serious 
fallacy which affects all three 
curves shown on the chart. The 
income figures from which the 
curves are plotted may not all 
be shown on the same basis. 
Men working on a salary have 
as net cash all the money they 
receive. Men in professions such 
as law, medicine, etc., where 
office rent and other expenses 
are likely to be very heavy, 
may report, as earnings, the 
total amount of money received 
without making corrections for 
the expenses of conducting their 
business. In other words, they 
may very possibly in this case re- 
port gross income instead of net 
income. Such procedure might 
tend to make the curves for 
average income considerably 
higher than they would other- 
wise be. 

Complex charts made up of 
groups of bars as seen in Fig. 
101 are much more common 
than they should be. This type 
of chart is very annoying to 



COMPARISON OF CURVES 



111 



read because it is difficult for the eye to follow, through the whole 
series, the bars representing any one set of facts which may be of 
special interest. The bar method is in itself a simple one, but 
when the bars are combined in the manner shown in Fig. 101 the 
presentation becomes really more complex than if the data were shown 
in the form of curves. 

Fig. 102 certainly brings out the information of Fig. 101 in much 
better form than any in which it is possible to show it by any com- 
bination of bars either vertical or horizontal. The person who is 
just beginning to chart data °°^5'-o''^% 
which he has used formerly 
in tabulated form is often =000 
surprised to find how many 
inconsistencies exist in the 

data and how many different 

^ 1000 

things there are which must 
be allowed for by some 500 
method of estimate. In Fig. 
102 the data for the United ° 
Kingdom are expressed in 





















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Yale, 
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net tons, and for the United pig. 100. Comparison of the Earnings for Five 
States in gross tons. Though Years after Graduation of the Yale University 

. • f 4.1, f Academic Department Class of 1006, the 

some correction of the forms yale Sheffield Scientific School Class of igoe, 

of the curves as they appear and the Princeton University Class of 1901 

in this chart would of There is a fallacy in making this comparison. The standard of 

living undoubtedly went up between 1901 and 1906 

course have to be made to 

get a true comparison of the shipping of the two countries, for our 
purpose the thing of greatest interest is the general tendency of ship- 
ping in the two countries. This we can study fairly well from the 
general shape of the different curves, even though the curves cannot 
strictly be compared with each other in so far as total quantities are 
concerned. 

Fig. 103 shows a convenient method for determining what fluctua- 
tions in the different months of the year are typical for any subject 
being studied. Instead of plotting one continuous curve by months 
for a long series of years to a rather small horizontal scale, a large 
horizontal scale is used and a separate curve is drawn for each year. 
The curves for different years are placed one above the other, so that 
any fluctuations which appear in the same months year after year 



112 



GRAPHIC METHODS 



will be apparent from the similarity in the shape of the curves for 
the different years. 

In order to use a fairly large vertical scale so as to make the fluc- 
tuations stand out clearly, it was necessary to avoid entirely the 
zero lines for the curves plotted in Fig. 103. The omission of the zero 
^^MM Tonnage engaged in Foreign Trade lines may cause the fluctuations 

C=Z1 Tonnage engaged In DomesticTrade from month to month to appear 

greater than their true size would 

Amounts ia thousands of tons 



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Gross tonnage given for United States 
Net tonnage giuenfbr United Kingdom 



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warrant. It is sometimes possible 

to plot a chart on the general 

scheme of Fig. 103 so as to use zero 

lines, but many times it will be 

found that the zero lines cannot 

be used without adding confusion. 

Though it would be preferable to 

have the zero lines included, the 

gain due to the arrangement of 

the curves as shown here for 

comparative purposes is great 

enough to offset the disadvantage 

of not having the zero lines on the 

chart. 

The zinc plate for Fig. 103 was 

prepared directly from typewritten 

copy, with no handwork involved 

except to make heavier some of 

the green background lines and to 

draw the actual curves themselves. 
loi. Comparison since 1850 of the -nt ■• • t;>- tao -i-u -1- -tu ti. 

Merchant Tonnage of the United Notice m Fig. 103 that the month 

Kingdom with that of the United at the left of the chart is December, 
States. Gross Tonnage is Given for ^nd that the point plotted in each 
the United States and Net Tonnage 1.-1-. 1 i 1 i> • 

for the United Kingdom case lor December at the lett is ex- 

The chart is arranged backwards in that it reads actly the SamC aS tllC poiut plottcd 

from right to left. At first sight one thinks » i -p. i , 4. 4."L 

everything is growing smaller instead of larger. lOr LUe J_yecemDer SUOWU at tnC 

The different bars so closely grouped together ^jo-tit of thp nrpppdino- piirvp "Rv 

are exceedingly difficult to interpret. See "gUL Ol LUe pieceuillg CUrVC. DJ 

Fig- 102 repeating the last month of each 

curve in this manner, the interpretation of the curves is much sim- 
plified SO that the reader can see at once what has been the tendency 
of the curve from December to January each year. If the December 



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Philadelphia Commercial Museum 



Fig 



COMPARISON OF CURVES 



113 



point were not represented at the left, it would be necessary for the 
reader to glance several times from the left-hand end of one curve 
to the right-hand end of the preceding curve to determine in his own 
mind just what changes had occurred from December to January 



Millions 

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11350 I860 1870 1880 1890 1900 

Fig. 102. Comparison since 1850 of the Merchant Ton- 
nage of the United Kingdom with that of the United 
, States 

Gross tonnage is given for the United States and net tonnage for the 
United Kingdom. Solid lines United States, dotted lines United 
Kingdom. The "total" figures are not strictly comparable because ' 

of the difference in registration method. The general tendencies 
of the curves are instructive, however. Note the reduction in the 
foreign trade of United States since the Civil War and the steadily 
increasing foreign trade of the United Kingdom 

at the end of each year. The repetition of the point for the last month 
in each year saves time to the reader and also insures against errors 
which might otherwise occur in the interpretation of the chart. 

In Fig. 104 three distinct subjects are compared on one chart 
and, at the same time, the data for each subject are shown for three 



114 



GRAPHIC METHODS 







MOHTmY AVERAOES OP KITTEE FAT DT UrDIAHAPOlIS MIIK. 










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Data of J. J, Hinman, Jr., Indianapolis Department of PuMic Health 

Fig. 103. Monthly Averages of Butterfat Contained in Milk on the Indianapolis 
Market, 1906 to 1913. The Curves Represent Averages from Several Hundred 
Samples each Month 

In order to find what fluctuations are typical for various months of the year, it is convenient to chart the 
data as seen here with curves for different years one above the other. Definite peaks in April and in 
October or November are seen at once. This chart is drawn on the same universal co-ordinate paper 
shown also in Fig. 57, Fig. 130, Fig. 134 and Fig. 156 



COMPARISON OF CURVES 



115 



JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC. 


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Comparative Monthly Earnings ana Expenses Per Mile cf Road 

Franli Haigh Dixon, in the Railway Age Gazelle 

Fig. 104. Comparative Monthly Earnings and Expenses per Mile of Road of Steam 
Railroads in the United States Having Annual Operating Revenues of $1,000,000 
or More 

It is frequently convenient to superimpose curves for successive years, so that seasonal similarities and definite 
mcreases or decreases may be accurately studied. Compare this chart with Fig. 103 and also with Fig. 
20-t. It would be better if the heavy line border around the edge of this chart were omitted. The 
heavy line at the bottom does not coincide with the zero line and the reader may be misled by reading 
the chart from the border line 

different years so that comparisons between these different years are 
easily made. This scheme of superimposing curves for different years 
is a very common one that frequently gives an arrangement more 
convenient than could otherwise be obtained. It will be noticed 



116 



GRAPHIC METHODS 



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Comparison of Electrical Output and Coal Consumption for Dec. 1912 
and Dec. 1911, in Plant of Acker, Merrall & Condit Co. Building. 


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100 



Dec.1911 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 26 26 27 28 29 30 31 1 
Dec.1912 12 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 25 27 23 29 30 
S S S C S 



Tlia Engineering Magazine 

Fig. 105. Comparison of Daily Electrical Output and Daily Coal Consumption of a 
Power Plant for the Same Month in Two Succeeding Years 

There is a relatively small quantity of power needed on Sundays. In order to make possible a comparison 
of the two curves for different years the horizontal scales for days were so placed that the Sundays would 
coincide. With curves thus arranged, the low points caused by Christmas do not fall on the same vertical 
line, since Christmas is fixed by the day of the month instead of by the day of the week 



COMPARISON OF CURVES 



117 




in this chart that the December points have not been repeated at the 
left and the reader is forced to glance between left and right in order 
to make certain in his own mind just what changes occurred from 
December to January each year. It can be seen that the January 
figures for "Operating Revenues" are all considerably lower than 
the December figures, but even so the reader has no clear idea of 
the slope of the lines which would be most typical to portray the 
changes from De- 
cember to January 
in each year. This 
question of repeat- 
ing one point for 
curves of different 
years superinlposed 
is referred to also in 
Chapter XIII, Fig. 
204. 

Fig. 105, Fig. 106, 
and Fig. 107 are self- 
explanatory. They 
show some interest- 
ing applications of 
curves to special 
problems, and dem- 
onstrate the great 
convenience which 
might result if curves 
could be more generally used for presenting every-day facts to non- 
technical readers. 

In Fig. 108 we see the application of curves to the kind of data 
of which it would be extremely difficult to give a clear understanding 
if only columns of figures were available in the presentation. With 
these two curves we are not so much interested in the total height 
of the peak as in the general shape of the curve on either side of the 
peak, showing whether there are any laws of uniformity in the increase 
of the flood level and in the speed with which the flood subsided. The 
two curves in Fig. 108 are quite different in their shape, although they 
were taken for the same period of time in districts not widely sepa- 
rated. The size and general character of different water-sheds have 



EdiDin D. Dreyfus, in Indusirial Enoineering 

Fig. io6. Average Temperature at Pittsburgh, Pa., for 
Each Hour in the Day for Different Months in the 
Year. Plotted for Monthly Averages of Twenty- 
Years Observations (1891-1910) of the United 
States Weather Bureau 

It would be impossible, using only columns of figures, to put this informa- 
tion in such convenient form for reference and comparison. The 
broad horizontal line at 10 degrees on the vertical scale of this chart 
and of Fig. 107 is unfortunate since that line has no special significance 
for persons reading the chart 



118 



GRAPHIC METHODS 



a great effect on the nature of the floods which may result from any 
definite rainfall. 

In Fig. 109 also we are particularly interested in comparing the 
shape of the curves for the distinctly different materials under con- 
sideration. Here the curves represent reactions affected by the defi- 
nite laws of physics, and we can join the plotted points resulting from 
different observations so as to get smooth curves. Work in engineer- 
ing, physics, and chemistry depends very largely on the interpre- 
tation of smooth curves like these, and world progress would be 
greatly retarded if the graphic method were not available to assist 
in preserving and interpreting the results of elaborate experiment and 

voluminous research. 
In selecting a 
scale for Fig. 110 the 
draftsman is torn be- 
tween a desire to 
show the San Fran- 
cisco fire peak at its 
correct height, and 
an opposing desire to 
show on a large scale 
the data for a whole 
series of years so 
that the fluctuations 
from month to 
month maybe clearly 
defined. It seemed 
best to cut off the 
top of the San Fran- 
cisco peak so as to 
show the monthly 
data on a scale large 
enough to assure 
clearness. To get the correct slope for the two sides of the San Fran- 
cisco peak, a piece of paper was laid down adjoining the chart and a point 
was located in the correct position for the top of the San Francisco 
peak. The sides of the peak were then drawn so that they would 
meet at that point if extended. Even though the figures for the San 
Francisco peak are given at the top of the chart where the peak is 




Edwin D. Dreyfus, in Jndyslrial Engineering 

Fig. 107. Mean Temperatures for Each Month in the Year 
at Different Cities. Plotted from Records of the 
United States Signal Service and of Blodgett's 
Climatology of the United States 

Information for eight different cities is so given that comparisons are 
easily made. Note the different Hncs used here instead of colors. 
Since Pittsburgh was the city under prime consideration, the Pitts- 
burgh line was made heavy ttiat it might be most clearly seen. This 
chart gives a great amount of data in smaller space than would be 
required to show the facts by any method other than the use of curves 



COMPARISON OF CURVES 



119 



broken oflf, most readers will not imagine correctly the great height 
to which that peak would extend if it were shown in full. The chart 
could have been greatly improved if the upper portion of the peak 
had been drawn in full size horizontally as though hinged near the 
upper margin of the drawing. Since the full height of the peak is 




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Fig. io8. 



26 ZT 28 29 30 " 25 26 27 28 29 

March, 1913 ■ March. 1913 

Engineering Reeord 

Comparison of Flood Rise in Two Rivers in New York State During the 
Floods of March, 1913 

In the preceding illustrations of this chapter there has been such similarity in the shape of the curves con- 
sidered that they were superimposed for comparison. Here the curves are of different shape and they are 
shown in separate fields so that the contrast may be more striking. The chart at the left should have 
had the zero line shown. It is dangerous to base conclusions on the comparison of two curves unless 
the zero lines are shown in each case 







NICK 


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Fig. 109. Comparison of Different Kinds of Steel Containing 0.2 per cent Carbon, as 
shown by Tensile Tests on Specimens 100 mm. long and 13.8 mm. diameter. The 
Vertical Scale Represents Thousands of Poxmds per Square Inch and also Per- 
centage of Contraction or Elongation 

The heavy line shows ultimate strength 

The dash line shows elastic limit 

The dash-dot line shows percentage contraction 

The light line shows percentage elongation 

In this chart the thing of greatest interest is the contrast seen by comparing the shapes of the curves for 
different steels. Though it is best to have curves of such distinct shape plotted in separate fields, it 
is ordinarily most convenient to have the fields themselves placed vertically instead of horizontally 



120 



GRAPHIC METHODS 



o < a m p* to ^ o '0 ft a ^ o <i f' a n o ^ 



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COMPARISON OF CURVES 



121 



almost three times the height of the portion shown on this illustration, 
it would be necessary to make two other hinges in the horizontal 
extension so that the peak could be bent downward and turned back- 
ward from right to left, giving something of a spiral effect. Though 
this bent peak may seem rather artificial, it is quite certain that the 



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1901 1302 1903 19 04 1905 1906 1907 1908 1909 1310 19H 

L I New Building BB Fire Losses 

NOTE- Values are given in Millions of Dollars 

Adapted from Article by Roger W. Babson in the New York Times 

Fig. III. Yearly Value of New Building Construction and Yearly Value of Buildings 
Destroyed by Fire in the United States, igoi to igii, Inclusive 

With this arrangement, the percentage value destroyed by fire can be seen more readily than from the 
arrangement used in Fig. 110. The fluctuation from month to month cannot, however, be seen here. 
If both charts are used, they supplement each other very well. Remember that for these two charts 
the buildings destroyed are not necessarily the new buildings whose value is given. The black area 
represents only the value of buildings destroyed whether new or old. Note the Ben Day shading 
on the upper ends of the bars and the figures for the data from which the chart was made 



122 



GRAPHIC METHODS 



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tapering form of the horizontal extension of the peak would be under- 
stood by even the untrained reader, much more certainly than the 
chart as shown here with only the figures to indicate the full extent of the 
loss which occurred in the San Francisco fire. 

While Fig. 110 
gives some general 
idea of the propor- 
tion which American 
fire losses bear to 
the value of new 
building construc- 
tion, the two fluctu- 
ating curves make it 
difficult for the reader 
to make an estimate 
of the percentage 
losses year by year. 
Fig. Ill supplements 
Fig. 110, and gives 
for each year the 
total values for new 
building construction 
and the total values 
of buildings de- 
stroyed by fire. Here 
the percentages of 
the fire loss are quite obvious when judged by the extent to 
whi'ch the black ink covers the shaded bar representing new build- 
ing construction. Figures are given in each case for the reader 
who may care to work out the actual percentage ratios. It must 
not be assumed from the titles of Fig. 110 and Fig, 111 that the 
buildings destroyed by fire are the same buildings whose value is re- 
corded in the charts as "new building construction." The rapid 
advance in the use of fireproof materials makes it likely that the fire 
losses were more largely from older buildings, built by methods which 
gave a structure less fireproof than the average for buildings put up 
in recent years. 

Fig. 114 shows an error in curve plotting into, which it is very 
easy for an inexperienced person to slip. One vertical scale is relatively 



5.00 5.30 6.00 6.30 7.00 7.30 8.00 8.30 9.00 

P. M Time Monday, Maich 14, 1910 P. M. 

Sam. L. NavMaJy, in J<mmal American Society of Mechanical Engineers 

Fig. 112. Record of Test of a Steam Turbine of 10,000 
Kw. Normal Rating at Plant of City Electric Com- 
pany, San Francisco, California 

The different curves shown in this chart supplement each other so as' 
to give all the data on one chart in compact form. The scale for 
each curve given at the left is only sufficient to show the maximum 
and minimum value for each curve. The zero lines have been 
omitted entirely. Though charts of this type with numerous curves 
are sometimes desirable, they must be carefully made or the reader 
will be misled hy the fluctuations of some one curve appearing more 
prominently than the data would justify 



COMPARISON OF CURVES 



123 



larger than the other, and on that account the curves have been 
made to coincide more closely than they would have done if both 
scales had the same zero line. In making comparisons of this kind 
care must be used to have the two scales start from the same zero 
line, or the person presenting the charts will be open to the unpleasant 
suspicion of attempting to "fake." 

If the reader cares to see how these two curves would contrast if 
properly plotted, the left-hand scale for "corn yield" can be changed 
so that the different horizontal lines will be represented by the figures 
0, 7, 14, 21, 28, etc. The data for "corn yield" can then be plotted 
to the new scale, and it will be found that the new curve does not 
coincide with the "rainfall" curve as closely as does the "corn- 
yield" curve shown in Fig. 114. Though there is some similarity in 
the shape of curves correctly plotted from these data, the similarity 
is not nearly so exact as Fig. 114 would indicate. 



E 



. 1908-1909 

< t^ O 2 Q .^ 



FREIGHT TRAIN OPERATION 
. 1909-1910 




Courtesy of System 

Fig. 113. Records of Freight-Train Operation on a Large Eastern Railroad 

Here, as in Fig. 112, the ^ero lines are not given and the reader must watch the left-liand scales carefully 
to study percentage fluctuation. Comparison between curves cannot be made accurately by judging 
from the slope or from the total fluctuation of the curves on the page. Percentage increases or decreases 
for one curve compared with percentage increases or decreases of other curves give the best basis for 
comparison 

Curves well made ordinarily need no embellishment. Anything used for an eyecatcher should apply definite- 
ly to the subject matter of the curves. Here the subject is freight-train operation, but the picture shows 
the interior of a passenger train 



124 



GRAPHIC METHODS 



J in 



Fig. 115 gives a good example of a total curve made by adding the 
figures for different curves. Instead of using addition to get a set 
of figures from which a total curve may be plotted, it is easier in most 
cases to get the location of the total curve by the graphic method. 
All that is necessary is to lay off, with draftsman's dividers, successively 
on each vertical line, the height above zero at which each of the dif- 
ferent curves intersects that vertical line. The totaling curve is 
drawn through the points thus found. When there are not too many 
curves, this method answers admirably. It sometimes happens that 
actual observations for the data of different curves are not simul- 
taneously taken and, for this reason, it may be impossible to add 
the actual numerical data so as to plot a total curve. In such cases, 

the graphic method 
of stepping off the 
height for the total 
curve is practically 
the only one avail- 
able. After each of 
the separate curves 
has been plotted 
from such data as 
may exist, it is a very 
simple matter by the 
graphic method to 
locate the total curve 
from the separate 
curves. A sufficient 
number of vertical 
lines are used to 
bring the points on 
the total curve close 
enough together to 
represent fairly the 
data of the separate 
curves which are 
totaled. 

In plotting curves relating to prices, it frequently happens that 
there is a necessity for showing in the chart both the upper and lower 
limits to which the prices may fluctuate in any given period of time. 



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'88 '89 '90 '91 '92 '93 l94 '95 '96 '97 '98 '93 '00 '01 02 

Adapted from Pennsylvania Farmer 

Fig. 114. Chart to Show the Dependence of Com Yield 
upon the Quantity of Rainfall during the Month of 
July. The Yield of Corn is Given in Bushels per Acre 

This chart is misleading. The close similarity of the two curves has 
been obtained by plotting one curve on a larger scale than that used 
for the other curve. The rainfall curve has been plotted with the 
bottom of the chart as zero. The corn-yield curve is, however, drawn 
with the scale starting at twelve. 



COMPARISON OF CURVES 



125 



800 

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an 
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600 



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Max. 
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Max. 



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A -Hotel 

B - Apartment House 

C- Department Store 

D- Combined Load Curve 

B-Loft Buildine 

F- Office Building 

Note; Combined Load Curve 
shown in true size 




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The £nyinGcj'ing Magasinq 

Fig. IIS. Typical Curves Showing the Twenty-Four Hour Demand for Electricity 
during the Summer Months in Various Types of Buildings in New York City 

Curve D shows the fluctuations in the load on a power house supplying all of the buildings represented by 
curves A, B, C, E and F. By combining loads of different types, the power plant can be kept more con- 
tinuously busy than otherwise possible. After the other curves are all plotted, curve D can easily be 
located by stepping ofl^ with draftsmen's dividers on each vertical line the heights of all the different 
curves at that particular line 

This is especially true where curves are plotted showing the fluctuations 
in the market prices of stocks or bonds. In such cases, it is desirable 
to plot two curves, one showing the minimum prices and the other 
showing the maximum prices. When the two curves lie quite closely 
together, it frequently assists in the clearness of the chart if the co- 
ordinate lines are erased between the two adjacent curves. The erasing 
of the co-ordinate lines makes the curves stand out much more dis- 
tinctly than they otherwise would. 

Charts on the general type of Fig. 116 are valuable to give a vivid 
comparison. A chart of this kind would be especially striking if used 
in advertising, or in a report where concentration upon only one gen- 
eral idea was needed, without a great amount of specific detail. Though 
Fig. 116 shows that telephone rates have had a constantly downward 



126 



GRAPHIC METHODS 




je99 1900 1901 



I90a (905 1906 1907 (908 (909 

Courtesy of Daia, Cfiicago 



Fig. ii6. Chicago Telephone Rates per Year Compared 
with the Nvunber of Telephones in Use in Chicago 

It is the object in this chart to show that the rates have been consistently 
reduced as the number of telephones has increased. The curves 
shown earlier in this chapter have varied directly, usually going up 
or down simultaneously. Here we have an inverse relation, with one 
curve coming down as the other goes up 



trend as the number of telephones in use has increased, there is, 
after all, no real proof in the chart that the rates have decreased 
in proportion to the increase in the number of telephones in use. 
Fig. 116 stimulates interest and makes one wish to plot another 

chart in which the 
number of telephones 
in use would be the 
horizontal scale and 
the average rate paid 
would be the vertical 
scale, somewhat on 
the general scheme 
of Fig. 119. The 
plotted points for 
different years on a 
chart of the kind 
suggested would 
show by the arrange- 
ment of the points whether the prices had changed exactly in accord- 
ance with the number of telephones in use. 

Fig. 117 has been very carelessly drawn in that the two curves 
do not have their vertical scales start at the same zero line. The 
zeros for each of these scales are so close to the curves as drawn that 
it would have been a very simple matter to have made one zero line 
for both scales at the bottom line of the chart itself. The adverse 
criticisms of Fig. 114 may be applied to this chart also. 

Though the two curves in Fig. 117 seem to show some inverse 
relation, since one curve frequently goes up when the other curve comes 
down, the chart does not permit any measurement by which the degree 
of correlation can be determined. The student who wishes to experi- 
ment with this interesting set of data would do well to make an en- 
tirely new chart with the two curves plotted from one zero line. After 
this first chart has been made, a second chart can be drawn in which 
the "Price" cvu've would be plotted exactly as in the first chart. The 
curve for the number of barrels of "Exports" should, however, be plot- 
ted downward from the top of the chart, after a good position has been 
selected for the top of the chart so that the "Exports" curve plotted 
downward from the top would coincide as nearly as possible with the 
"Price" curve plotted upward from the bottom. The scales for the 



COMPARISON OF CURVES 



127 



curves in the second chart should be the same as those for the first 
chart, so that there may be no "faking" in any similarity which 
may show up in the shapes of the two curves. It frequently happens 
that the relations between two curves are such that the most striking 
presentation can be obtained by plotting one curve upside down so 
as to bring the two curves as closely into coincidence as possible, 
and the scheme should be kept in mind as it is frequently of assistance 
in making facts stand out vividly. 




CoiiTlcsy of Penn.il/tvanta Farmer 



Fig. 117. Exports of Apples from the United States as Compared with the Average 
Wholesale Price in the United States 

A little inspection shows that the export curve usually goes up when the price curve comes down. Though 
this fact indicates an inverse relation between the two curves under consideration it does not give 
satisfactory proof that exports fluctuate relatively as much as price. 

This chart is likely to mislead the reader because the two vertical scales do not have the same zero line. 
Curves compared in this manner without having a common zero line should always be distrusted 

Another interesting study can be made from Fig. 117 by drawing 
a chart with "Price" as the horizontal scale and quantity of "Exports" 
as the vertical scale. Dots for the different years placed on such a 
chart, after the general manner of Fig. 119, will appear so widely 
scattered over the whole field that the reader will find it almost hope- 
less to draw any general conclusion from the arrangement of the 
dots. Though the dots indicate by their position a general tendency 



128 



GRAPHIC METHODS 



for exports to decrease as prices increase, there would seem to be 
so many complex factors entering into the relation that no very gen- 
eral law of dependence can be proved. 

It can be seen from inspection that the relations existing between 
the two curves of Fig. 118 are much closer than exist between the 
two curves of Fig. 117. It is unfortunate that in Fig. 118, as well 
as in Fig. 117, the chart was carelessly prepared so that the two curves 
do not have the same zero line. 




Courtesy of Pennsylvania Farmer 

Fig. ii8. The Average Price of Apples in the United States as Compared with the 

Total Supply 

Here again an inverse relation is indicated, but the chart has carelessly been made with the two vertical 
scales starting from separate zero lines so as to cause distrust by the reader. The chart is printed show- 
ing a finely ruled co-ordinate background, though only every tenth line is desirable for the reader. The 
use of more lines than necessary should be avoided as it tends to cause confusion. See Fig. 119 as 
another method of charting the same data 

In order to determine just how closely the price of apples depends 
upon the supply, Fig. 119 was prepared from the data of Fig. 118. 
Though the dots in Fig. 119 represent a rather long series of years, 
they nevertheless have a fairly symmetrical arrangement and the 
general tendency might be approximated by a smooth curve drawn 
as shown. It must be remembered that there are many conditions 
which may affect the position of these dots on the chart. For one thing. 



COMPARISON OF CURVES 



129 



Price per Bbl 
$eoo 



the standard of living has very greatly changed in the period of time 
from 1895 to 1912. Prices in recent years might be expected to be 
considerably higher than in the earlier years, without any regard to 
the size of the apple crop. Besides this, numerous diseases have 
affected apple trees in recent years, requiring more care than formerly 
to produce good fruit. This would also have some tendency to raise 
prices in spite of the tremendous number of apple trees which have 

come into bearing in the 
later portion of the period 
of time under consideration. 
The general method of plot- 
ting shown in Fig. 119 is 
of great importance and it 
should be kept in mind 
whenever two curves are 
found having similarities 
such as are seen in Fig. 
118. Other examples of this 
method of plotting to study 
the correlation of two related 









































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EO E5 30 35 40 45 50 55 GO 65 70 75 

Quantity in Millions of Bbis, 



Fig. iiQ. The Average Price of Apples in the 



. 119. ine Average ir-nue oi Appies m uie „,,v- _^.„ ^-ii i,_ fo„„H m thp 
United States as Compared with the Total subjects wUi be lound m tne 



last portion of Chapter X. 
Fig. 120 contains much 



Supply 

By this method, the positions of the dots on the chart show 
whether there is any close relation between supply and 

price. The dots fall in fairly regular order, proving better information f Or the Studcut 

than Fig. 118 that the price does largely depend upon the o i • . -ittt i 

supply. A smooth curve has been drawn to represent Ot hlStory. We are here lU- 

approximately the general relation between supply and 4-„„„„4.pJ -nartinnlnrlv I'n thp. 

price which the dots might seem to indicate. Note that tereSLCU pdrtlCUldny in tne 

the year is stated for each dot shown rCCOrd of the United StatCS. 

That curve line has accordingly been made much heavier than any 
of the others, so that it may be brought prominently to the eye of 
the reader. By visually projecting the curves for Russia and the 
United States beyond the limits of the chart, it appears that we should 
equal Russia's population within the next few decades. It must be 
remembered in viewing this chart that the populations of the Asiatic 
countries (especially the populations of China and India) are not shown 
here. If all the countries of the world were considered, it would be 
seen at once that for many years to come there is no likelihood of the 
United States having the greatest population in the world. It is only 
because Asiatic countries have been omitted that we seem to be so 
nearly the head of the list. 



1800 1810 

no 



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100 



95 



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1620 1830 1840 I850 1860 1870 1680 1890 • 1900 

— I to 



INCREASE OF POPULATION 

IN THE 

UNITED STATES 

ANDTHE 

PRINCIPAL COUNTRIES OF EUROPE 

FROM 

1600TOJ900 




1800 1810 leZO 1830 18^10 



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From the Untied Slates Slalisttcal Atlas, Census of 1900 



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Fig. 120. The Population of the United States Compared with the Population of 
the Principal Countries of Europe from 1800 to 1900, Inclusive 

Written words requiring one hour to read could not convey as much information as this chart gives. 
In considering the slope of the curve for the United States it must be remembered that the slope of a 
curve does not indicate the percentage rate of increase or decrease. The increasing slope of the United 
States curve does not in itself prove any increase in the percentage rate of growth. Compare Fig. 121 

130 



COMPARISON OF CURVES 



131 



The reader should keep constantly in mind when viewing Fig. 120 
that the slope of a curve line crossing a field ruled with ordinary rec- 
tangular co-ordinate lines on an arithmetical scale tells nothing about 
the percentage rate of growth from period to period. The slope of 
the United States curve is very much steeper in the upper portion 
of Fig. 120 than in the lower portion, but the greater slope does not 
prove that we are growing more rapidly on a percentage basis than 
early in the century. The slope of a curve plotted on a natural scale 
of rectangular co-ordinates shows only the size of the increments added 
from period to period and it tells nothing whatever about percentage 
growth. 

Fig. 121 has been drawn to 
assist in proving the preceding 
statement regarding curve slope. 
Starting with one dollar, it was 
assumed that a uniform increase 
of 10 per cent of the accumu- 
lated amount would be made at 
the end of each year. This is the 
same as though the dollar were 
placed at 10 per cent compound 
interest. At the end of thirty-six 
years it can be seen that the one 
dollar has increased to nearly 

thirty-one dollars. Though the ^'^- ^f • Curve Showing the Growth 
•^ , p 1 • 1 1 of One Dollar at lo per cent Corn- 

accumulated fund IS shown by a 

smooth curve throughout the 
period of thirty-six years, the curve 
is constantly changing its slope in 
spite of the fact that the rate of 
increase remains constant at 10 per 
cent per year. The curve in Fig. 
121 is very similar in shape to the curve for the United States in Fig. 
120. This similarity in shape shows conclusively how much the reader 
would be misled if he should assume that the increasing slope of the 
curve in Fig. 120 proved in itself an increase in the rate of growth. 
The actual percentage rate of the growth for Fig. 120 can best be stud- 
ied by making an entirely new chart for the purpose of observing 
percentage rates only. 





































































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pound Interest for Thirty-six Years 

Here the rate of increase is uniformly 10 per cent 
per year, but the slope of the curve is constantly 
changing. The general shape of this curve is 
somewhat similar to the shape of the population 
curve for the United States seen in Fig. 120. 
The slope of a curve plotted on ordinary co- 
ordinate paper tells nothing about the per- 
centage rate of growth. See Fig. 122 and Fig. 
123 



132 GRAPHIC METHODS 

* The ordinary form of graphic chart plotted on rectangular co- 
ordinate paper with the natural or arithmetical spacing of the lines 
has some serious limitations which may cause a chart to be misleading. 
The true function of such a chart is to portray comparative fluctua- 
tions. This desired result is secured clearly and satisfactorily when 
the factors or quantities compared are of nearly the same value or 
volume, but analysis will show that the result is not accomplished 
when the amounts compared differ greatly in value or volume. The 
extent or degree of the fluctuation as indicated on the ordinary chart 
depends in a measure on the proximity of the curves to the top or bot- 
tom of the chart. The chart registers the actual change in the value 
rather than the ratio or percentage of change. The wider the range 
of scale the greater the variation between the actual and the relative 
changes. 

This same criticism applies to charts which employ two or more 
scales for various records or curves. If the different scales are in 
proper proportion the result is the same as with one scale, but when 
two or more scales are used which are not proportional, an indication 
which is absolutely false may be given with respect to comparative 
fluctuation. Charts made on a percentage basis are used to some 
extent in graphic work, and these correct the deficiency in the ordinary 
chart by showing the changes in the percentages of increase or decrease. 
In correcting one deficiency, however, another is introduced. The 
percentage scale gives no clue to the magnitude of the quantities 
represented by a curve. The true proportions of relative changes are 
shown, but the actual values are not indicated. The use of the per- 
centage scale also requires considerable labor for computing the per- 
centages of change. 

As a substitute for the ordinary (or natural) scale and for the scale 
of percentages, as well as for compound scales, the logarithmic scale, 
or scale of ratios, practically meets all the requirements. The logarith- 
mic scale permits the exhibition of both actual and relative values 
and actual and relative fluctuations. While some knowledge of log- 
arithms will make plain certain features which otherwise are hard to 
understand, no special knowledge of higher mathematics is essential 
to the use of the logarithmic scale. The principles involved are the 
same as those embodied in the slide rule, and any treatise on the slide 

* Portions of this discussion on charts plotted by the logarithmic scale are adapted from an article by W. J. Cunningham, 
in the Railway Age Gazette, June 25, 1909. 



COMPARISON OF CURVES 133 

rule will make them sufficiently clear. A person who can plot a chart 
to the ordinary scale should have no difficulty in using the logarithmic 
scale. 

No matter what the location on the chart, if the logarithmic 
spacing is used on the vertical scale, for curves, the angle of the upward 
or downward inclination is the same for all curves affected by the 
same percentage of change. Curves having an increase equaling 
the distance from 100 to 200, 200 to 400, 300 to 600 (or the distance 
between any number on the scale and double that number) have an 
increase of 100 per cent and show the same slope. It will be noticed, 
for instance, from any paper ruled logarithmically, or from Fig. 123, 
that the distance on the logarithmic scale from 10 to 20 is the same 
as from 200 to 400. 

In Fig. 122, we have curves plotted for comparative study in the 
manner most convenient when ordinary arithmetically ruled cross- 
section paper is used. Some of these curves represent large quantities, 
so that they are on the upper portion of the chart, while others rep- 
resent comparatively small quantities and fall near the bottom of the 
chart. 

Just because the curves in the upper portion of the chart represent 
numerically larger quantities, they have much more vertical movement 
up and down on the face of the chart than those curves in the lower 
portion of the chart which may have an even greater amount of per- 
centage fluctuation. This wide difference in the amount of vertical 
movement on a page is one unfortunate source of confusion to persons 
who are just beginning to study curve charting. 

Fig. 123 is plotted from the same data as Fig. 122, but it is on 
paper having logarithmic spacing for the vertical scale with the ordi- 
nary arithmetical spacing for the horizontal scale. With the logarith- 
mic spacing on the vertical scale the fluctuations in the different 
curves show in true proportion. Curve F appeared insignificant in 
Fig. 122 because it happened to fall near the bottom of the chart 
where percentage fluctuations are not prominently shown. In Fig, 
123, however, curve F shows up as having far the greatest percentage 
changes of any curve on the whole chart. For persons who under- 
stand even slightly the principles involved in reading charts plotted 
on logarithmic paper. Fig. 123 shows up the facts in much more con- 
venient form than Fig. 122. To make comparison most convenient, 
the two figures are placed on facing pages, 134 and 135. 



134 



GRAPHIC METHODS 





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W. J. Cunningham, in the Railway Age Gazette 

Fig. 122. Passengers and Employees Killed and Injured 
in Train Accidents for All Railroads in the United 
States. (From Quarterly Reports of the Interstate 
Commerce Commission) 



Curve A. 
miles) 
Curve B. 
Curve C. 
Curve D. 
Curve E. 
Curve F. 



Passenger miles (2000 on scale equals 20 billion passenger 



Ton miles (2000 on scale equals 20 billion ton miles) 

Number of employees injured 

Number of passengers injured 

Number of employees killed 

Number of passengers killed 
Compare this chart with Fig. 123. The data plotted here by the or- 
dinary natural scale of co-ordinates are replotted in Fig. 123, using 
logarithmic co-ordinates. Note the peak in 1904 in Curve D. 
The number of passengers injured was approximately doubled in a 
short period of time. In the same period of time the number of 
passengers killed increased to seven times what it had been, yet the 
peak on Curve F does not attract great attention. Notice these same 
peaks in Fig. 123 with the logarithmic scale 

It is unfortunate that there is so much difficulty in obtaining 
paper liaving the logarithmic ruling in one direction and the arith- 
metical ruling in the other direction. The arithmetical ruling in one 
direction is essential for statistical work, since we must ordinarily 
plot as one scale data representing years or other subdivisions of 
time. In statistical work we cannot well use a paper having logarith- 
mic ruling in both directions, yet that is the only kind of logarithmic 
paper which can be obtained from most stores selling drawing materials 



COMPAKISON OF CURVES 



135 



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1902 






1903 






1904 






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W. J. Cutiiiingham in Railway Age Gazette 



Fig. 123. Passengers and Employees Killed and Injured 
in Train Accidents for All Railroads in the United 
States. (From Quarterly Reports of the Interstate 
Commerce Commission) 



Curve A. 
miles) 
Curve B. 
Curve C. 
Curve D. 
Curve E. 
Curve F. 



Passenger miles (2000 on scale equals 20 billion passenger 



Ton miles (2000 on scale equals 20 billion ton miles) 

Number of employees injured 

Number of passengers injured 

Number of employees killed 

Number of passengers killed 

This illustration is a replot of Fig. 122 by using the logarithmic scale in 
the vertical direction. In reading a chart in which a logarithmic 
vertical scale is used, attention may be given to the slope of the curve 
lines. Curves having the same slope upwards or downwards have 
the same percentage change. Note that curves with a logarithmic 
scale do not have zero for the bottom line of the chart. It is, how- 
ever, desirable to have the bottom line either at ten or some power 
of ten on the vertical scale 

and engineering supplies. A person doing statistical work for which 
paper with the logarithmic ruling is desirable may occasionally have to 
rule his own paper. This, however, is not an impossible task especially 
if one has a slide rule. The spacing of the lines can be copied from 
either scale of the slide rule, or it may be worked out easily to fit any 



136 



GRAPHIC METHODS 



given space by dividing into tenths and hundredths and using tables 
of logarithms. 

It is of interest to note here that the data of Fig. 121 would show 
as a perfectly straight line if plotted on paper having the logarithmic 
ruling for the vertical scale. Since the increase from year to year is 
uniform, on a percentage basis, the points of the curve all fall on a 
straight line drawn from the first point to the last point. 



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W. J. Cunningham in Proceedings of New England Railroad Club 

Fig. 124. Book Value of Material on Hand for a Large Eastern Railroad 

The logarithmic scale is particularly valuable for an operating chart such as this when there is a great differ- 
ence in the size of the figures which must be compared. The lower curve here averages about $60,000 
while the upper curve averages about $1,100,000. The logarithmic scale permits accurate comparison 
of various curves to determine whether any curves are out of harmony with the other curves 

Fig. 124 gives an especially interesting use of curves on the log- 
arithmic ruling. Executives who have puzzled over methods for 
controlling the quantity of materials or supplies on hand realize full 
well that it is sometimes just as im.portant to watch the curves for 
materials having only a relatively small consumption as it is to watch 
the curves for those materials of which the greatest quantity is used. 
The mere fact that great amounts of capital are tied up in stocks 
of certain largely used materials tends in itself to cause very careful 
scrutiny of those accounts, while numerous small or inactive accounts 
may be entirely overlooked or neglected. A little study often shows 
that there is no necessity for carrying so much material on hand. 



COMPARISON OF CURVES 



137 



If charts similar to Fig. 124 are used, the executive can tell instantly 
whether the stocks in different departments or of different kinds of 
material are increasing or decreasing simultaneously and propor- 
tionately. 

"To summarize — with the ordinary arithmetical scale, fluctuations 
in large factors are very noticeable, while relatively greater fluctua- 
tions in smaller factors are barely apparent. The logarithmic scale 
permits the graphic representation of changes in every quantity with- 
out respect to the magnitude of the quantity itself. At the same 
time, the logarithmic scale shows the actual value by reference to the 
numbers in the vertical scale. By indicating both absolute and rela- 
tive values and changes, the logarithmic scale combines the advantages 
of both the natural and the percentage scale without the disadvantages 
of either." 



Chapter VIII 



COMPONENT PARTS SHOWN BY CURVES 



: 4Hfi C*KDLC-PO«CR Q 



TMC DirrtHENT TY("Ca C 



8TAM)AAD IMCftNOCSCEHT LAMPS 



« CO. AB PC»»CCWT»OEB or TMt JOTALB or ALL LAMPS QELIVCBED 



S cahsoh I ocw 



QTfcWTALOM Jg TUNOBTtH 



IN Chapter I various examples were given in which the component 
parts or factors making up a complex whole were shown in their 
relative sizes. It frequently happens that it is necessary to 
show the changes which occur in the size of different components 
as time goes on. In this chapter we shall consider only examples 
of charts showing the fluctuating size, at different times, of com- 
ponents which make up a total of 100 per cent. 
^^^^^^^^^^^^^^^^^^^^^^ In Fig. 125 the 

proportionate num- 
ber, voltage, and 
candle-power of 
various types of 
standard incandes- 
cent lamps delivered 
in different years by 
the New York Edi- 
son Co. are shown 
in a series of vertical 
bars which are all of 
the same length, 
representing 100 per 
cent. No statement 
is made or implied 
in regard to the total 
figures, which may 
have increased or 
decreased from year 
to year. x\ll we are 
interested in, in this chart, is the proportion of the different components 
which in their aggregate make up the bar representing 100 per cent 
in any year. 

In Fig. 126 the total height of the chart represents 100 per cent. 

138 





New York Ediaon Company 

Fig. 125. The Number, Voltage, and Candle-Power of the 
Different Types of Standard Incandescent Lamps 
Delivered by the New York Edison Company in 
Different Years, Shown as a Percentage of the Totals 
of All Lamps Delivered 

The chart was drawii in four contrasting colors and was framed for a 
wall exhibit 



COMPONENT PARTS SHOWN BY CURVES 



139 




1820 



1S30 



1640 



Per 


Cen^ 


US, 


Foreign 


100 


O 


SO 


10 


80 


EO 


70/ 


30 


60 


40 


50 


50 


40 


60 


30 


70 


20 


eo 


lO 


90 


o 


lOO 



I850 



I860 



1670 



1880 



1890 



1900 



Fig. 126. Percentage of United States Foreign Trade Carried in American Vessels 
and in Foreign Vessels by Decades, 1820 to 1900 

This t}T)e of chart requires a more highly educated reader than the type of chart shown in Fig. lio, but it 
gains by making the information stand out more clearly than possible with a series of bars 

To show that the chart is absolutely limited to the height represent- 
ing 100 per cent, we use a broad line for the zero line and another 
broad line at the top for the 100 per cent line. Instead of showing 
the percentages at different decades by the method of shaded bars 
used in Fig. 125, the vertical lines representing decades are first marked 
with points dividing the lines into component parts, then the points 
on the various lines are joined to give a curve. The area under- 
neath the curve is shaded in this illustration simply to give a great- 
er contrast between the two portions of the chart. Charts of this 
kind made with shaded or colored areas are understood by a sur- 
prisingly large number of people who ordinarily would not under- 
stand a chart made by using curve lines without the shaded or col- 
ored areas. 

The double scale at the right of Fig. 126 is worth noting. The 
percentage for the United States can be read for any decade. The 
percentage for foreign vessels can also be read for any decade by using 
the reversed scale, in which zero is placed at the top and 100 per cent 
at the bottom. Though a double scale is scarcely necessary on a 
chart as simple as Fig. 126, it is frequently desirable to have a double 
scale. 

Another very striking wall chart is shown in Fig. 127. Here as 
in Fig. 125 the chart was framed, but the frame shows in the photo- 
graph only as a black border. In making up this chart co-ordinate 



140 



GRAPHIC METHODS 



paper was used for a background. The upper half of the chart shows 
the 24 hours of the day divided between hours of darkness, hours of 
twihght and cloudiness, and hours of sunshine, totaling 100 per cent 
for each month in the year. The hours of darkness are definitely 
known from almanac figures and can be plotted as a smooth curve. 




New York Edison Company 

Fig. 127. Industrial Accidents in Different Months 
of the Year Compared with the Hours of Stm- 
light Each Day in Different Months According 
to Weather Records for New York City in 1 9 1 o 

Twenty-four hours in a day are shcmi as 100 per cent divided 
between darkness, semi-darkness, and sunshine. Curves 
showing accidents for three different years liave the same 
general shape as tlie upper curve representing hours of dark- 
ness. The scale for the accident curves should have been 
started so as to show zero at the bottom of the curve field 

The hours of cloudy weather, however, vary in different years. The 
area showing cloudiness and twilight was drawn from actual weather 
observations made in New York City during the year 1910. The per- 
centage of sunshine in different months fluctuates considerably, as 
will be noticed in the chart. 



COMPONENT PARTS SHOWN BY CURVES 141 

The lower half of Fig. 127 contains three curves showing the 
monthly distribution, for three successive years, of about 700 deaths 
annually from industrial accidents reported from an area embracing 
80,000 plants. The similarity of these curves, showing the number 
of fatal accidents per month, to the curves showing the percentage of 
darkness, is intended to convey to the person seeing the wall exhibit, 
the truth of the statement at the top of the chart, that "an abundance 
of light tends to prevent industrial accidents." Though Fig. 127 is 
a very commendable and effective piece of work, it should be pointed 
out that there is danger of exaggerating the facts in the way in which 
the chart is prepared. The lower left-hand scale does not begin at 
zero. By measuring, it can be seen that the scale begins at 20 acci- 
dents per month. The bottom line of the curve field should have 
been drawn near the edge of the picture frame to represent zero. 
This change in the bottom line would have given the reader a more 
accurate idea of the increase of deaths in those months having the 
greatest proportion of darkness. This chart really does not exaggerate 
the facts seriously, for the three curves for deaths and the curve for 
darkness would really be of approximately the same shape even if 
the zero line had been shown in its correct position. Yet it is a fact 
that the omission of the full scale in the chart may cause a person 
glancing hastily at the chart to distrust it simply because the zero 
line is not shown. 

In Fig. 128 a number of different components are shown to make 
up a total of 100 per cent. This type of chart is especially good to 
give instantly a general idea of the relative size of the components 
or factors which enter into any total, and to show the changes in these 
factors as time goes on. Though it is fairly easy to see in Fig. 128 
what the changes are which have occurred in, say, the item for "Gen- 
eral" expenses, it is not at all easy to determine the changes which 
have occurred in the item for "Conducting Transportation." The 
eye cannot measure correctly the increase or decrease in width of any 
area as great as that representing the item for "Conducting Trans- 
portation," especially if there is no straight line to gauge by, either 
at the top or the bottom of the area under consideration. 

Though the method of presenting the facts in Fig. 128 is excellent 
to give a rough general idea or to reach unskilled readers, the method 
of presenting the facts in Fig. 129 is likely to give the more accurate 
impression. In Fig. 129, each of the different expense accounts is 



142 



GRAPHIC METHODS 



Percent 
100 



plotted as a separate curve measured from zero as a base line. It can 
be seen at once in Fig. 129 that the component for "Conducting 
Transportation" increased rapidly until 1895, ran along fairly uniformly 
to 1900, then slightly decreased, then increased again. By having 
each curve plotted separately with the points measured from a zero 
base line, the eye can judge instantly and accurately the changes 
which have occurred over a period of years in any component which 
enters into the total. In an illustration like Fig. 129 it should be 

shown in the title, 
or preferably on the 
chart itself, that the 
sum of the heights 
of all the curves 
given on the chart is 
constantly 100 per 
cent as indicated by 
the broad line at the 
top of the chart. 
The reader will then 
know that if any one 
curve on the chart 
goes up, some other 
curve or curves must 
come down in order 
that the 100 per cent 
line may remain 
straight and hori- 
zontal. 




o STi 5) ,<n .0) .(D 0) 0) .0) ,(n 
CO 



O — (Ni <o ^ in (0 
O .O -O jO .O .O J3 



Adapted from Railway Age Gazette 

Fig. 128. Percentage Distribution of the Expenses of 
Operating the Raihoads of the United States 

Here a number of different factors enter into the total 100 per cent. 
Since the strips representing different expenses vary at both top and 
bottom, it is not easy to see from year to j'ear how much any strip 
may be increasing or decreasing. Compare with Fig. 129 



Fig. 130 is an interesting application of the method of using areas 
to show components with 100 per cent shown as a straight line at the 
top of the combined area. As in this case a large part of the con- 
struction work was finished, the actual number of accidents in the 
construction department dropped to almost nothing, and, because 
the shaded area for construction grew less, it was necessary that the 
other areas should widen out if the 100 per cent line at the top were 
to remain a straight line. Here the weak point in the method of 
charting is the same as that indicated for Fig. 128. The person ob- 
serving the chart has no way of telling whether the factors included 
in the 100 per cent have grown less or grown greater, and whether 



COMPONENT PARTS SHOWN BY CURVES 



143 



Percent 
too 



the quantities represented by the different areas have changed in 
actual size or only in relative size. Where great fluctuations occur 
from time to time and many factors enter into the total, it is best 
to draw charts in the form of Fig. 129 with a common zero line, or in 
the form of Fig. 131, where each factor has its own separate base line, 
or in the form of Fig. 132 and Fig. 133, in which the lines on the chart 
represent actual quantities rather than percentages of an aggregate or 
total sum. 

Note in Fig. 130 and Fig. 131 the 8V^-inch by 11-inch co-ordinate 
paper on which the ruling is so arranged that the paper may be used 
for almost any subdivisions of time, such as days, weeks, months, 
etc., as seen in Figs. 
57, 103. 131, 134, and 
156. 

In Fig. 130 the 
paper was used for a 
time-scale of three 
years by months, 
the total height of 
the chart being put 
at 100 per cent, us- 
ing fifty out of the 
fifty-two spaces on 
the paper. Fifty-two 
spaces, correspond- 
ing to the number of 




Fig. 129. Percentage Distribution of the Expenses of 
Operating the Raihroads of the United States. The 
Combined Height of All the Curves Shown Equals 
100 Per Cent on the Scale 

This illustration represents the same data as Fig. 128. Here the per- 
centage for each expense is read from the zero base line instead of 
from one to the other of the fluctuating lines on either side of an 
area. This method, though not so popular as the method of Fig. 128, 
pennits more accurate reading 



Aveeks in a year, of 
course are necessary 
when the paper is 
used to represent 
weeks on the long 
dimension of the 
sheet. 

Fig. 131 and Fig. 130 depict exactly the same data. In Fig. 131 
the facts, Avhich in Fig. 130 were represented by areas, are shown as 
separate curves, each curve with its own base line. Having this series 
of separate curves on one sheet of paper permits an executive to com- 
pare the number of accidents in one department with the number 
of accidents in any other department at any one time, or to study 



144 



GRAPHIC METHODS 



O 



o 



HuEi"ber of aooldente occurring in each department, as 
rERCEMTASES OF THE TOTAL. 
12 Months Averages. 



j'^t Section A ; - 

rj-prr^iTTi-^ i 
^-,f..|. . 




erceni 
100 
96 
92 
86 
84 
80 
76 
72 
68 
64 
60 
56 
52 
48 
44 
40 
36 
32 
28 
24 
20 
15 
12 

8 

4 





0>OHNHMn'4<lO<Ot-CDa>Oi-4NHNtOTl<lOtOK-a}0>OHMH01l<}Ti<U)OC-CQ 



1910-11 



~Sri 



1911-12 



1912-13 



Fig. 130. Percentage of Accidents Occurring in Each Department of a Large Industrial 
Plant. Plotted Monthly by Twelve-month Averages 

By this method, with a consteint width to represent 100 per cent, any great change in any component 
affects all other components. Here the decrease in construction accidents causes the areas depicting 
other accidents to increase in mdth, even though there may be no increase in the actual number of 
accidents. Compare Fig. 131 

This cut was made from specially ruled co-ordinate paper 8}/^ inches by 11 inches, with all lettering done by 
typewriter. The ruling as used here shows 100 per cent and three years by months. Note also Figs. 57, 
103, 134 and 1.56, for which this same universal ruling has been used 



COMPONENT PARTS SHOWN BY CURVES 



145 



ACTUAL irai,raER O? ACCIDEITTS 

occurring: in each department. 

12 Llonths Averages. 
O ITumter. Ilunber. 




























































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"*"»" HfHH HHi-t 

1910-11 1911-12 1912-13 



Fig. 131. Actual Number of Accidents Occurring in Each Department of a Large 
Industrial Plant. Plotted Monthly by Twelve-month Averages 

In this chart the actual condition in each department can be seen much more clearly than bj' the method 
used in Fig. 130. Here each department is judged by its own record without danger of unjust criticism 
based on conditions in other departments 

For a more complete discussion of Figs. 130 and 131 and of the contrast of methods followed in preparing 
them the reader is referred to pages 142, 143 and 146 



146 



GRAPHIC METHODS 



the fluctuations in the accidents of any one department over a long 
period of time. 

As accidents never occur with any regularity, curves representing 
the actual number of accidents are likely to fluctuate a great deal. 
There was such variation in the different months for the number of 
accidents represented in Figs. 130 and 131 that it was almost im- 
possible to draw any definite conclusion from curves for monthly 




data, 
basis 



Ne.w Yorlc Edison Company 

Fig. 132. Nature of the Electrical Load Connected to the System 
of the New York Edison Company, 1893 to 1912 

In the preceding illustrations 100 per cent was indicated by a straight line at the 
top of the chart. Here the line representing 100 per cent is a curve. Though 
the actual sizes of different components can be seen by this method, percentages 
can only be estimated from the widths of the areas. The scale for this type of 
chart must read in actual quantities rather than in percentages. On this wall 
exhibit the scale has been omitted entirely 

The data for Fig. 130 and for Fig. 131 were plotted on the 
of giving, monthly, the average number of accidents in each 
department during the last twelve months for which records were 
available. Actual figures in tabulated form were used to show for 
immediate reference the number of accidents in any month. The 
curves on the twelve-months average basis were consulted to deter- 
mine whether there was any great increase or decrease in any de- 
partment. 

In Fig. 132 the vertical scale was omitted, perhaps with the idea 
that the chart would thus appear more simple to the average indi- 



COMPONENT PARTS SHOWN BY CURVES 



147 



vidual attending a large exhibition. If the scale, were given, however, 
it would be plotted on the basis of actual horse-power rather than 
on percentage, for the top curve here represents the total quantity. 
Percentage scales cannot well be used in diagrams of component parts 
if a fluctuating curve line instead of a horizontal line representing 
100 per cent is given at the top. The reader may, however, get a 
fair idea of the percentages if he roughly calculates the height of the 
areas in question on any vertical line of the co-ordinate ruling and 
then, using that vertical line as a measuring rod, estimates the height 
of the areas as a percentage of the total height of the chart. 

In Fig. 133 the straight line at the top of the chart does not have 
any significance, as it is due only to the co-ordinate ruling which 
serves as a background to the chart itself. The important part of the 
chart ends at the top of the shaded area. We may consider the top 
of the whole shaded area as a curve and read the values accordingly 
from the scales on the right- and left-hand sides. In fact, any curve 
on the whole chart may be considered as a sub-total, which includes 
all of those components or factors shown as separate areas beneath 
that curve. Thus the "Total Shop Cost" includes all those com- 
ponents shown below the "Total Shop Cost" curve. 




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Apr May 



June 



July 



Aug Sept 



Nov Dec 

Adapted from Factory 



Fig* 133* Factors Entering into the Total Costs and Estimated Value of the Product 

of a Manufacturing Plant 

The various elements entering into total shop cost are plotted, each built up 0.1 the areas below. The 
"Estimated Valuation" is based upon market prices for the finished goods. Vertical distances between 
the "Total Cost" curve and the "Estimated Valuation" curve show the estimated profit. Note the 
use of dimension lines in combination with the scales 



148 GRAPHIC METHODS 

The use of engineering dimension lines in Fig. 133 is of interest, 
for the dimension hnes add considerably to the clearness of the drawing. 
In the center of the chart the vertical dimension lines on both sides 
of the names for each area show distinctly that the chart must be 
read on the basis of the vertical distance between the two curves on 
either side of any area. At the right- and left-hand edges of the chart 
the over-all dimension lines show the reader at once how to read the 
chart so as to include all the various components entering into any 
total which may be under consideration. The use of dimension lines 
should be thoroughly understood by everyone drawing charts or 
plotting curves, and by everyone having graphic presentations to 
read. Dimension lines may add much to the clearness of a chart 
without being in themselves unduly conspicuous. 



Chapter IX 
CUMULATIVE OR MASS CURVES 

THE curves tlius far shown have practically all been of a type 
in which the thing plotted was a value or a rate per week, per 
month, or per year. The tendency of such curves is to follow 
a horizontal direction unless affected by conditions which cause sea- 
sonal fluctuations or gradual increases or decreases. In this chapter 
we shall consider curves in which the data plotted concern total out- 
put, rather than the rate of output. With cumulative or mass curves, 
such as are considered here, each point on the curve represents a total 
output up to the time for which the last point is plotted. The figure 
for each successive period of time is added to the total already re- 
corded, and the new total point is plotted. Because the figures re- 
lating to the last unit of time are always added to the total figures 
already recorded, curves of this type are called cumulative curves or 
mass curves. The tendency of a cumulative curve is to start at the 
lower left-hand corner of the co-ordinate ruling and move toward 
the upper right-hand corner of the sheet, according to the scale which 
may have been selected. 

Fig. 134 is a half-tone illustration of a cumulative-curve chart 
representing the output of an automobile factory for one fiscal year 
of the business. In a conference betw^een the sales, engineering, and 
manufacturing heads of this business, it was decided that the quantity 
of automobiles desired was fifty per week until the first of April, then 
sixty per week until the first of June, and seventy per week there- 
after, giving a total production of three thousand two hundred auto- 
mobiles for the whole season. It w^as thought that the rate of pro- 
duction on the new model automobile could be increased after the 
factory had been put into thoroughly good running shape, and the 
schedule rate of production was accordingly increased gradually in 
the manner shown. On account of the delay in getting drawings 

149 - 



150 



GRAPHIC METHODS 



o 



o 



Factory Schedule and Actual Output 



Number 

3600 
3400 
3ZOO 
3000 
2800 
2600 
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1000 
800 

600 
400 

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Fig. 134. Production Schedule and Actual Output of an Automobile Factory for 

One Year 

The schedule is shown by the straight lines drawn according to the desired output per week. Actual 
output is indicated by the waving line showing at any date the total number of autos shipped since the 
beginning of the year. Note the co-ordinate paper of letter-sheet size and the scheme for marking off 
weeks and months so that any fiscal year may be shown on this standard ruled paper 

from the engineering department, the factory was able to ship prac- 
tically no cars during the month of January, though the schedule 
shows that one hundred and fifty cars should have been made that 
month. During February, the factory produced cars but fell further 
behind schedule constantly, as can be seen by the difference between 
the angle of the schedule line for February and the angle of the actual 
output line for February. 

It must be remembered that with cumulative curves the angle 
between the curve and the horizontal line gives the rate of production 
per unit of time. The angle of the curve on the page gives much 
valuable information to the reader. It is for this reason that cumu- 
lative curves are sometimes much more useful than curves in which 
the rate of output is plotted horizontally from time to time. In the 
cumulative curve the total output is plotted, and changes in the rate 



CUMULATIVE CURVES 151 

of output, judged by the angle of the curve at different times, may 
be seen very easily. 

During March the output curve took a rapid upward turn and we 
can see from its angle that, until the end of the first week in xA.pril, 
the output curve gradually approached the curve for schedule. During 
the latter part of March the factory not only got out its quota of 
cars each week but produced more than its quota, making up a little 
for the distance it fell behind during the first part of the year. Owing 
to a lack of material, because of a fire in a factory which supplied the 
crank shafts for the automobiles, not a single automobile could be 
shipped during the second week in April and only a few in the third 
week of April. The automobile factory was busy, however, accumu- 
lating a large supply of parts and assembling automobiles as com- 
pletely as it was possible to do without the crank shafts which were 
lacking. By measuring the vertical distance between the output 
curve and the schedule curve, it will be seen that the factory was 
furthest behind its schedule during the first week in May, which is 
one of the best automobile-selling months of the year. If we count 
the squares between the output curve and the schedule curve we see 
that the factory was about four hundred and twenty automobiles be- 
hind schedule at the end of the first week in May. As, however, a 
large supply of parts and of nearly completed automobiles accumu- 
lated while the crank shafts were delayed, the factory was able to 
assemble and ship cars very rapidly when the crank shafts were finally 
received from a new source of supply. The factory turned out much 
more than fifty cars per week during the latter part of May and was 
rapidly catching up with the schedule, until the supply of accumulated 
parts was used up and the assembling departments were limited to 
the rate at which parts could be produced in the machine shop. By 
making every possible effort in the machine shop, the weekly rate of 
seventy sets of parts was exceeded, and the curve shows that during 
June and July the rate of shipping automobiles exceeded the schedule 
rate to such an extent that by the end of the third week the factory 
had caught up with the schedule production asked for by the sales 
department. There was, however, a slump in the factory output about 
the first of August, and it was not until the middle of August that the 
factory was able to furnish the desired quota of automobiles regularly. 

A conference held between the sales manager and the factory 
manager in September resulted in a statement from the sales manager 



152 GRAPHIC METHODS 

to the effect that he could sell all the automobiles that the factory 
could produce by the end of the year. The factory manager was told 
to go ahead as fast as he wished and turn out all the cars he could 
up to a total of three thousand five hundred cars. The schedule line 
was accordingly changed from the second week in October, by drawing 
the line so that it came out at three thousand five hundred cars at 
the end of the year. It will be noticed that, though the factory had 
a setback due to delayed material in the second week in October, 
it was able to exceed the new schedule during the early part of No- 
vember and it made the three thousand five hundred cars by the end 
of the year as requested. 

The foregoing account will give a fair idea of the application of 
cumulative curves to problems involving output and sales. In work 
of this sort, the cumulative curve is one of the most valuable aids 
to the busy executive. The last point on the curve gives him the 
total output since the beginning of the period for which the curve 
was plotted. From the angle of the curve he can see the rate of output 
for any period of time he may wish to consider. It must be kept in 
mind that a cumulative curve never trends downward. It can move 
only upward or horizontally. If there is no output during any period 
of time the curve simply moves horizontally. Like a clock recording 
time, it cannot go backward. 

Though the cumulative curve proper cannot go backward, a 
modified curve may nevertheless be made to show quantities which 
have been added to and subtracted from, giving total net quantities. 
Thus the modified cumulative curve may be used to show the quan- 
tities of stock on hand, additions to stock being plotted upward and 
reductions to stock being plotted downward. Any point on the curve 
then shows the ciuantities on hand at that particular time. In mak- 
ing a curve like this it is ordinarily the practice to strike a balance 
of the additions and reductions for the latest period of time, and 
then to change the curve only by the net amount added or taken away. 
Such a curve gives not only a perpetual inventory in the last point 
plotted, but it shows the quantity on hand at different seasons of the 
year as a guide for future operations. A curve of this kind can be 
plotted for the total number of men employed in a large organization 
just as well as for quantities of goods in store rooms. 

Fig. 134 was photographed from a sheet of co-ordinate paper 
specially ruled for convenience in curve plotting. The paper is eight 



CUMULATIVE CURVES 153 

and a half by eleven inches (a standard letter-sheet size), and has co- 
ordinate ruling printed in green ink with wide margins on all four 
edges to allow space for lettering, scales, etc. Note in Fig. 134 that 
the green ink of the co-ordinate lines shows much lighter in color 
than the black drawing ink used for the scales and the curves. Though 
the co-ordinate lines are distinct enough for ease in reading they are 
not nearly so conspicuous as they would be if a line cut had been used 
instead of a half-tone. In making a line cut, the green lines of the 
paper must, of course, be printed as black and the color value of the 
green lines is entirely lost. The finished line cut shows only the rela- 
tive widths of lines, not relative colors. For many illustrations of 
curves, conspicuous co-ordinate lines are not desired. In such cases 
it is better to use a half-tone, as has been done in Fig. 134, than to use 
a line cut. 

In Fig. 135 we have curves for two successive fiscal years plotted 
so that they may be compared easily. The double-line curves and the 
dotted-line curves are plotted to show the rate of shipments, while 
the heavy-line curves are plotted on a cumulative basis and give the 
total number of carloads shipped since the beginning of each fiscal 
year. Ordinarily it is not desirable to put on one sheet of paper curves 
giving both rate of output and cumulative output, as there is danger 
of confusing in the reader's mind two different types of curves. This 
illustration is included simply to show the possibility of comparing 
two cumulative curves for succeeding years by plotting both cumu- 
lative curves on the same sheet. 

It must be remembered that cumulative curves always refer to 
some definite length of time and that they must always begin at the 
beginning of the period for which the summation is made. Cumulative 
curves do not extend outward indefinitely, but start over again at 
zero with each succeeding period of time. Thus, cumulative curves 
plotted by months or weeks on a long sheet of paper, for a series of 
years, would be seen in the shape of saw teeth, with the highest point 
at the end of each fiscal year and then a drop to zero again at the 
beginning of the next fiscal year. The saw-tooth shape makes it 
feasible, and sometimes desirable for easy comparison, to plot cumu- 
lative curves for several successive periods of time in the same space, 
as the two cumulative curves in Fig. 135 are plotted. 

The progressive average shown by means of the dotted lines in Fig. 
135 is obtained by averaging each month the values for all the points 



154 GRAPHIC METHODS 

given on each curve since the beginning of each fiscal year. For No- 
vember the average includes two months, for December three months, 
for January four months, etc. The progressive averages in this chart 
mean comparatively little and can be of almost no assistance to the 
manager studying them. The daily averages and the progressjve 
averages would have been much more striking if the averages for the 
two years had been plotted horizontally instead of as superimposed 
curves. A moving average could then be shown continuously so that 
the average would always take in twelve months without having to 
start over again at the beginning of the second fiscal year. The in- 
formation in Fig. 135 would have been more simple in appearance 
and more quickly apprehended if it had been given on two separate 
sheets of paper, the daily average curve and the suggested moving- 
average curve being shown for two years horizontally on one sheet, the 
cumulative curves being shown on a different sheet with the two years 
superimposed on the same scale, as in Fig. 135. 

It is freciuently desirable to show two cumulatiA^e curves on the 
same ruled sheet of co-ordinate paper so that each curve may be 
studied separately and the distances between the curves noted. Thus, 
in Fig. 136, the upper curve shows the amount of money loaned since 
the beginning of the operation of a factory loan-department. The 
lower curve, the dotted line, indicates the amount of money repaid 
by the persons obtaining loans since the beginning of the department. 
The difference between these two curves thus represents the amount 
of money outstanding at the end of any month. At the bottom of 
the chart the actual amount of money outstanding is plotted, also 
in the form of a curve. On the curve showing the amount outstanding 
the height of each point above the zero line represents the distance 
between the two cumulative curves in the upper portion of the chart. 
It is much easier to see fluctuations if the amount outstanding is plotted 
in this way from the zero line than if one must gauge the amount 
outstanding by reading the space between two fluctuating cumulative 
curves. When data must be read by the length of vertical lines be- 
tween two curves, the eye is likely to take as the distance between 
the curves the shortest distance instead of the distance measured on 
the vertical ruled lines. 

In Fig. 136 it was very important to watch the total amount out- 
standing, for the fund available for loans from the beginning of the 
loan system until Januar}', 1912, was limited to $200. From January, 



CUMULATIVE CURVES 



15.5 



Cars Shipped 

Monthly Daily 

2000 10 



1 600 9 

1600 8 

14.00 7 

1200 6 

1000 5 

eoo 4 

600 3 

400 2 

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Progressive Average 
per Day 



Cumulative Carloads 
Shipped 

Adapted from Factvru 



Fig. 135. Carload Shipments from a Manufacturing Plant 

Two separate fiscal years are compared on the chart. The right-hand scale shows monthly averages of the 
number of carloads shipped per day of factory operation. The double-line curves for daily averages 
and the dotted-line curves for progressive averages are read from the right-hand scale. The heavy 
solid-line curves are read from the left-hand scale and show cumulatively the total number of carloads 
shipped since the beginning of each fiscal year 

1912, until the end of the period under consideration the fund avail- 
able for loans was $500, of which $30 (reserved for a special purpose) 
could not be used for the loans for which these curves were plotted. 
Note that in January, 1912, the amount outstanding exceeded the 
funds formerly available for loans, and thus required an increase in 
the capital of the loan fund. Though the lettering of this chart is 
not as clear as it should be, the chart is nevertheless an excellent 
presentation of facts and a good demonstration of the utility of cumu- 
lative curves. 



156 



GRAPHIC METHODS 



Fig. 137 shows in detail for the same loan department the opera- 
tions which are summarized in Fig. 136. In Fig. 137 the heavy line 
shows the actual amount of money loaned each month, while the 
dotted line shows the amount of money paid back each month. The 
data for these two curves were later added month by month on a 
cumulative basis and plotted into the two curves, "Loaned" and 



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Fig. 136. Total Loans Made to Employees by a Large Industrial 
Corporation and Total Amount Paid Back, Shown Monthly Since 
the Beginning of Loans 

The two upper curves are plotted on a cumulative basis. The bottom curve shows the 
amount outstanding and is equivalent to the vertical distance between points on 
the two upper curves. The capital devoted to loans is indicated, and the chart 
permits easy reading of the amount of capital not on loan at the end of any month 

''Paid-back," in Fig. 136. Because of the great fluctuation in the 
amount loaned and paid back each month, the operation of the depart- 
ment as a whole can be seen much more easily from the cumulative 
curves of Fig. 136 than from the actual monthly-loan curves of Fig. 137. 
In general, the cumulative curA^e is of very great assistance in showing 
phenomena in which there are violent fluctuations such as are seen 
in the loan curve in Fig. 137. 

It is interesting to note in Fig. 137 that the peaks and valleys 
in the ciu've showing the amount paid back follow ordinarily one or 
two months behind the peaks and valleys in the curve showing the 



CUMULATIVE CURVES 



157 



amount loaned. This is entirely natural, for these loans were made 
only in eases of extreme emergency when employees were in tem- 
porary need. This relation of two curves to each other, with the peaks 
of one curve following at some definite distance behind the peaks of 
another curve, is generally referred to as "lag." Students of eco- 
nomics are continually finding curves which are seen to have a very 
great dependence upon each other when "lag" is taken into account. 
If "lag" is not considered, a great difference in the shape of the curves 
might be taken to show that there was absolutely no relation between 
the facts from which the curves were plotted. 






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Fig. 137. Loans Each Month Made to Employees of a Large Indus- 
trial Corporation and Amounts Paid Back Each Month. Number 
of Accounts Opened and also Number of Accounts Closed Are 
Shown on a Cumulative Basis 

Note how the curve for repayment lags behind the peaks and valleys of the curve for 
loans. The extent of the lag gives a good idea of the length of time loans are out- 
standing. This illustration is for the same loan department shown in Fig. 136 

Great care must ordinarily be taken in determining to just how 
great an extent the element of "lag" enters in. The best way of de- 
termining this is to plot the two curves on separate sheets of trans- 
parent bond paper, tracing paper, or tracing cloth, plotting each curve 
to a separate scale, if necessary, so that the peaks and valleys in the 



1.58 GRAPHIC METHODS 

two curves will be as nearly as possible at equal distances from the zero 
line. It is difficult to prove a "lag" unless the scales are selected so 
that the peaks and valleys in the two curves are at the same height 
above zero. After the two curves have been plotted separately to 
carefully selected scales, they may be superimposed and read through 
both sheets of paper held in front of a bright light. xVs the horizon- 
tal scales for the two curves are the same, it will be found, if the 
curves depend upon each other without the element of "lag." that 
the peaks and valleys will almost coincide. If there is "lag," it will 
be found necessary, in order to make the peaks and valleys coincide, 
to shift one sheet horizontally over the other so that the horizontal 
scales disagree. When the paper has been shifted back and forth un- 
til the nearest possible coincidence of the two curves has been ob- 
tained, the extent of the "lag" may be determined by seeing how far 
the two horizontal scales are out of agreement. "Lag" is an impor- 
tant feature of many different sets of curves and must be kept con- 
stantly in mind when curves are being compared. 

In Fig. 137 the growth in the importance of the loan department 
can readily be seen by considering the twelve-months progressive 
moving average showing the average total monthly loans. Though 
there is, in January, 1912, a very high peak which overshadows all 
other peaks, the general tendency of the curve is still rapidly upward, 
because of the fact that a number of high points follow each other 
in close succession, each nearly as high as the peak of January, 1913, 
which stands out alone with low points on either side. 

The number of separate loan accounts opened and the number of 
accounts closed is shown in Fig. 137 by means of cumulative curves. 
The fact that the cumulative curve for the number of accounts closed 
follows so nearly the angle of the cumulative curve for the number 
of accounts opened, shows that the number of accounts outstanding 
has not greatly increased. It also shows that since numerous accounts 
are being closed, the loans are being made to other employees rather 
than being repeated continually to the same employees. 

Fig. 138 is a study made to determine the size of tank necessary 
to supply sufficient boiler-feed water for a number of locomotives 
and tugboats. The average amount of water used each day by all 
the locomotives combined is given in the lower cumulative curve. 
The shape of the curve shows that locomotives fill their tanks chiefly 
between six and nine o'clock in the morning and between five and 



OolloMa 


CUMULATIVE CURVES 






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Fig. 138. Cumulative Curves Plotted to Determine the Minimum Size of Tank and 
the Minimum Steady Flow of Water Required for a Group of Locomotives and 
a Group of Tugboats Taking Boiler-Feed Water from the Same Source of Supply 

Curves for locomotives and tugs are plotted separately. A third curve is then made by adding the vertical 
distances of points on the two curves to get the vertical distance for points on the third curve. The 
sloping straight line shows the minimum rate of steady flow. The greatest vertical distance between 
the sloping line and the combined curve shows the necessary minimum tank capacity 



seven at night. The points are plotted in the middle of each space 
because the values are based oij the average quantity of water taken 
between any two hours specified in the horizontal scale. The next 
curA'e above gives on a cumulative basis the average of the amount 
of water taken by the tugboats each day. It can be seen that the 
tugs take water between six and eight in the morning and between four 
and eight at night, the greatest quantity of water being taken be- 
tween seven and eight. In order to see what would happen if the loco- 
motives and the tugs should take water from the same tanks, the 
combined curve was made for both locomotives and tugboats by 
adding the quantities for each one-hour period. The easiest way to 
make a combined curve when only two curves are to be combined, 
is to use a pair of dividers, taking the vertical distance above zero 
for each point on one curve and stepping off that measured distance 
above each point on the other curve. The prick marks showing the 



160 



GEAFHIC METHODS 




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CUMULATIVE CURVES 161 

distances stepped off by the dividers locate the new combined curve 
so that it can be quickly drawn in. The combined curve in Fig. 138 
shows at a glance that the locomotives and tugs together take water 
in such manner that the greatest rate of flow from the tank occurs 
between six and eight in the morning. 

One problem involved in Fig. 138 was to determine the minimum 
steady rate of flow into the tank and the size of the tank so that there 
would always be sufficient water available. By drawing a line diag- 
onally touching the hump on the curve between seven and eight 
in the morning and the hump on the curve between six and seven 
at night, we get at once the smallest size flow which will keep the tank 
full throughout the whole twenty-four hours if locomotives and tugs 
always draw out the water as the average curves shown in Fig. 138 
would indicate. The actual rate per hour at which the water should 
flow is obtained most easily by assuming a horizontal distance of 
several hours on the scale, and then reading upward to the diagonal 
line that vertical distance which corresponds with the horizontal 
distance taken. Thus, if from the point on the line for 40,000 at which 
the diagonal line intersects the vertical line for five a. m., we count 10 
blocks horizontally to the right, we see that it takes 9.1 blocks before 
we again reach the diagonal line. Nine and one-tenth vertical blocks 
correspond on the scale to 45,500 gallons of water flowing in 10 hours, 
so that the minimum steady rate of flow must be 4,550 gallons per hour. 

The dimension marks at "C" and "D" indicate the great amount 
of water used between four and eight p. m. The diagonal line drawn 
parallel to the minimum-flow line shows the amount of water which 
flows into the tank between three and eight p. m., thus reducing the 
quantity to be supplied from the storage space of the tank to the 
amount indicated on the vertical scale by the dimension mark "C". 
Between six and eight a. m., when the amount which can flow into 
the tank through the regular flow-pipe is limited to the cpantity 
indicated by the dimension mark "B", the draught on the tank is 
so rapid that all of the water indicated by the dimension mark "A" 
must be furnished by the storage capacity of the tank itself. The 
water does not flow into the tank nearly so fast as it is taken out by 
the tugs and locomotives at that particular time of the day. If we 
count the squares included vertically in the dimension line "A" we 
find 7.6 squares. This shows that the amount of water which must 
be furnished by the tank during the rush hours cannot be less than 



162 GRAPHIC METHODS 

7.6 times 5,000 (the value for each square on the scale), or 38,000 
gallons. The distance "A" is really the same as the vertical distance 
between the point representing the average for the hour from five 
to six a. m. and the diagonal line of minimum flow. The storage 
capacity necessary in any case of this sort is very simply determined 
by means of curves or mass diagrams on the general scheme of Fig. 
138. The measurement of the greatest distance which shows between 
any depression in the consumption curve and the minimum-flow line 
which joins the peaks on either side of it gives the minimum steady 
rate of flow. 

There is great practical value in charts like Fig. 138. In this 
case the minimum-flow line determines the size of the pipe, pumps, 
or other machinery which must be installed to provide the requisite 
quantity of water if the water is kept running steadily all the time. 
The tank capacity must be as great as the diagram demands or there 
will not always be sufficient water. In practice, it would, of course, 
be customary to put in a pump considerably larger than that needed 
to provide the minimum flow which the chart shows to be necessary, 
and the tank would also be of larger capacity than the minimum- 
storage determination of the curve would indicate. The extra capacity 
of both pump and tank are, however, only a safeguard against ab- 
normal conditions. The graphic solution shows the exact rate of flow 
and the storage capacity which would be satisfactory if the conditions 
indicated by the data on the curves were to be constantly maintained. 

Fig. 139 shows the application of the cumulative or mass curve 
to problems of municipal water-supply. In working up data for 
rainfall in different watersheds and determining the greatest possible 
amount of water which can be obtained from watersheds when dif- 
ferent sizes of reservoirs are used, the cumulative curve is almost 
indispensable. In Fig. 139 the method is nearly identical with that 
used in Fig. 138, except that in Fig. 139 we are determining the great- 
est possible rate of uniform consumption from a fiuctuating supply, 
instead of determining the smallest possible rate of uniform supply for 
a fluctuating consumption. In Fig. 139, the lines beginning at the 
hump in 1870 are drawn at different angles to touch the different 
humps and show various rates of possible consumption. These flow 
lines are also continued in the other sections of the curve just as if 
the curve had been shown continuously in one line instead of in three 
separate sections. The scale for Fig. 139 is selected to show "million 



CUMULATIVE CURVES 163 

gallons per square mile." The scale could just as well have been 
made to show the total gallons of rainfall in the whole watershed, 
but it was more convenient to put the scale on a square-mile basis, 
dividing the total rainfall by the number of square miles in the water- 
shed. 

Cumulative or mass curves are very frequently used for the study 
of quantities in earth work, especially in railroad construction. Cumu- 
lative curves showing the total quantities of earth removed from cuts 
and the total amount used in fills can be kept to give the whole in- 
formation in the most convenient form for quick reference and accurate 
study. 



Chapter X 
FREQUENCY CURVES. CORRELATION 

MANY business problems can be studied most rapidly and con- 
veniently if the data are put in the form of frequency curves. 
Though engineers have used curves for many years to repre- 
sent data relating to the laws of physics, the engineer has made prac- 
tically no use of frequency curves such as are used by the biologist. 
This is probably due to the fact that the engineer can determine the 
laws of physics from mathematical computations based on a relatively 
small number of observations, while the biologist must deal with 
statistical averages based upon observations and measurements in 
thousands of different cases. The laws of biology are not so definitely 
mathematical as those of engineering and physics. The biologist 
must have more observations than the engineer if he is to draw accu- 
rate conclusions. 

A frequency chart is based on the number of times a certain char- 
acteristic is found repeated in a large number of observations. The 
number of repetitions is referred to as the "frequency". A comparison 




C. B. Davenport, in Popular Science Monthly 

Fig. 140. Frequency Chart Based on the Number of Ribs in Scallop Shells. Shells 
Are Sorted into Different Piles According to the Number of Ribs, the Piles (from 
Left to Right) Having Respectively 15, 16, 17, 18, 19 and 20 Ribs 

The heights of the different piles show the relative frequency of shells having the different numbers of ribs. 
Seventeen-rib shells were found much more commonly than shells with any other number of ribs. K 
a line were drawn through the tops of the different shell piles, we should have a frequency curve 

164 



FREQUENCY CURVES 



165 



relating to the frequency with which different characteristics or items 
are found repeated is commonly referred to by the biologist as "fre- 
quency distribution", and the charts showing frequency are quite 
often called "distribution charts" or "distribution curves". 

In Fig. 140 a frequency diagram is shown at the right by photo- 
graphing piles of shells arranged so that all shells in any one pile con- 
tain the same number of 

ribs. The pile of shells at .HBBMSiaKSi^^?jaP**.la^ «■- *- 

the left, having the smallest 
number of ribs, contains 
but three shells. In the pile 
of shells at the extreme 
right, having the highest 
number of ribs, there is only 
one shell. The middle pile 
shows conclusively that the 
greatest number of the shells 
have seventeen ribs. There 
is a fairly large number of 
shells in the pile for sixteen 
ribs, and a somewhat greater 
number of shells in the pile 
for eighteen ribs. Though 
it is unfortunate that no 
horizontal scale or vertical 




Fig. 



C. B. Davenport, in Popular Science Monthly 

141. Forty University Students Arranged in 
Rows, According to Stature by Inches, as 
follows: 56 to 57.9, 58 to 59.9, 60 to 61.9, 
62 to 63.9, 64 to 65.9, 66 to 67.9, 68 to 69.9, 
70 to 71.9 

This illustration gives a good idea of the basis on which a 
frequency chart is constructed. A rough frequency curve 
could be made by drawing a line through the ends of all 
the different rows of men. The curve would show a 
definite peak for the height 64 to 65,9 inches. Such a 
peak is called the "mode", since it shows the type which 
occurs with greatest frequency 



scale is shown in the picture, 

the reader will nevertheless be able to see from this illustration the 

general scheme on which frequency curves are based. 

In Fig. 141 a group of men have been arranged in different rows. 
There is only one man in the shortest class at the left, and only one 
man in each of the tallest two classes at the right. Most of the men 
are of that height shown by the row to the right of the center of the 
diagram. A glance at the photograph taken looking down on this group 
of men shows that there are more men shorter than the most fre- 
quent height than there are men taller. If an ink line were drawn as 
a smooth curve to represent the outline of the whole group of men, 
when arranged in rows as shown here, the top of the curve at the 
end of the longest row would be called the "mode", as it would show 
the type found most frequently in all the individuals under observation. 



vl 



106 



GRAPHIC METHODS 



In the following illustrations, curves of this kind will be noticed using 
the diagrammatic form rather than the actual photographs of a classi- 
fied group like Fig. 141. In Fig. 141 it is regrettable that the illustra- 
tion does not show a scale giving for each row the maximum and mini- 
mum height of men in that row. Some scheme, of course, was neces- 
sary to divide these men up into 
height classes, but the reader has 
no way of knowing the limits of 
height for each class except by re- 
ferring to the title of the illustra- 
tion. 

Frequency charts are some- 
times made for popular illustra- 
tion by drawing vertical lines to 
represent the number of individ- 
uals found in each class designated 
by the horizontal scale. Thus, a 
representation could be made for 
the data of Fig. 141 by having a 
horizontal scale to represent 
heights, and drawing vertical lines 
to a scale by, which the length of 
each vertical line or bar would 
represent the number of individ- 
uals of that particular height. The 
series of bars would then have the 
same general arrangement as the 



NUMBER OF PERSONS WORKINGON ANDABOVETHE S 

Cloak and Suit Industry Dress and Waist 1 

1/ \ III/ \ 


IXTH FLOOR 

ndustry 


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40 19 
47 IB 
140 17 
257 16 
406 15 
62 « 
287 D 


















47 

121 

25 
388 

91 
2347 
2344 
2584 
2823 
2353 
2583 
3416 

, 69.12% 


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J aim hoard of Sanilaru Control, New York City 

Fig. 142. The Number of Persons Work- 
ing On and Above the Sixth Floor 
in the Cloak and Suit Industry and 
the Dress and Waist Industry in 
New York City 

This chart was made first for a wall exhibit and was 
later used in a widely distributed report. The 
co-ordinate ruling has the shape of a New York 
manufacturing building. By observing this illus- 
tration from the left edge of the page the reader 
may get the general effect of a frequency curve 



photograph of Fig. 141 representing the number of men actually seen. 
These bar diagrams to represent frequency are not of very great use, 
except possibly in advertising work where it may be necessary to get 
some kind of chart which can be understood by any untrained reader. 
In Fig. 142 an effective use has been made of the frequency-curve 
scheme in a report intended for wide circulation among persons who 
have not been trained in reading curves. The general outline of a 
tall New York manufacturing building is given very clearly as a field 
of co-ordinate ruling, on which the actual numbers of workers for any 
floor level can be read from the horizontal scale with a fair degree 
of accuracy. The numbers working below the sixth floor are very 
large, and only those on and above the sixth floor are shown. 



FREQUENCY CURVES 



167 



This allows the use of a large scale for the data of the upper floors. 
In order to see the general shape of a frequency curve when plotted 
with flat tops instead of peaked tops, the book may be turned so 
that the illustration is seen from the left-hand edge. This chart was 
drawn primarily as a wall exhibit, to be used later as an illustration 
in a printed report. The general scheme is excellent and it could 
scarcely be improved upon, even though the independent variable 
has here been made the vertical scale instead of the horizontal scale. 
Putting these data in the form of a curve such as is used in Fig. 143 
would probably not be as effective for untrained readers as the black 






A 



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20 22 24 26 28 



Sa 40 42 44 



bars of Fig. 142, 
placed against a field 
in the general shape 
of a New York man- 
ufacturing building. 
Fig. 143 shows a 
frequency diagram of 
the kind found most 
useful in ordinary 
work. The vertical 
scale here represents 
percentage, and the 
total of all the figures 
shown at the upper 
part of the chart 
added together is 100 
per cent. Frequencj^ 
curves are very often 
used, however, with 
numbers rather than 
percentages repre- 
sented on the vertical 
scale, and the vertical scale then shows the actual number in each class. 
To assist the reader, the total number of observations made would 
usually be recorded, perhaps in the title of the illustration. In bio- 
logical work observations are usually made in vast number, to permit 
making a very accurate conclusion regarding the general laws of fre- 
quency for any particular subject under consideration. For a great 
many problems of everyday life, however, the observations are not 



30 32 34 36 

Aqe at Marriage 

Dala of Amy Hcwes, in Publications Am. Statistical Assn. 

Fig. 143. Age at Marriage of 439 Married Graduates of 
Moxrnt Holyoke College who Graduated from 1890 
to 1909 

The vertical scale shows the percentage of the whole 439 who married 
at each age given on the horizontal scale. The totals of all pei'cent- 
age figures at the upper margin of the chart is 100 per cent. If a 
greater number of persons were included in a frequency curve of this 
sort the curve would be less irregular and the mode would show more 
distinctly 



168 



GEAPHIC METHODS 



of sufficient number to permit the formation of any general laws. 
Thus for Fig. 143 we are not justified in saying that-all college women 
marry at the particular ages indicated by this chart. The number 
of women taken into consideration for the preparation of the chart 
was not sufficient to allow any final conclusion, certainly not to justify 
any general statement that college women are less likely to marry at 
the age of twenty-six than at either twenty-five or twenty-seven. 

Aggregate Population 
Males Females 



65 + 
55-S4 
•45-5.1 
35-44 
00-0.4 
25-29 
20-24 
15-19 
0-I5 



65 + 

55-64 

45-54 

35-44 

30-3-4- 



20-24 
15-19 



0-15 




65+ 

55—64 
45—54 
35-44 
30— 34 
25—29 
20-24 
15 — 19 
0-I5 



20 O 20 

Per Cent 



100 



Chinese and Japanese 
Males Females 




65 + 

55—64 

^5—54 

35—44 

30-34 

25-28 

20— 24 



^^ 15-19 



O — 15 



CZl Single 



20 O 20 

Per Cent 

^S Married 



40 



60 



60 



Widowed 

United States Stalistical Atlas, 1900 Census 



Fig. 144. Conjugal Condition of the Population of the United States in 1900 in 
Proportions of the Total Number of Each Age Group 

This chart was printed in color in the Statistical Atlas. Here shading is used instead of color. The arrange- 
ment to the right and left of a zero line at the center makes visual comparison difficult between the data 
for males and females. Note the contrasts between the upper and lower charts. Compare the upper 
chart with Fig. 145 

In biological work the number of observations taken is ordinarily 
sufficient to permit drawing a smooth curve to represent the general 
law, after a chart drawn with numerous straight lines has been made 
by the method used in Fig. 143. It would not be desirable to draw 
a smooth curve in the case of Fig. 143, as the smooth curve would 
be misleading because of the small number of observations made. 
For most business problems, and in many problems actually in the 
field of statistics, the laws which affect frequency are so indefinite 



FREQUENCY CURVES 



169 



and the number of observations so limited that it is much better to 
use the straight-hne method of Fig. 143 than to attempt to make a 
smooth curve. Sometimes a smooth curve may only mislead the 
reader, making the chart appear very accurate when in reality the 
data were so crude that only the roughest approximation is possible. 
Fig. 144 is copied from the Census Atlas for the 1900 Census. In 
the Atlas, colors were used for the different areas which must be repre- 
sented here by cross-hatching. Though these illustrations hold some 
very valuable and interesting information, the information is contained 

Per CenT 

lOO 
90 
80 
70 
60 
50 
40 
30 
20 
10 



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under 

15 



15-19 25-29 

20-24 30-34 



35-44 45-54 



55-64 over 

65 



Male —--Female 



Fig. 145. Conjugal Condition of the Population of the United States in 1900 in 
Proportions of the Total Number of Each Age Group 

Here the arrangement of Fig. 144 has been reversed so as to place age on the horizontal scale, since age 
is the independent variable. Having the data expressed in curves permits much clearer interpretation 
by the reader. Curves for male and for female may be instantly compared. The term "widowed" 
as applied to men was used to harmonize with the preceding illustration 

in such manner that it is almost impossible for the reader to get it out. 
In the first place, age is the independent variable, but it has been made 
the vertical scale. The information sought is the percentage at different 
ages for each of the sexes, and this must be read from the horizontal 
scale, in violation of one of the most important rules for graphic work. 
Another bad feature of the chart is that data for male and female are 
shown in the right and left direction from the center line, making it 
almost impossible for the reader to compare the figures for male and 
female at any age under consideration. The data for the upper half 
of Fig. 144 are replotted in Fig. 145, and the reader would do well to 



170 GRAPHIC METHODS 

compare the two illustrations to see just how much more clear Fig. 145 
is than Fig. 144. 

The bottom portion of Fig. 144 is shown here by way of contrast with 
the upper portion. Notice, for instance, the difference in the shape of 
the chart for the female Chinese and Japanese population of the United 
States as compared with the chart for females in the aggregate popula- 
tion of the United States. A very large percentage of female Japanese 
and Chinese are married by the age of thirty-five, but after that age 
there is a fairly large percentage reported as single. It would appear 
that many widows must be reporting themselves as single instead of 
as widows, or the chart would probably not be so different in shape from 
the chart for the aggregate population of the United States. 

In Fig. 145 the scale for age has been properly placed horizontally 
and the scale for percentage placed vertically. The whole population 
is considered as single under the age of fifteen. The total of the figures 
for single, married, and widowed on any vertical line equals 100 per 
cent; thus, as the number married in succeeding years increases, the 
number who are single is seen to decrease. The curves prove at a 
glance that the women start to marry much earlier than the men. 
Between twenty and thirty-five the horizontal difference between the 
two curves shows that the women marry about four years earlier than 
the men, or, in other words, taking the population as a whole, the 
women marry men about four years their seniors. In considering 
these curves it must be remembered that this chart is made up on a 
different basis from Fig. 143. In Fig. 143 all the women who married are 
recorded as married, and the top of the curve (the mode) shows at 
once the age at which marriages are most frequent. In this chart, how- 
ever, we are considering three things, and the chart shows the percentage 
who recorded themselves as married, rather than the actual age at which 
marriage occurred. The percentage of those who report themselves 
married is affected by the number who are single and also by the num- 
ber who are widowed. If in the later age classes, deaths of husbands 
occur more rapidly than marriages of spinsters for any particular age, 
the "married" curve will trend downward even though a very large 
number of spinsters may be marrying at that age. It is simply a ques- 
tion of balancing the death rate of husbands against the marriage rate 
of spinsters. The curve marked "married" on this chart does not show 
the age at marriage, but simply shows the percentage in any age class 
who report themselves as married and not widowed. 



FREQUENCY CURVES 171 

The men marry later than the women. Many of the men marrying 
over forty marry women much younger than themselves. As the hus- 
bands are older than the wives, the expectation of life for the husband is, 
of course, less than for the wives, and the number of widows at any age 
is far in excess of the number of widowers, on this account alone. In- 
dustrial accidents, war, etc., also tend to make a high death rate among 
the men and cause more widows than widowers. In Fig. 145 the curve 
for men has been labeled "widowed" to follow the Census Office prac- 
tice in Fig. 144. 

With Fig. 144 some of the age classes are for an interval of only five 
years while other age classes have an interval of ten years, yet the 
different lengths of interval are shown by the same distance on the scale. 
For Fig. 145 the horizontal scale has purposely been made such that 
the ten-year age intervals are set off by twice the distance used for the 
five-year intervals. As there are very few marriages under fifteen, 
the space for "under fifteen" has been made three times the space for 
the five-year interval. Taking the standard life as four-score j^ears, 
the space for "over sixty -five" has been made three times the distance 
used for the five-year intervals. This selection of horizontal distances 
makes the curves into much more nearly their correct shape than is 
possible on the Census Office chart, where five-year and ten-year 
class intervals are shown by equal scale distances. 

Perhaps the greatest gain made in clearness in Fig. 145 is due to 
the placing of the curves for male and female on the same ruled field, 
so that they can be compared instantly and correctly without need 
for any right-hand and left-hand measurements such as were necessary 
in Fig. 144. No claim is made that Fig. 145 is suitable for untrained 
readers. Since, however, it is doubtful whether many unskilled read- 
ers ever refer to the Census Atlas, it would seem desirable to use the 
general scheme of Fig. 145 for clearness and convenience. 

In Fig. 146, also taken from the Census Atlas for the 1900 Census, 
a right-and-left measurement must be made to compare death rates 
in two different years, ten years apart. The chart was drawn to bring 
out the data clearly and, if clearness is not attained, the data might 
just as well be expressed in columns of figures. Here again the vari- 
ables have been reversed and the independent variable improperly 
made the vertical scale. 

In Fig. 147 the data of Fig. 146 are redrawn into two curves by 
which the number of deaths occurring at different ages can be readily 



172 



GRAPHIC METHODS 



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United States Stalislical Atlas, 1900 Census 



Fig. 146. Comparative Proportion of Deaths at Different Ages from Pneumonia 
per 1,000 Deaths from Pneumonia in the Registration Area of the United States, 
1890 and 1900 

The right-and-left arrangement of this chart makes comparison for the two different years almost impossible. 

Contrast this illustration with Fig. HI 

compared for the two years under consideration. Notice that in the 
later year, 1900, deaths from pneumonia between the ages of ten and 
sixty years were much less frequent, while deaths after the age of 
sixty were more frequent. There was also an increase in the number 
of deaths at ages less than four. Certainly the facts relating to deaths 
from pneumonia for the two years are much more clearly brought 
out in Fig. 147 than in Fig. 146. 

There are some peculiarities in Fig. 147 which should be pointed 
out. The Government figures are given by one-year intervals up to 
the age of five, and then on five-year intervals to ninety-five. Fig. 147 
really should have been made so as to indicate a change in the hori- 
zontal scale at five years. If the chart had been made the full width 
of the page it would have been possible to get room enough to show 
the figures for single years at ages under five by using a space 
only one-fifth of the horizontal distance used for the five-year inter- 
vals. The large number of deaths at ages five to nine inclusive is 
very striking on the curve. Possibly the large death rate from five 
to nine may be due to the lessening of parental care at an age when 
exposure becomes more frequent. By ten years of age, the children 
have learned better how to take care of themselves and the number 
of deaths from pneumonia comes down to about the lowest point. 
Though the foregoing explanation of the large number of deaths 
from five to nine years may be correct, it is probable that the figures 
are more or less in error, due to the tendency to state ages in numbers 



FREQUENCY CURVES 



173 



per looo 
200 



which are multiples of five. The peaks for the period five to nine 
may be due largely to parents giving the age roughly as "five years". 
In Fig. 148 the data in which the reader is interested are shown 
at the peaks of various triangles. The shaded triangles on the chart 
give a geometrical figure which at first glance might be considered 
as a curve. It is not until after a considerable amount of puzzling 
that one notices that the triangles have absolutely no significance 
and that they are only a means of showing the distance from the 
base line to the various points representing decrease or increase. It 
would have been better if plain black bars had been used for Fig. 148 
instead of the tri- 
angles. Bars are so 
familiar to everyone 
that there would be 
no danger of error in 
interpretation. This 
illustration was used 
in a Sunday news- 
paper article where 
a non-technical class 
of readers had to be 
reached. For such a 
class of readers the 
solid black bars 
would probably be 
the most easily un- 
derstood method of 
presentation. 

For anything ex- 
cept newspaper pres- 
entation, the method 
of Fig. 149 would 
probably be more 
acceptable • to the 
reader than the solid 
black bars suggested in the preceding paragraph. The curve drawn 
in Fig. 149 shows a fairly uniform increase in death rates as ages 
increase up to the age of sixty. The degree of uniformity in increase 
is much more readily seen from the curve line than it could be shown 























































































































































































































































































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<00 I I I I I I I I I I I I I I I I I I I I I I I + 

<0-NO^inOiDOiooinoinoinoinOinOinOin 

Fig. 147. Comparative Proportion of Deaths at Different 
Ages from Pneumonia per 1,000 Deaths from Pneu- 
monia in the Registration Area of the United States, 
1890 and 1900 

Comparison of the two years can be made instantly throughout the whole 
range of ages. Age is the independent variable and, hence, is shown 
here as the horizontal scale. It would be better if a vertical wavy 
line or some other signal were used to show the change in the horizon- 
tal scale for ages below five years 



174 



GRAPHIC METHODS 



by the use of bars. Granted that the curve of Fig. 149 might not 
be understood by all the readers of a newspaper, it is nevertheless 
much more desirable, even in newspaper work, than the method shown 
in Fig. 148. Though Fig. 149 might not attract deep interest on the 
part of a newspaper reader, it would not be likely to be misinter- 
preted. Fig. 148 might serve to attract attention, but what is the use 
in attracting atten- 
tion unless a correct 
impression is given 
after attention has 
been attracted.'* 

Frequency curves 
thus far considered 
have permitted read- 
ing from the vertical 
scale only the actual 
number or percent- 
age observed corre- 
sponding to any 
point which may be 
selected on the hori- 
zontal scale. Thus, 
in Fig. 143 (see page 
167) we can read 
from the vertical 
scale only the per- 




Bquitable Life AssvTance Society 

Fig. 148. Change Since 1880 in the Death Rates of 
Americans at Various Ages 

The use of the separate triangles here is confusing to the reader. One is 
apt to interpret the chart by the contour of the shaded areas rather 
than by the points at the tips of separate triangles. Compare this 
illustration with Fig. 149 



centage of marriages which corresponds to any selected age on the hori- 
zontal scale. In Fig. 150, however, we have the same data of Fig. 143 
plotted in the form of a cumulative frequency curve. With a cumulative 
frequency curve the vertical scale shows not the actual number for 
any point of the horizontal scale, but the number cumulatively up 
to any point which may be selected on the horizontal scale. In Fig. 
143 the percentage who married at each age is given in figures at the 
top of the chart. By observing the figures at the top of Fig. 143 
and the figures at the top of Fig. 150, the method for plotting a cumu- 
lative frequency curve will be apparent. Beginning with the per- 
centages for the later ages in Fig. 143, the figures for the various 
years are added cumulatively to give the figures seen at the top of 
Fig. 150. The figures and the curve of Fig. 150 thus show the per- 



FREQUENCY CURVES 



175 






centage ^Yllo married at ages greater than any specific age selected 
from the horizontal scale of the chart. 

Fig. 151 gives an example of a class of information which can be 
sho^^'n to very great advantage by the use of cumulative frec^uency 
curves. In an annual report of a railroad a tabulated statement of the 
number of miles of different weights of rail in use at the end of the 
fiscal year makes the information difiicult for the stockliolder to inter- 
pret. Putting the data in the form of a curve like Fig. 151 lets the 
stockholder see at once just what conditions are on his road, in so far as 
rail weight is concerned. Thus, in Fig. 151, the stockholder may see 
at a glance that a very small percentage of the rails on this railroad 
weigh in excess of 75 pounds per yard, and that only about half of the 
rails weigh niore than 70 pounds per yard. In order to compare difi^er- 
ent years it would be well to have a chart of this kind printed in the 

annual report, wdth 
curves for dlfi^erent 
years plotted on the 
same co-ordinate rul- 
ing, so that the 
stockholder could see 
by the change in the 
shape of the curves 
just what has been 
done toward replac- 
ing light rails with 
heavy rails. If de- 
sired, rail-weight 
curves for different 
railroad systems 
could be shown in 
the same chart, so 
that the stockholder 
might see how his 
railroad compares 
with others in the 
matter of rail weights. 



o 
a. 

5 

lO 


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u 

to 20 



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< 1 



se 



Data 0/ Elmer RUteiihouse, of the Equitable Life Assurance Socivty 

Fig. 149. Change Since 1880 in the Death Rate of 
Americans at Various Ages 

The increase in deatti rates for ages over forty is here showTi in great 
contrast with the decrease in death rates for ages less than forty. 
The hea^"^' zero line and the arrows pointing upward and downward 
make misinterpretation almost impossible 



It would have been better if Fig. 151 had, at the lower left-hand 
corner, the words "more than", with an arrow pointing horizontally 
to the right as can be seen in Fig. 158. In cumulative frequency curves 



176 



GRAPHIC METHODS 



^ omcootooior^ioio — (31 o<nr~ 



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OVER- 



ZQ 22 24 26 28 



34 36 38 40 4Z .44 



such as this it is well to give the reader a clew that it is a cumulative 
frequency curve he is observing, and the arrow with the words more 
than" accomplishes this result in a satisfactory manner. 

There are two scales used in Fig. 151 with the expectation that the 
reader would ordinarily use the left-hand scale when reading the chart, 

using the words 
"more than". The 
right-hand scale 
reading downward 
permits the reader to 
get at once the com- 
plement of any figure 
on the left-hand 
scale, so that, by 
using the right-hand 
scale, the reader may 
interpret the curves 
on a "less than" 
basis. Thus, in con- 
sidering the weight, 
roughly 6 per cent of 
all the rails on the 
system are more 
than 75 pounds per 
yard, and using the 
right-hand scale it is 
seen that, roughly, 
94 per cent of all the rails are "less than" 75 pounds per yard. There 
is not ordinarily any necessity for using a double scale in this manner. 
It is done here only to show the difference in reading a two-scale chart. 
In Fig. 152 and also in Fig. 153 the cumulative curves have been 
plotted on a different basis from that used in plotting Fig. 150 and Fig. 
151. In Fig. 150 and Fig. 151, the curves begin at the 100 per cent line 
at the top of the chart and extend downward toward the right. In Fig. 
152 and Fig. 153 the curves start at the zero line at the bottom and ex- 
tend upwards toward the right of the chart. The differences in the 
shape of the curves will point out to a trained reader the manner in 
which he must read the curves. Fig. 152 and Fig. 153 should be read 
using the words "less than" instead of the words "more than". Thus, 



Fig. 



30 32 

Age 

Data of Amy Hewes in Publications Am. Statistical Assn. 

150. Percentage of 439 Married Graduates of 
Mount Holyoke College (Women) Graduating 1890 
to 1909, who Married at Ages Greater than Any 
Specific Age Selected from the Horizontal Scale of 
the Chart 

This is a cumulative frequency curve plotted from exactly the same data 
as Fig. 143. The word "over" with the arrow at the lower left-hand 
corner of the chart shows that the chart does not indicate the per- 
centage who marry at any age but the number who marry later 
than any specific age read from the horizontal scale 



FREQUENCY CURVES 



177 



in Fig. 152 considering the curve "A", 60 per cent of all the telephone 
calls of this class were answered in "less than" four seconds and 76 per 
cent of the calls were answered in "less than" five seconds. Of course, 
all those calls which were observed as having been answered in "less 
than" four seconds are also answered in "less than" five seconds, so 
that the curve is on a strictly cumulative basis. In Curve "C" it 
can be seen that only 30 per cent of the calls of that class were answered 
in less than four seconds, as against 60 per cent for curve "A". Though 
curve "A" is higher up on the chart than curve "C", it really represents 
a smaller length of time required to answer telephone calls than shown 
by curve "C". Since twice as large a percentage of the calls were 
answered in "less than" four seconds, .the average time for answering 
calls in curve "A" is certainly smaller than the average time for curve 

C , yet curve A ap- 
pears on the upper part of 
the chart. It is confusing 
to the average reader to 
have curves appear on the 
upper part of a chart when 
they really represent numer- 
ically smaller quantities 
than other curves appearing 
on the lower portion of a 
chart. Yet this is the result 
when curves are plotted on 
a "less than" basis. In 
order to avoid danger of 
misinterpretation, it seems 
desirable that cumulative 
frequency curves should be 
plotted on a "more than" 
basis. Most of the cumula- 
tive frequency curves in 



Per Cent 
A B 



90 10 



60 20 



70 30 



30 70 



eO SO 



10 90 



Fig. 



70 60 90 100 

Weight of Rail in Pounds 



no 



151. Weight of Rails per Yard in the Main 
Line Track of the Seaboard Air Line Railway 
as Published in the Annual Report to Stock- 
holders for the Fiscal Year Ending June 30, 
1912 

When using the left-hand scale the chart is read on a "more 
than" basis as if the words "more than" had been used 
with the horizontal scale as seen in Fig. 158. If the right- 
, , . 1 1 1 ■ ■ 1 hand scale is selected the words "less than" are used 

this book are plotted on a 

"more than" basis, so that curves involving the larger quantities or 
percentages may appear on the chart above those cumulative fre- 
quency curves for smaller quantities or percentages. 

Fig. 152 and Fig. 153 show the application of the cumulative fre- 
quency curve to commercial problems. The full explanation of these 



178 



GRAPHIC METHODS 



two charts cannot be gone into here, but the reader can see for himself 
the use of the cumulative frequency curve in studying different problems 
in the telephone business. In Fig. 152 the curves show the time required 
to answer calls in different cities, while Fig. 153 shows a comparison 
of answering times in different classes of service. Notice that in each 
of these two charts it seems that two seconds is about the minimum 
which can be expected in answering telephone calls with the existing 
types of equipment. Fig. 153 certainly gives in excellent manner the 
comparison between the answering times for different classes of service. 
It would be very difficult to convey the complex information contained 

in Fig. 153 by using tabu- 



lated figures only. Tabu- 

















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/ 


Telephone Service in Wisconsin 
Prompinei5 of Operators in Answering Calls 
Curves Shotting Conditions inCities of Various 5ize^ 
A. Average Speed in all Cities over 10,000 CU3 Calls ~ 
S - ... ■ of WOO to 10,000 634 ■• 
C ■ .... Under i,0O0[ £76 - 








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lated figures would take up 
as much space as the chart 
and they would be less in- 
telligible to any person who 
knows even the rudiments 
of reading graphic presenta- 
tions. 

In Fig. 154 an attempt 
was made to apply cumu- 
lative freciuency curves to 
a comparison of wage rates 
in different sections of the 
United States. The chart, 
however, is likely to be very 
misleading, as it has been 
plotted by methods which 
are not in accordance with 
usual practice. The variables have been reversed, and the independent 
variable has incorrectly been made the vertical scale. Besides that, 
the vertical scale reads downward instead of upward. In all kinds of 
curve plotting it is common to have the two scales begin with zero 
at the lower left-hand corner of the chart. Here the two scales begin 
the zeros at the upper left-hand corner of the chart. Unless the reader 
will turn Fig. 154 on its side so as to make the two zeros at the lower 
left-hand corner, he may find great difRculty in interpreting the chart. 
Fig. 155 shows a replot of the data of Fig. 154. Here the curves are 
plotted on a "more than" basis, but it would have been better if the 



= 50 
'hit 

a JO 
to 

10 



1 £34 56 7 e 9 10 II le 13 14 15 16 n le 19 £0 

Time of Answer in Seconds 

Courtesy of Data, Chicago 

Fig. 152. Time Required for Operators to An- 
swer Telephone Calls in Towns of Different 
Size in Wisconsin 

These curves start at the lower left-hand portion of the field 
and trend upward, showing that they are plotted on a 
"less than" basis. Curve A shows a smaller time required 
to answer calls than Curves B or C, yet the actual position 
of Curve A on the chart is higher than either curves B or C. 
If cumulative frequency curves are plotted on a "more 
than" basis the position of several curves on a chart is 
relatively such that the reader is not confused so much as 
when curves are plotted on a "less than" basis 



FREQUENCY CURVES 



179 



words "more than", with an arrow, had been placed at the lower 
left-hand corner of the chart. In Fig. 155 a little study will show 
the advantages of plotting curves on a "more than" basis. The reader 
can see at a glance from this illustration that the wages for the western 
States are very much higher than the wages in the south Atlantic 
States. The position of the curves one above the other would lead 
the reader at once to think of the upper curves as showing higher 
wages. Here the upper curves do indicate the higher wages, but they 
would not do so if they were plotted on a "less than" basis instead 
of on a "more than" basis. Though it may cause some confusion 
at first, it seems desirable as a general rule that cumulative frecpency 
curves should be plotted on a "more than" basis rather than on a 
"less than" basis. 



loo 



eo 



lO 



TiME IN Seconds 

IS 



20 



25 



30 



60 



b 



1 40 



20 





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Courtesy of W. S. Gifford, American Telephone & Telegraph Co. 

Fig- 153- Answering Time of Different Classes of Operators in Telephone Work 

Cumulative curves of this sort give information in much more condensed and clear form than possible with 
other methods of presentation. This particular chart is read on a "less than" basis, as can be seen by 
the general position of the curves as related to the scales. Notice that none of the calls is answered in 
less than two seconds 



180 



GRAPHIC METHODS 



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Fig. 154. Comparison of Earnings of Men Wage Earners in Different Portions of 

the United States in 1905 

This chart is almost hopelessly confused because the scales have been so arranged that the two scale zeros 
appear at the upper left-hand comer of the chart instead of at the lower left-hand comer. The vertical 
scale reads downward when it should read upward. See Fig. 155 for these same data redrawn 



FREQUENCY CURVES 



181 



In Fig. 156 we have cumulative frequency curves applied to a 
comparison of wages in different departments of a corporation. Here 
again the words "more than" and the arrow would have been de- 
sirable at the lower left-hand corner of the chart. The general position 
of the curves beginning at the upper left-hand corner, however, assists 
the reader to see that these curves are plotted on a "more than" 
basis. A chart of this kind is of great utility in making a study of 
wages. It may be noticed, for instance, in the curve for laborers, 
that there is a very decided change in the shape of the curve at about 
$9.00 per week. Only 62 per cent of these laborers make more than 
$9.00 per week and but 80 per cent of them get more than $5.00 per 

Pen Cent 
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7 8 9 10 12 15 

WEEKLY EARNINGS - DOLLARS 

.. .^. r- United States 

N.Atlantic ■■ o . S.Atlantic 
N. Central .— .— . s. Central 
Western Alaska 



25 



Fig. 155. Chart Showing What Percentage of the Wage Earners in Different Portions 
of the United States Receive More than any Specified Amount of Earnings up to 
Twenty-Five Dollars per Week 

Here the scales are correctly arranged so that the two zeros appear at the lower left-hand comer. The 
plotting of these curves on a "more than" basis causes curves which show the largest earnings to appear 
in their proper position toward the top of the chart. Plotting of cumulative frequency curves on a "more 
than" basis is usually desirable, since it reduces the chances for confusion to ths reader. This chart 
could have been improved if the words "more than" and an arrow had been placed at the lower left- 
hand corner on the general scheme of Fig. 158 



182 



GRAPHIC METHODS 



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Fig. 156. Comparison of Actual Weekly Earnings in Different Departments of a 
Large Industrial Plant Showing Percentage of Men in Each Department Receiving 
More than Any Specified Amount of Earnings per Week 

This illustration was made by photographing directly from the universallj' ruled paper shown also in 
Figures 57, 103, 130 and 134. The scales and the different titles were put on the paper with a typewriter. 
Lack of steady work caused many of the laborers to get the very small earnings sho-n-n by the upper 
portion of the curve marked "Laborers" 



FREQUENCY CURVES 183 

week. The fact that 20 per cent of all the laborers earn less than 
$5.00 per week is due to intermittent employment given laborers in 
this particular business. As $5.00 per week is not a living wage for 
any man, the shape of the cumulative curve for the laborers at once 
points out the desirabilitj^ of some change in management by which 
fewer men might be employed and all the men employed more steadily 
than indicated by the curve for laborers in Fig. 156. Since all the 
laborers were paid the same rate per hour, the only possible explana- 
tion of the fact that a large number of men earn as little as $5.00 per 
week must be that the laborers were not employed continuously. 
More continuity of employment for a smaller number of laborers 
would, in this particular case, have resulted in more money being 
paid on an average to each man, so that the men would, to all essential 
purposes, have received an increase in pay even though the hourly 
wage rate were not increased. 

Though that portion of the curves for the office forces seen at the 
upper left corner of Fig. 156 appears somewhat similar to the curve 
for laborers, the low earnings of a large percentage of the office force 
were due to the employment of office boys and other young employees 
who would have a fair chance to get a good training and grow up 
with the business. Therefore, the curves for the office forces need 
not attract the same attention as the curves for the laborers, who 
are all full-grown men having comparatively little chance for promo- 
tion. 

The cpick change at $11.00 per week in the shape of the curve 
relating to the foremen and clerks is due to the fact that some of the 
foremen in this business are paid by the hour and not by the week. 
That some of the foremen receive as low as $6.00 per week and that 
only 93 per cent of the foremen receive over $11.00 per week is due 
to the fact that some of the men were off because of sickness or on 
leave of absence. If the attendance of these men were more regular 
the curves would not have such a decided peak at $11.00 per week. 
Though Fig. 156 has been plotted on a "more than" basis, the reader 
may, if he wishes, read it on a "less than" basis by referring to the 
right-hand scale which has zero at the top instead of at the bottom 
of the page. 

Fig. 156 was made directly from typewritten copy with only the 
curves and the marginal lines drawn in by hand. This same uni- 
versally ruled paper has been referred to elsewhere as being con- 



184 



GRAPHIC METHODS 



venient for general use. Here the paper is used to indicate 100 per 
cent in the vertical direction, and the horizontal scale is chosen for 
data unrelated to time. 



No of Percent & 
Pieces No orOrders 

2000 100 



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80 



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Size of Order in Number of Pieces 



Fig. 157. Cumulative Frequency Curve Study of the Number and the Size of All 
Orders Handled During a Ten-days Test in a Certain Kind of Freight-handling 
Work 

The orders are sorted into various classes or groups arcording to the number of pieces called for by each 

order. The limits for the various classes were fixed by the exercise of a little judgment and are shown 

by the vertical lines on the chart 
Curve "D" shows by small circles the actual number of orders found in each group. The curve is read 

from the right-hand scale 
Curve "C" shows by small circles the total number of pieces (or packages) carried by the various orders 

which are found in each group. Curve "C" is read from the left-hand scale 
Curve "A" shows the percentage of the total orders handled which contain more than any given number of 

pieces considered on the horizontal scale of the chart 
Curve " B " shows the percentage of the total number of pieces carried by those orders containing more than 

any given number of pieces considered on the horizontal scale of the chart 
Curves "D" and "A" refer to the number of orders or the amount of clerical work while curves "C" and 

"B" relate to the number of packages handled or the actual volume of business transacted 

In Fig. 157 we have an application of the cumulative frec[uency 
curve to a class of work which would be extremely difficult to under- 
stand if the graphic method were not used. In handling large quan- 
tities of freight the different orders cover many diverse kinds of ma- 
terial, and the jobs vary from one package up to many thousands of 
packages on one order. The pieces or packages referred to here may be 
anything from a single casting weighing 20 tons to a shipment of canned 
goods with 5,000 boxes or cases on a single shipping order. In the 
long run, however, the different classes of goods could be averaged, 
and it will be found that in any one locality there would be but shght 



FREQUENCY CURVES 185 

change from year to year in the average size or weight of package 
handled. The average weight of package might happen to be 150 
pounds, and, considering a whole year, there would probably be very 
little change in the average weight from month to month. Thus, for 
our purpose here, the term "piece" or "package" refers simply to 
the average package handled in different divisions or departments 
of the work under consideration. 

In order to obtain the data regarding the orders referred to in 
Fig. 157, Fig. 158 and Fig. 159 the order slips are sorted into different 
piles according to some definitely thought-out plan by which there would 
not be too many or too few orders in any one class or size group. A 
little preliminary trial work in sorting would show the best places to 
set the class limits for sorting the orders into separate piles. After 
the orders have been separated into piles, it is a simple matter to count 
the number of orders in each pile to obtain the data from which curve 
"D" is plotted. It will be noticed from the shape of the curve that 
the upper and lower limits for each class are well selected so that there 
is a fairly uniform decrease in the number of orders in each group as the 
size of the orders increases. The order slips in the different piles sorted 
according to the size of the order are taken to an adding machine, and 
addition made to obtain the total number of packages carried by the 
combined orders found in any one pile or class. This gives the data from 
which curve "C" is plotted. Though curve "D" shows a constantly 
decreasing number of orders as the size of the orders becomes greater, 
curve " C " proves that there is an increasing number of packages 
handled as the orders grow larger toward the right-hand side of the 
chart. 

Though there are not so many orders of large size as of small size, 
the small numbers of large orders nevertheless carry many more packages 
than the large numbers of small orders. The executive is, of course, 
interested in revenue and, for revenue purposes, as mentioned above, 
all packages may be considered of the same size. Revenue obviously 
depends upon the number of packages handled, rather than on the 
number of orders handled. Curve "C", then, shows at a glance that 
the small number of large orders are of much greater interest to the 
financial manager than the large number of small orders. 

Fig. 157 shows that during the ten-days test period there were no 
orders in this particular class of work which exceeded two hundred 
packages. Curves "D" and "C", though interesting, do not show all 



186 GRAPHIC METHODS 

the information which is desirable from the standpoint of management. 
In order to show up the facts more clearly, curves "A" and "B" are 
plotted from the same data as curves "D" and "C" respectively. 
Curve "A" is plotted on a cumulative basis by the same general method 
used for Fig. 150 and Fig. 151. The total number of orders for the 
whole test period is first obtained, and then the cumulative number 
adding up to any class-limit line on the horizontal scale of the chart is 
plotted as a percentage of the total number of orders. Curve "A" 
joins the zero line at 200, showing that none of the orders was larger 
than 200 packages. We can see instantly that, because of the large 
number of small orders, only 22 per cent of all the orders handled were 
larger than twenty-five pieces per order. Only 13 per cent of all the 
orders handled exceeded fifty pieces per order. Also, by reading from 
the vertical scale opposite the figure for 50 per cent, we can see at once 
that only half of all the orders handled carried more than twelve 
packages. 

In a manner similar to that used in making up curve "A", the cumu- 
lative curve "B" is made up from the data relating to the number of 
packages shown in curve " C ". It may assist the reader to follow these 
charts if he keeps clearly in mind that curves "D" and "A" relate to 
the actual number of orders of various sizes, while curves " C " and "B " 
relate to the number of packages, or the amount of total business car- 
ried by orders of various sizes. In other words, curves "D" and "A" 
relate to the amount of clerical work needed, while curves "C" and 
"B" show the actual amount of freight-handling labor involved and 
measure the amount of revenue earned. Curve "B" thus shows that, 
though there are not many large orders, about 69 per cent of all the 
revenue comes from those orders which contain more than twenty -five 
packages. Fifty-six per cent of the business (and the revenue) is due 
to orders containing more than fifty packages. Twenty -nine per cent 
of all of the revenue comes from orders containing more than one hun- 
dred packages, yet none of the revenue for the ten-days time considered 
came from orders larger than two hundred packages, since there were 
no such orders during the period. 

It is by reading curves "A" and "B " in conjunction with each other 
that the manager may obtain the greatest information relating to his 
business. Considering first the orders which contain more than ten 
pieces, curve "A" shows that 55 per cent of the orders contain more 
than ten packages, while curve "B" shows that 91 per cent of the reve- 



FREQUENCY CURVES 187 

nue comes from those orders which are larger than ten pieces each. In 
other words, the manager, because of handhng so many small orders, 
is doing 45 per cent of the total clerical work in order to obtain 9 per 
cent of the revenue. Since clerical work depends chiefly on the number 
of separate orders, the manager would be able to reduce his clerical 
work on this particular class of orders somewhere near 45 per cent if 
he would refuse to handle orders of less than ten packages, and, by such 
a decision, he would lose only 9 per cent of his revenue. For most 
businesses, it would pay handsomely to neglect entirely 9 per cent of 
the revenue if 45 per cent of the clerical work could be avoided. In 
freight handling, the work is of course mostly under the jurisdiction 
of the Interstate Commerce Commission, so that even if the manager 
should wish to refuse orders of small size, he would not be permitted 
to do so. 

Though the small orders must be handled to give service to the 
public, a chart such as Fig. 157 is nevertheless of very great assist- 
ance in pointing out the actual conditions existing. When it is 
seen what a large amount of clerical work is involved in handling 
orders which produce only a small portion of the revenue, thought 
could be given to the methods of handling small orders so that the 
small orders may not cause any more expense than absolutelj^ neces- 
sary. Usually it is possible to handle small orders in a different man- 
ner from the large orders, and, if the true situation is thoroughly 
understood, small orders may possibly be handled by methods which 
will result in much less loss than would be incurred if small orders 
are handled by the same methods used for large orders. 

One may see from Fig. 157 the percentages of orders and of business 
or revenue for any size of order which it may be desired to consider. 
Thus, taking orders which contain more than twenty-five packages, 
it can be seen that 22 per cent of all the orders contain more than 
twenty -five packages and that these orders carry 69 per cent of the 
total business and bring in 69 per cent of the total revenue. Though 
these orders of over twenty -five packages do not involve a large amount 
of clerical work, they nevertheless bring in such a large percentage 
of the revenue that any dividends from this particular department 
must probably be paid from the revenue brought in by orders in excess 
of twenty-five packages each. 

The general methods used in plotting Fig. 157 have been con- 
sidered at rather great length because it is felt that a chart of this 



188 



GRAPHIC METHODS 



Per Cent & 
No of Orders 



Percent 8t 
No, of Orders 



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Size of Order in Number of Pieces 



Fig. 158. Cumulative Frequency Curve Study of the Number and the Size of All 
Orders Handled During One Week in a Certain Kind of Freight-handling Work 
Carried on in Two Closely-related Departments 

Curve "H" shows by small circles the actual number of orders found in each size-ot-order-elass. Note that 
at the left of the chart there are numerous orders shown in each class even though here the limits of 
each class have been purposely made very close together 

Curve "B" shows the percentage of the total orders handled which contain more than any given number of 
packages considered on the horizontal scale of the chart 

Curves "A" and "C" are similar to curve "B" and show subdivisions of the total number of orders accord- 
ing to which of two related departments handled the work 

Curve "F" corresponds with curve "B" but shows the percentage of the total number of pieces carried by 
those orders containing more than any given number of pieces considered on the horizontal scale of the 
chart 

Curves "G" and "E" are similar to curve "F" and show subdivisions in the total number of pieces accord- 
ing to which of two related departments handled the work 

One sub-department of the business handled the orders portrayed by Curve "A" and Curve "E". The 
other sub-department handled orders portrayed by Curve "C" and curve "G". The combined work 
of the two departments is shown by Curve " B " and Curve " F" 

The percentage of the total number of orders handled in each of tlie two different departments, up to any 
size of order read on the horizontal scale, may be seen by considering the distances on the chart above 
and below Curve "D" 

kind can be of service in a sales analysis for almost any kind of busi- 
ness. A company selling fairly uniform products — shoes, for example 
— could use for the horizontal scale the actual number of pairs of 
shoes contained on various orders received for the test period of, say, 
a week or a month. Companies having a diversified product, as elec- 
trical machinery, could best make a chart of this kind by basing the 
horizontal scale on the actual value in dollars of the various orders 
received. Thus, the scale could be made for orders in sizes larger 
than $50, $500, $1,000, etc. If charts are made for different depart- 
ments, very interesting comparisons could be made which would bring 



FREQUENCY CURVES 189 

out information valuable to a corporation executive. Department 
stores might also have use for charts on the general plan of Fig. 157. 
Different departments could be considered by the number of orders 
of various sizes. As the margin of profit in different classes of goods 
in different quantity sold would be fairly well known, the manager 
could get a good idea as to how much of the time of his sales force 
was occupied in handling small orders, and how much in handling 
large orders. 

Fig. 158 is drawn on the same general scheme as Fig. 157. In 
Fig. 158, however, we have the additional complexity that the freight 
under consideration must be handled by two distinct departments 
working in very close harmony with each other. As there is a dif- 
ference in the cost of doing the work handled by the two departments, 
the chart was purposely so drawn as to show the number of orders 
and the number of packages handled by each of these two distinct 
departments which together do all of the work under consideration. 
Curves "B" and "F" show respectively the percentage of orders 
and the percentage of business handled as a whole. The other curves 
show the relative proportions of the orders and the business done by 
the two departments. The position of the curves on the chart gives 
a fairly clear idea as to whether the first department or the second 
department handles the larger number of orders and the larger per- 
centage of the actual business. 

In Fig. 153 it was shown that, because the curves were plotted 
on a "less than" basis, the curve showing the smaller length of time 
appears at the top of the chart, when one would naturally expect to 
find the smaller quantities of time recorded relatively toward the 
bottom of the chart. In Fig. 158 the data are plotted on a "more 
than" basis, and the curves are seen in their proper relation to each 
other. Since the reader knows that the chart is plotted on a "more 
than" basis (as can be seen by the words "more than" at the lower 
left-hand corner of the chart), he may know instantly that the curves 
relating to the two different departments show in their correct rela- 
tion to each other. Curves "G" and "C" relate to one department, 
while curves "E" and "A" relate to another department. Curve 
"C" appears above curve "A" on the chart, and the reader may ac- 
cordingly know without detail study that the department to which 
curve "C" relates handles larger orders than the department to 
which curve "A" relates. In a similar way, the upper portion of the 



190 GBAPHIC METHODS 

chart shows that the department to which curve "G" relates handles 
a larger percentage of the total number of packages and produces a 
larger percentage of the revenue than the department to which curve 
"E" relates. If this chart had been plotted on a "less than" basis 
instead of on a "more than" basis, the position of these two curves 
giving detailed information for the main curve "F" would be exactly 
reversed, Avith curve "E" appearing above the heavy line "F" and 
curve "G" appearing below the heavy line. 

It is perhaps well to point out an error in drafting which occurred 
on Fig. 158. The information most needed relates to orders containing 
less than three hundred packages each. It was, however, desired to 
show on the chart that none of the orders contained more than five 
hundred packages, and the right-hand portion of the chart is accord- 
ingly shown with a break, indicating that a section has been omitted. 
As a general rule, when making a break in a drawing in this manner, 
the two portions on either side of the break are made exactly as though 
a piece of paper had been torn out of the middle of a drawing made 
large enough to include the whole chart. Fig. 158 is incorrectly made 
in that the curve lines to the right of the figure 300 on the horizontal 
scale have been drawn pointing down toward the right-hand corner 
of the chart where they show at the left of the break. These lines 
would not appear this way if a piece of paper had been torn out of 
a large-size chart. The curve lines should have continued up to the 
break in the drawing more nearly on the slope seen in the left-hand 
portion of the chart. The lines for curves "G", "F" and "E" would, 
if correctly made, show much less slope also at the right of the break 
where they lead down to the lower corner of the chart. This error 
is mentioned here simply that the reader may have some guidance 
if he finds it necessary to make charts including a break, similar to 
that shown in Fig. 158. 

It is customary in cost-keeping work to make costs which show only 
an average of the cost per unit, on an average for all orders completed 
during a period of time, say one month or one year. Though this 
method of averaging all orders together without respect to the size 
of the order is sufficiently accurate for many purposes, there are times 
when such a method may gravely mislead an executive. It is almost 
invariably true that small orders cost more per unit of output than or- 
ders of large size. A man who makes a selling price for his work on 
the average cost of small orders and large orders combined may be 



FREQUENCY CURVES 191 

losing money unnecessarily, because he does not realize the true cost 
of work when it is done in only small quantities on different orders. 

Fig. 159 proves the great variation in the cost of doing the work of 
handling a certain class of freight. The position of the dots on the 
chart shows that work done in orders of only twenty -five packages 
costs over twice the average for orders of four hundred or over. In 
keeping track of the cost of handling freight of different kinds for a 
large steamship terminal and warehouse company it was found im- 
possible to get reliable cost figures by averaging, day by day, the labor 
cost of handling freight for preceding days. On some days all the orders 
for one commodity might be small orders, and on the next day a very 
large quantity of that same commodity might be handled all in one 
large order, so that a gang of men could work steadily all day on that 
one order. Naturally if a large gang of men work all day on one order, 
the cost per package handled would be very much less than if several 
different gangs were used in handling numerous orders of only ten or 
twenty-five packages each. In order to get a clear view of what was 
actually happening, considerable study was given to the problem and 
the method shown in Fig. 159 is the result. 

It was decided to make a pin board about 24 by 30 inches, on the 
general scheme seen in Fig. 159, by which separate orders could be 
shown on the chart by a dot to represent each order handled. As it 
was desired to keep continuous records for the chief commodities, it 
was not feasible to make ink marks for it would then be necessary 
to start over again frequently with a completely new sheet of paper. 
To overcome this difficulty, short pins were used having spherical 
glass heads only ^32 inch in diameter like those seen at the right in Fig. 
186. The co-ordinate paper for the chart itself was mounted on three 
layers of corrugated straw-board, having the ribs of the middle layer at 
right angles to the ribs of the two outside layers, as described in Chapter 
XII. A binding of gummed cloth -tape around the edge of the board 
gave a neat appearance and assisted to preserve the boards during 
rough service and long use. These boards were very light, yet remark- 
ably strong on account of the corrugations running in both directions. 

One cost clerk could not possibly figure out the cost of all orders 
and all commodities handled each day. The cost method was more 
in the nature of an automatic inspection system or check, so that the 
general efficiency of the work done by numerous gangs and hundreds 
of men could be judged by what might be called occasional analyses 



192 



GRAPHIC METHODS 









































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FREQUENCY CURVES 193 

taken at random. Because of the numerous commodities which were 
handled on which it was desirable to watch the cost of freight handling, 
the cost clerk figured the cost of any one commodity perhaps only one or 
two days in a month. Each morning the cost clerk would sort out 
all the labor tickets relating to some one particular commodity which 
had been handled on the preceding day. The cost per package would 
be figured up for each order ticket and, in the board reserved for that 
particular commodity, a tall pin would be placed for each order com- 
pleted the preceding day, showing by the position of the pin the number 
of packages on the order and the cost per package of handling that 
particular order. In considering the pin marked 8 at the right of Fig. 
159 we can see that it represents an order for 900 packages and that the 
cost per package was 1.1 cent. After some time in operating a pin 
board the position of the various pins on the board would show in the 
general form of a curve, and would indicate the cost of handling freight 
of that particular commodity in lots of different sizes. Since commodi- 
ties received from ocean ships are usually packed in some standard 
size of bales, boxes, or bags, the pin method of charting cost is a remark- 
ably reliable one. 

The pin board can be of great assistance to the general superintend- 
ent. As the cost of handling certain orders for certain commodities for the 
preceding day is known about eleven o'clock each morning, the super- 
intendent can look over the boards and note the special tall pins which 
show the exact cost of various orders handled. Thus, a superintendent 
seeing a board of the kind described would know that on the preceding 
day those orders had been completed which in Figure 159 are shown by 
numbered dots. His attention would be drawn at once to the orders 
represented by dots numbered 4, 5, 6 and 8. These dots show costs 
much above the average cost recorded for orders of those sizes. The 
cost clerk could furnish the order numbers of these particular orders 
and could also give the names of the foremen who had been in charge 
of the work. The superintendent could then ask for an explanation 
as to why these orders had cost much more than the work should have 
cost for lots of the size handled. Considering dot 6, notice that the 
average cost for 500 packages is about . 80 cent, but the order repre- 
sented by dot 6 cost 1.50 cent per package, almost twice what it should, 
have cost. Though dot 4 shows considerably above the average dots 
for 100-package lots, the percentage excess is not so great as in the case of 
dot 6. Dot 4 shows a cost of about 2.20 cents, while the average cost 



194 GRAPHIC METHODS 

for 100 packages is about 1.25 cents. What the superintendent wants 
to know is the percentage excess in the cost above what the chart shows 
should be the normal cost for any number of packages under considera- 
tion. The chart brings out this information very clearly. Since the 
superintendent can take the matter up with the various foremen before 
noon of the day after the work was completed, the foremen soon get 
the feeling that the superintendent knows what the cost should be, and, 
if anything happens to prevent work being done cheaply and quickly, 
the foremen are likely to report the conditions at once to see if assistance 
can be given them so as to keep the cost low. 

After the superintendent has seen the pin boards each morning, the 
long pins represented by numbered dots in Fig. 159 are removed and in 
their places are put the short glass-head pins having shanks so short 
that the pins may be pushed into the straw-board until the head of the 
pin touches the co-ordinate paper. The pins are then quite secure, 
and the boards may be worked upon and handled month after month 
without danger of the pins becoming lost from the boards. The 
ordinary type of tall pins or tacks used with wooden boards would not 
be at all satisfactory for this class of work, as it would be impossible to 
work with such boards containing thousands of tacks without knocking 
the tacks loose, so that they would be in a continuous process of becom- 
ing lost — much to the detriment of accuracy and to the disgust of a 
cost clerk. The short glass-head pins pushed in until the heads touch 
are very convenient and they give a thoroughly accurate record. 

As above mentioned, cost boards of the kind described would not 
be satisfactory if made with ink dots because the boards would soon 
have so many dots that information would be no longer easily obtain- 
able. By using the glass-head pins it is feasible to change the color of 
glass heads used on any board each six months. The position of the 
pins of different color would then show clearly whether work was being 
done more cheaply than it had been done in preceding periods of time. 
Thus, if any particular campaign were made to reduce the cost for 
small orders by handling small orders on some different method from 
that previously used, the pins near the left-hand side of the board might 
appear considerably lower down on the chart than the pins of the color 
which had been used in the six months preceding the change in method. 

When the board gets so full of pins as to make the pins crowded it 
is a very simple matter to remove from the board all of the pins which 
Avere inserted in the most remote period of time. Thus, it might be 



FREQUENCY CURVES 195 

found feasible to keep on the chart pins relating to four different periods 
of six months each, so that every six months one color of pins would be 
removed from the board and the pins removed would be those which had 
been placed in the board two years previously. A board would then 
show at all times the record of cost in handling this particular commodi- 
ty during the last two years. Boards used where pins must be put 
in and taken out very often may be faced with cork composition so that 
the pin holes may injure the surface as little as possible. Where pins 
are not to be changed very frequently, the straw-board covered with a 
layer of cloth before the co-ordinate paper is mounted will be found 
entirely satisfactory. 

In the upper portion of Fig. 159 is shown a summary chart of the 
data contained on the pin board itself. Curve "C" is a smooth curve 
drawn through the center of gravity of all pins on any vertical line 
which shows the size of order. It will be noticed that the cost decreases 
very little when orders become larger than three hundred packages, 
but for this particular commodity with the methods of handling used, 
the cost increases rapidly as orders decrease below three hundred pack- 
ages. Knowing the revenue obtained for doing the work, it is a simple 
matter to determine from the curve the smallest size of order of this 
commodity which can be handled under average conditions without 
incurring a loss. If the revenue for Fig. 159 were 1.5 cents per package 
it could be seen at once that (since the overhead expenses are not con- 
sidered) there must certainly be a dead loss on orders containing less 
than sixty-five packages each. If the overhead expenses are taken 
into account as well as direct labor, there would be shown a loss on 
orders of larger size, probably up to one hundred or one hundred and 
fifty packages. Assuming that a loss occurs on all orders shown on 
Fig. 159 up to the size of one hundred and fifty packages per order, 
the number of dots to the left of the line for 150 on the horizontal scale 
indicates just how great the total monetary loss would be. 

Curve "A" in Fig. 159 shows the percentage of orders which contain 
more than any specified number of packages selected on the horizontal 
scale of the chart. Curve "B" shows the percentage of the total 
packages which are found in orders containing more than any specified 
number of packages selected on the horizontal scale of the chart. 
Curve "A" indicates the amount of clerical work involved, and curve 
"B" shows the amount of actual labor and the amount of revenue in 
exactly the same manner described for Figures 157 and 158. 



196 



GRAPHIC METHODS 



too 



• • • • • •'«L.*'k* • 



Curves "A", "B" and "C" are shown in Fig. 159 only by way of 
proving the utihty of the pin-board method of keeping costs where there 
is a large variation in the size of the orders worked upon. The illustra- 
tion shows these curves superimposed on the pin board only to save 

space in printing. 

In Fig. 160 is shown a 
chart which may help to 
make clearer the general 
principles used in drawing 
the charts seen in Fig. 157, 
Fig. 158 and Fig. 159. Fig. 
160 shows the appearance 
of the curves if there are 
the same number of orders 
in each class or group and 
if all classes or groups are 
of uniform size. It makes 
no difference in the shape 
of the curves how many 
orders there may be if those 
orders are always uniformly 
distributed throughout the 
whole length of the hori- 
zontal scale of the chart. 
It would perhaps have been 
better if Fig. 160 had been 
so drawn that the length 
of the vertical scale would 
be the same as the length 
of the horizontal scale. The actual shape of the curve line referring 
to the percentage of business or the percentage of the total number 
of pieces would then be free from any possible distortion which it may 
have received because of the vertical scale being of less total length 
here than the horizontal scale. 

It is especially interesting to compare Fig. 160 with Fig. 159. 
In Fig. 159 the reader may easily see for himself that there are many 
more small orders than there are large orders, because the pins are 
largely concentrated toward the left-hand side of the chart. It is 
this concentration at the left-hand side which has so greatly affected 



Fig. i6o. Chart to Show the Theoretical Shape 
of Cumulative Curves for the Percentage of 
Total Orders and the Percentage of Total 
Business if There Is a Uniform Number of 
Orders in Each Class or Group 

It makes no difference in the shape of the curves, as long as 
all classes contain the same number of orders, whether there 
is one order or one thousand orders in each class between 
vertical lines 

The straight line shows the percentage of orders which contain 
more than any given number of pieces considered on the 
horizontal scale of the chart 

The curved line shows the percentage of the total number of 
pieces carried by the orders which contain more than any 
given number of pieces considered on the horizontal scale 

If there is not the same number of orders in all groups or zones 
the curves will take some other shape and the shape will 
depend on the peculiar distribution of orders as may be 
seen in Fig. 157, Fig. 158 and Fig. 159 



FREQUENCY CURVES 



197 



the shape of curve "A" and curve "B" in Fig. 159. By comparing 
Fig. 160, we can see that if the distribution of orders in Fig. 159 had 
been uniform, curve "A" would have been a straight diagonal hue 
and curve "B" would have been a curved line bowed upward instead 
of bowed downward. 

Though Fig. 161 
somewhat resembles 
Fig. 160, it is never- 
theless constructed on 
an entirely different 
plan. In Figs. 157, 
158, 159 and 160 the 
independent variable 
related only to size 
of order. For charts 
of the type shown in 
Fig. 160 the inde- 
pendent variable is a 
percentage. The de- 
pendent variable is 
also expressed as a 
percentage. 

Imagine the whole 

] I* ■r»lfir»Arl in M. O. Lorenz, in Ihe Publications, the American SlalUHcal Assn. 

^/ ,. ' ^ ^ , Fig. i6i. Curves to Show the Percentages of the Total 

Population of Prussia in 1892 and in 190 1 that Re- 
ceived Various Percentages of the Total Income as 
Considered on the Horizontal Scale 



100 

90 
80 

70 

L. 
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30 40 50 60 70 

Percents of Total I ncome 



80 90 100 



EQUALITY PRUSSIA 1892. PRUSSIA 1901 

M. O. Lorenz, in the Publications, the American Statistical Assn. 



If incomes were all equal the relation of population and income would be 
expressed by the straight diagonal line. The amount of inequality 
between various incomes is shown by the amount the curve diverges 
from the straight line. There was greater inequality of incomes in 
Prussia in 1901 than in 1892 



a long line and ranked 
according to income. 
The people in this 
line could be counted 
off into several equal 
groups so that each 
group would contain say 10 per cent of the total number. It would 
then be simple to compute the income of each group as a percentage 
of the combined income for all groups. The resulting group percentages 
would be plotted cumulatively as the dependent variable on a chart 
for which percentages of population would be the independent vari- 
able. Fig. 161 unfortunately shows the independent variable used 
for the vertical scale. A better arrangement may be seen by observ- 
ing the illustration through the back of the paper with the two zeros 
appearing at the lower left-hand corner. 



198 



GRAPHIC METHODS 



Diagrams made on the scheme of Fig. 161 are of very great assist- 
ance in studying such matters as the distribution of ^^ealth for any 
country. The subject of weahh distribution is so complex that unless 
data are expressed graphically there would be very serious difficulty 
in getting a true understanding and appreciation of the different 
factors involved. In Fig. 161 we have the curves for two widely sep- 
arated years plotted side by side, so that we may tell from the general 
shape of the curves whether the distribution of wealth is approaching 
uniformity of tending in the direction of great concentration in the 
hands of a few people. The more nearly the curve approaches a straight 
line the more nearly wealth is distributed uniformly among all the 



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3,000 4000 5,000 e,0OC 7,000 epOO 9.000 lO.OOO 

Rating of Truck in Pounds 
9 Report by Operator a Estimcrte by Manufacturer 

* Average reported Figure 

H. F. Thomson. Massachusetts Institvte of Technology, Vehicle Research 

Fig. 162. Cost of Gasoline in Cents per Truck-Mile for Different Sizes of Motor 

Trucks 

Since motor trucks are rated by the manufacturers in multiples of 1,000 pounds, the dots representing the 
records of different trucks naturally fall on the lines spaced by 1,000-pound intervals on the chart. 
The solid line is drawn through points at the "center of gravity" of all dots for any vertical line on the 
chart and represents the average condition as reported by truck operators. The dotted line is drawn 
through points on the chart for data furnished by the manufacturer as his estimate of good practice 

A curve of this general type, proving a close relationship between two variables, may be called a correlation 
curve 



CORRELATION 199 

members of the population. In Fig. 161 the hne was more bowed 
in the later year than in the earlier year, and the conclusion may ac- 
cordingly be drawn that wealth in Prussia tended toward further con- 
centration in those years intervening between 1892 and 1901. 

In Fig. 162 a study has been made to see how the gasoline con- 
sumption of motor trucks varies in trucks of different sizes. The hori- 
zontal scale shows the rated size in pounds of the trucks under con- 
sideration. On the vertical scale, the cost of gasoline is given in cents 
per car mile. The data of the different motor trucks were indicated 
by separate dots on the chart. The solid line was then drawn through 
a point which represents the center of gravity of all the dots on each 
vertical line. The total number of dots on this chart is rather small. 
Too much dependence cannot be placed in the resulting curve, as 
special conditions may have affected some of the records so as to 
cause the dots to be misleading. Thus, considering the two dots 
which are given for trucks of 2,000-pounds capacity, it will be noticed 
that both of these dots are far below the position on the chart which 
one would expect the average to occupy if one should judge by the gen- 
eral tendency of the curve as a whole. It may have happened that 
the particular trucks which these two dots represent were run with 
very light loads, thus making the gasoline consumption lower than 
would naturally be expected for trucks of that size. In Fig. 162 the 
object is to determine what relation, if any, exists between the cost 
for gasoline and the size of the truck. 

"Correlation" is a term used to express the relation which exists 
between two series or groups of data where there is a causal con- 
nection. In order to have correlation it is not enough that the two 
sets of data should both increase or decrease simultaneously. For 
correlation it is necessary that one set of facts should have some defi- 
nite causal dependence upon the other set, as seen in Fig. 162. 

Correlation studies can frequently be of assistance in business prob- 
lems. A manufacturer of machinery has recently revised many of 
his manufacturing and selling policies from the information obtained 
from a chart showing the relations of cost and selling price of his 
equipment to the actual size of the equipment. On the horizontal 
scale of charts used for this study the size of the apparatus was shown 
according to its actual working capacity. In a vertical direction a 
scale was selected for the cost of the apparatus and for its selling 
price. Dots were then placed on the chart in a manner similar to 



200 GRAPHIC METHODS 

Fig. 162, and a line was drawn on the chart through the different dots 
representing the factory cost of the machinery. The hne was not at 
all straight and the chief executive spent much time in finding out 
why there were so many variations from uniformity. He found, 
among other things, that some of his machinery had not been re- 
designed for several years, and that the weight of material used was 
much greater than necessary when taking into account the greater 
strength of steel and iron made by modern processes. Though mate- 
rials of the modern kind were being used to a large extent in his ma- 
chinery, the weight of material had not been reduced and there was 
more weight of employed material than was actually necessary if new 
designs were made. Another cause for fluctuation in the curve line 
Avas found in the quantities in which the product was manufactured. 
Some sizes of apparatus were particularly suitable to the public, 
and on these sizes the quantities were much larger than on other 
sizes. The sizes more commonly sold were naturally better equipped 
with jigs and tools than other sizes, and for that reason the cost was 
lower than would otherwise be expected. After the cost curves had 
been thoroughly studied for different kinds of apparatus, the selling- 
price curves were drawn in on the same sheets. It was found that 
for selling prices, also, there were numerous inconsistencies which 
could be corrected with advantage to the company. Though some of 
the peaks and valleys of the selling-price correlation curves were to 
be expected, there was no justification for others and a little concen- 
trated study brought forth methods by which the selling-price curves 
could be changed materially with advantage to both the producer 
and the consumer. 

In the study of physics and of experimental engineering, there are 
many times when a correlation curve is of assistance in the discovery 
and understanding of the laws of nature. For Fig. 163, many ob- 
servations were made and recorded on a sheet of co-ordinate paper. 
After sufficient observations had been made throughout the whole 
range of the horizontal scale, smooth curves were drawn which would 
most nearly represent the various dots plotted. In drawing curves 
of this kind, care should be taken to have each portion of the curve 
as nearly as possible at the center of gravity of the dots in any vertical 
section of the chart. Accuracy is not necessarily obtained by having 
the same number of dots on either side of the curve. If there are 
only three dots at some vertical line, it may be that two of these dots 



CORRELATION 



201 



would be close together and their combined weight must be considered 
as compared with one dot which may be some distance away. As a 
simple rule, consider the dots in anj' vertical section of the chart as 
though arranged on a see-saw, as used by children, and then shift 
the point through which the curve line is to be drawn so that the 
see-saw will just balance evenly. 



80,000 




2 3 4 5 B 7 8 9 ,10 i: 12 

Velocity of circulating- "water -=ft. per sec. '~^1\ 
Geo. A. Orrok, in Journal American Society of Mechanical Engineers 

Fig. 163. Relation of the Rate of Heat Transmission to the 
Velocity of the Circulating Water in Surface Condensers 

Correlation charts of this type have sometimes been called "shot-gun diagrams " 
The investigator makes a dot for each observation recorded, and then judges 
from the arrangement of the dots whether there is any general law expressing 
a relation between the two variables studied 

Curves like those seen in Fig. 163 may be sketched in free-hand, 
or they may be much more conveniently drawn by using the irregular 
or so-called "French curves" which may be obtained in any store 
selling drafting instruments or artists' materials. As it frequently 
happens that an irregular curve available does not exactly fit the dots 
through which the curve line is to be drawn, care must be taken to 



202 



GRAPHIC METHODS 



shift the irregular curve along and draw only short portions of the 
curve line at any one stroke of the pencil or pen. Care in shifting the 
irregular curve will permit drawing a clean, smooth curve line, even 
though the irregular curve used is quite different in shape from the 
curve line which is drawn. 



69- 








































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52 63 54 55 56 57 59 59 60 61 62 63 64 6S 66 67 60 69 70 71 7e 

Noiher't Span (=1/) in Inches. 

Karl Pearson in "Blometrika" 

Fig. 164. Correlation Curve Showing Probable Span of a Daughter from Finger Tip 
to Finger Tip, for any Given Span of the Mother. 1,370 Cases were Studied 
in Making up this Chart 

Here the dots for the 1,370 observations are not all sho-rni. The dots seen represent the averages of alt 
cases studied in each 1-inch range of mother's span according to the horizontal scale. The curve line 
is then drawn through these dots. Instead of using the curve line, the mathematical relation may be 
expressed by the formula D = 34.18 + .473 M 

This chart would have been easier to interpret clearly if both the vertical and the horizontal scales began 
with the same figure, say 51 inches. The reader is not apt to notice that the vertical scale here begins 
at 58 while the horizontal scale begins at 51 

Curves like those seen in Fig. 163 are properly drawn as smooth 
curves because they are based upon some definite laws of nature. 
It is only because of the crudity of the observations of mankind that 
the dots are so widely scattered. If human knowledge were sufficient 
to obtain measurements with exactness, curves for data relating to 
the laws of nature would fall exactly on points plotted according to 
the observations and there would be no difficulty in getting smooth 
curves. The curves in this book are nearly all plotted from statistical 
data for which there are ordinarilj^ some hundreds of variables, of 
which many do not follow any definite laws of nature. For most 
statistical work it is much better to join the points showing the ob- 
servations by straight lines without any attempt to draw smooth 



CORRELATION 203 

curves. Smooth curves would by their smoothness implj' a degree 
of accuracy in the data much greater than would ordinarily be justi- 
fiable. By using the straight lines instead of the smooth curves to 
connect points, the reader is warned that the chart represents facts 
as found, rather than facts which are assumed to be in accordance 
with any definite laws. Where smooth curves are proper, as in Fig. 
163, it is feasible to have a mathematical formula to represent the 
shape of the smooth curve. As the determination of mathematical . 
formulas to suit the shape of any curve is a whole study in itself, there 
will be no attempt to cover that subject in this book. 

Biologists have constant use for correlation curves. Fig. 164 
shows a curve used in the solution of a typical problem such as biolo- 
gists are constantly attacking. It was desired here to find out what 
laws govern the physical characteristics of the ofi^spring when certain 
characteristics are found in the mother. In all, 1,370 cases were 
measured, both mother and daughter, to get the data from which 
Fig. 164 was plotted. All the cases were classed according to the 
span of the mother, with the class limits made 1 inch apart. A single 
point was plotted on the chart as an average for each class. A curve 
line was then drawn so as to represent most closely the data shown 
on the chart, and it is seen that the curve is a straight line. There were 
naturally fewer observations at either end of the chart, for the very 
small spans and for the very large spans, than for the intermediate 
spans. It was probably because of the small number of observations 
at either end of the curve that the dots there are so far away from the 
curve line. If more numerous observations were taken it is probable 
that all the averages would fall more closely on the curve line than seen 
in Fig. 164. 

The ordinary course of procedure in making a correlation chart 
is to plot all the observations by the method seen in Fig. 163. Some- 
times, however, the observations are so many as to make an extremely 
confusing chart if the observations are shown in the form of separate 
dots. In Fig. 164 the observations in any 1-inch class have been 
averaged and all the observations in one class are represented by a 
single dot. In Fig. 165 the dots would be very numerous, so numerous 
as to make it not feasible to show them on a small size chart. For 
Fig. 165 it was desired to show the maximum income and the minimum 
income, as well as the average income. Instead of showing all the 
dots on the chart, cross-hatching was used to represent the area in 



204 



GRAPHIC METHODS 



whicli the dots fell. The upper edge of the cross-hatching shows the 
maximum of the incomes, and the lower limit of the cross-hatching 
shows the minimum of the incomes reported for different years after 
graduation. The reader can thus get the whole story at a glance 
without being con- 
fused by the com- 
plexity which would 
result if all the dots 
were shown. Atten- 
tion should be called 
to the fact that the 
curve of average in- 
come falls much 





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YEARS AFTER RECEIPT OF B.S. DESREE OR COMPLETION OF FOUR YEAR COURSE 

Courtesy of Data, Chicago 



Fig. 165. Income of Graduates of Worcester Poly- 
technic Institute at Various Years After Graduation 

Instead of showing hundreds of dots to represent the data received from 
different graduates, the chart was simplified by shading the area 
representing the range of income. The shading thus sliows the maxi- 
mum and the minimum incomes. This general method is a worthy 
one 



closer to the bottom 

of the shaded area 

than to the top of the 

area. This fact shows 

that, though there 

are several graduates getting high salaries much above the average 

income, nevertheless, if all of the dots were shown, most of the dots 

would fall below the average line rather than above the average line. 

A few extremely large incomes near the maximum line of the chart could 

greatly raise the average line but still most of the dots would be found 

beneath the average. 

Fig. 166 is a very interesting correlation chart. Here a single dot 
has been used for each observation and the dots are shown in the 
chart. Instead of showing each dot in its exact position, the dots 
have been grouped so that all the dots are arranged uniformly inside 
of squares formed by co-ordinate lines spaced 10 units apart in the 
scales for examination marks. Classification by class limits 10 units 
apart on the scale of marks is sufficiently accurate for all practical 
purposes, as is proved by the gradual change in shading on the chart 
as a whole. With few observations it might be desirable to show dots on 
the chart to actual scale rather than in classes by tens. 

Ordinarily a line drawn like the heavy wavy line in Fig. 166 would 
be so placed that the points on the line would be at the center of 
gravity for the dots vertically on either side of the line. Here, however, 
the line is so drawn that there are an equal number of dots on either 
side of the line, at right angles to it at any point throughout its course. 



CORRELATION 



205 



Notice that in the upper portion of the chart the hne shifts across the 
equahty hne, showing that some of the more brilhant girls obtain 
higher marks in arithmetic than they do in English. The lower por- 
tion of the chart shows that the larger number of girls get considerably 
better marks in English than in arithmetic, and that this is a general 
condition to be expected. In the case of those girls who do well in 
both English and arithmetic, there seems to be improved facility in the 
field of arithmetic. 



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English Marks — ► 

Data of W. Garneti in the Journal of the Royal Statistical Society, 1910 

Fig. i66. Examination Marks Obtained by 9,396 School Girls in England 

Each girl is represented by one dot showing to scale the grade in English and the grade in arithmetic. The 
dots are arranged uniformly inside of squares formed by co-ordinate lines spaced ten units apart in the 
scales for marks. The straight diagonal line drawn from zero shows equal ability in the two studies. 
The heavy wavy line is drawn through points having an equal number of girls represented on either 
side of the line, and its position proves that girls have much more ability in English than in arithmetic. 



206 



GRAPHIC METHODS 



The data of Fig. 166 are shown by another method m Fig. 167. 
Though Fig. 167 appears to represent a soHd model, there was in reahty 
no sohd model made in order to obtain this illustration. By using iso- 
metric paper a chart like Fig. 167 can be made with comparatively 
little work. Isometric paper has lines ruled on the paper right and left 
at an angle of 30 degrees to the horizontal. By selecting a vertical 
scale to portray by separate columns the number of girls represented 
in any square of Fig. 166, it becomes a comparatively simple matter to 
draw the illustration. The various necessary lines can be drawn free- 
hand in pencil on top of the isometric co-ordinate ruling, until the chart 
is completed; then the various lines can be inked in to get the final 
effect seen in Fig. 167. The total number of girls represented in any 
column is shown by the figures at the top of the column. 




Daia of \V. GarneiL in ihc Journal of the Royal Statistical Society, 1910 

Fig. 167. Examination Marks Obtained by 9,396 School Girls in England 

This illustration was made from the same data as Fig. 166. Here the number of girls in any square is shown 

by the height of the vertical column drawn to scale. 
The arrangement of scales here is different from that in Fig. 166 as will be noticed by observing the direction 

of the arrows 



CORRELATION 207 

The reader should note carefully that the scale arrangement of 
Fig. 167 is entirely different from that used in Fig. 166. In Fig. 166, the 
two zeros fall together as they ordinarily should do in chart work of 
this sort. In Fig. 167, however, the two scale zeros are not together 
and the reader is accordingly prevented from interpreting Fig. 167 
directly from the location of dots seen in Fig. 166. It would seem as 
though a better chart could have been made if the isometric chart, 
instead of being as in Fig. 167, had been arranged with the two zeros 
together. Such an arrangement would have permitted easier interpre- 
tation, for the reader would have secured a more close similarity 
to Fig. 166. Another possible arrangement which would have been 
better than that used in Fig. 167 would put the two 100 per cent marks 
of the scale together, with the zero marks at the diagonally opposite 
corners. A chart of this nature would show as two mountain peaks, 
one on each side, with a valley in the center. 

Where an actual model is desired more than an illustration, a very 
convenient, yet cheap, arrangement can be had by stringing beads on 
separate wires, each mounted in the center of ruled spaces, like those 
shown in Fig. 166. The number of beads on each wire can represent 
to scale the data for the particular square at the center of which the 
bead wire is placed. The heights of the columns of beads on the differ- 
ent wires would then show clearly the facts for any one section of the 
field in a manner similar to that of Fig. 167. The beads would probably 
be more generally understood by an untrained person than the isometric 
drawing of Fig. 167, and it is for this reason that the scheme is mentioned 
here. The arrangement by columns seen in Fig. 167 is satisfactory 
for the trained reader, but the separate beads on wires would probably 
give a less abstract impression, more easily grasped by the average 
person. 



Chapter XI 
MAP PRESENTATIONS 

MAPS marked, colored, or shaded in different ways, or used in 
conjunction with pins or other signals, form one of the most 
convenient means of conveying information. Such maps may 
be used to advantage in a surprising variety of ways, only a few of 
which can be mentioned here. 

Engineers who have with great labor prepared complete plans, 
specifications, and estimates for some proposed improvement are fre- 
quently disappointed that they cannot arouse enough enthusiasm in 
the proposed scheme to obtain the approval of the government or 
municipal officials, or members of a corporation board of directors, who 
must vote in favor of the plan and appropriate the money necessary to 
carry it into effect. It is always difficult to get non-technical persons 
to take an interest in proposals which are shown only by blue prints 
and ordinary maps. Architects realize this so well that it is common 
practice among them to submit carefully prepared wash-drawings to 
show the appearance of the building for which they are submitting 
plans. Most engineering work cannot be easily represented by wash- 
drawings, and the engineer is accordingly somewhat handicapped as 
compared with the architect in arousing interest in his project. 

Fig. 168 shows a picture developed by H. W. Holmes, Chief of the 
Bureau of Highways and Bridges, of the city of Portland, Oregon, to 
present his plans advantageously to the common council and the tax- 
payers to obtain their approval for the expenditure. A photograph 
of the actual site of the bridge was made, and then the picture of the 
bridge Avas drawn in by hand on the photograph. Most engineers 
submitting plans for an improvement of this kind would send only a 
set of blue prints and perhaps a map marked to show the location of 
the proposed bridge. A picture like Fig. 168 can be used in conjunc- 
tion with a map if desired. Certainly a proposition carefully worked 

208 



MAP PRESENTATIONS 



209 



up and submitted, as was the 
proposed bridge shown in Fig. 
168, is more hkely to receive 
favorable consideration than 
one in which only the ordi- 
nary blue prints and maps are 
used. 

If maps must be printed 
in a report, a book, or a maga- 
zine, it is usually necessary, 
on account of the high cost of 
color printing, to use some 
arrangement of black ink for 
shading those areas which on 
a single map would ordinarily 
be colored by hand. Fig. 169 
is a sample of what can be 
done without the use of color. 
If the drawing is made con- 
siderably larger than the fin- 
ished illustration, the shading 
can be put on effectively by 
hand work. Mechanical shad- 
ing by the Ben Day process, 
as regularly used by good en- 
gravers, gives excellent results 
but its use makes zinc cuts 
rather expensive. Many illus- 
trations in this book are made 
by the Ben Day process. Any- 
one wishing to know more 
about the possibilities of this 
process should look up Fig. 
233 or consult the engraver 
who is to make the line cuts. 

Often the matter to be 
presented calls for maps of 
a large size, which can be 
obtained only at considerable 



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210 



GRAPHIC METHODS 




Plains 



Engineering Record 



Fig. 169. 



Drainage Area of the Canadian 
River, New Mexico 

Areas of different kinds may be distinguished on maps 
by various classes of shading when color printing 
is not available 



expense. Sometimes only one 
map is available when a variety 
of plans must be presented. 
In such cases, it is not feasible 
to draw plans for new con- 
struction work, or alternative 
working schemes, on the map 
itself. Most draughtsmen put 
the map on a large drawing 
board and then draw the new 
constructions on separate sheets 
of tracing cloth. The tracing 
cloth is not very transparent, 
however, and it will not help 
greatly to get a project voted 
upon favorably if the plan must 
be presented to a board of direc- 
tors on tracing-cloth drawings 
with the map itself only very 
dimly visible through the trac- 
ing cloth. A much more effective scheme is to use a sheet of almost 
transparent celluloid made with a rough surface that will take drawing 
ink fairly well. The different alternative plans may then be drawn on 
the celluloid in colored inks, and the different sheets of celluloid super- 
imposed upon the map one by one as cjuickly as any executive com- 
mittee or board considering the proposals may desire. The main 
difficulty with the celluloid method is that the inks will rub off if the 
celluloid is handled too much with moist hands. Ease of erasure has 
some advantages, however, for tentative schemes can be rubbed out 
or changed at will, simply by using a damp cloth. After the final 
adoption of the plan, tracing cloth can be laid over the combined map 
and celluloid sheet, and the important features of both may be traced 
for blue-printing or for general reference later. Where maps must have 
constant use, it is sometimes convenient to have them mounted be- 
tween two sheets of clear celluloid. The celluloid-manufacturing com- 
panies are prepared to do this kind of mounting to order. 

Contrasts in map areas as shown in Fig. 170, by superimposing 
one portion of the world on top of another portion, or by placing two 
portions side by side on the same scale, are of considerable value. 



MAP PRESENTATIONS 



211 



In geography books, and in other places where maps are most com- 
monly seen, contrasted territories are frequently drawn to such dif- 
ferent scales that a true idea of their proportions cannot be obtained. 
The relative proportion can be indicated best when care is taken to 
have the several areas drawn to the same scale and placed in a good 
position for comparison. 

Fig. 171 is shown here only as an example of the almost unlimited 
range which the application of graphic methods may have. The av- 
erage person would never think of charting a football game, yet the 
graphic method certainly gives the information more concisely than 
could words alone. 

Fig. 172 will be recognized by many readers as similar in general 
scheme to the weather maps on which lines are drawn through all 
points having the same temperature or the same barometric pressure. 
Contour lines to show those points which are at the same height 
above sea level give another application of the same general method. 
Profile drawings similar to Fig. 173 are commonly used by engi- 
neers, but are not as well understood as they should be by others. 
The main feature of the profile chart is the very great difl^erence be- 
tween the horizontal scale used to 
mark distance and the vertical 
scale showing the height of the 
points represented. The vertical 
scale of Fig. 173 should have been 
shown on the chart. The heights 
stated for different cities give a 
fair indication of what the vertical 
scale is and a reader can, if he 
must, measure on the drawing the 
height for any city and from that 
determine to what scale the draw- 
ing has been made. As a broad 
rule, the scale should be indicated 
in an easily seen position on every 
chart, if the scale can be of assist- 

Fig. 170. The Comparative Size of the \^^*^ ^« ^^^ °^^ ^^^'^^^ ^^^ ^^^^^^ 
Philippines of the chart. 

By drawing the islands to scale and in solid black Considerable time and ingCUU- 

on a map of the eastern part of the United . i • i • 

States, the relative size is clearly brought out ity may be UScd lU drawing Up a 




2l!2 



GRAPHIC METHODS 



•SJECOBfB MAJLJT' 

CC/rZ S ■ JO !S ■ 20 2S JO JS- -fO fS <:""" -fs- -^O ■ JS ■ JO ■ 2S ■ ZO ■ JS JO ■ S- COffZ 




mjfjiRmmffffS3s££ 



>/i^Wy^fiI^J?^AZiS 



I I 






Boston Globe 



Fig. 171. Second Half of the Harvard-Yale Football Game, November 23, 1912, 

Final Score, Harvard 20, Yale 

The scale of the football field has been changed so as to give sufficient width for representing the plays by 

lines and symbols of various kinds 



MAP PRESENTATIONS 



213 











chart like Fig. 174 so that 
the facts which it is desired 
to prove may be brought 
out clearly . Numerous 
methods are available for 
presenting such data. 
There is no general rule for 
determining which method 
is the best, and judgment 
must be used to choose the 
method w^hich is best fitted 
to each individual case. 
Note that in Fig. 174 we 
have a scale reading to 
quarters of a mile, and we 
also have circles promi- 
nently drawn on the map 
at one-mile intervals to give 
a clear idea of the distances 
involved. 

Though an illustration in the general method of Fig. 175 is at- 
tractive, and will effectively gain the attention of the reader, the 
method itself has all the inherent weakness of Fig. 36, Fig. 37 and Fig. 
38 in Chapter III. If the reader wishes to practice some mental 
gymnastics, he may try to work out the ratio between the number 
of cattle in Idaho and the number of cattle in Texas. Though it 
cannot be made certain, it is probable that the chart was drawn on 



Country Gentleman 

Fig. 172. Dates for Planting Com, Showing How 
the Season Advances in Different Parts of 
the United States 

This illustration is similar to the well-knowB weather maps on 
which lines are drawn through all points where conditions 
are the same 




Railroad Operating Costs, Suffern & Son, New York 



Fig. 173. Profile of the Pennsylvania Railroad from Jersey City to Chicago. The 
Tabulated Figures Below the Profile Refer to the Spaces Between the Dotted 
Lines 

This is an example of a valuable method of presentation by which a horizontal scale much smaller than the 
vertical scale is used so that great distances may be represented in a small space 



214 



GRAPHIC METHODS 



an area basis. For the purpose of a visual and mental test, the area 
basis may be used if Idaho and Texas are compared. 

The method of Fig. 176 is now quite commonly used in Govern- 
ment publications. This scheme for presenting data is not so striking 
to the eye as that of Fig. 175, but it is more accurate. The scale given 
with the map permits the number of cattle for any State to be read 
fairly accurately. The degree of accuracy depends upon the map 
size selected, and upon the number of dots used to represent any given 
quantity. The more dots used the greater the accuracy. There is. 




GTaham Romeyn Taylor on "'Satellite Cities" in the Survey 



Fig. 174. Map Showing that Factory Workers of Norwood and 
OaJdey (Cincinnati) Live Long Distances from Their Work, 
Many in the Heart of Cincinnati Rather than in the Sub- 
urbs Near the Factories 

The use of much heavier Hues on the small circles and the figures in them would 
have improved this chart. Pins or black-ink dots, each representing say 20 
workers, would give a good result by using the method of Fig. 198 

however, a limit to the number of dots which may be used, or the dots 
will of necessity be so small in diameter that the quarter circles will 
be impossible for the eye to distinguish. In Fig. 176 it would not 
be feasible to use a much smaller circle if the quarter-circles are used. 



MAP PBESENTATIONS 



215 




Country Gentleman 

Fig- 175- Relative Distribution in the United States of Cattle Other than Dairy Cows 

For popular presentation, if great accuracy is unimportant, this method of illustration would be difficult to 
improve upon. It is not possible to get a correct comparison between any two States because any one 
circle cannot be fitted visually into the area of another circle. Compare the method used in Fig. 176 




• 200,000 cattle. 

9 ISO.OOO to 200,000 cattle. 

9 100,000 to U0,000 cattle. 

O eO,00O to 100,000 cattle. 

O Less than tO.OOO cattle. 



The heavy lines (mm) show geographic divisions. 

Abstract of the Thirteenth Census of the United States, 1910 

Fig. 176. All Cattle on Farms in the United States, by States, April 15, 1910 

Here a definite scale is given which permits fairly accurate reading of the number of cattle for any State. 
The visual contrast between States is also quite striking. Though not so clear-cut as Fig. 175, this 
Illustration has more accuracy 



21G 



GRAPHIC METHODS 



In making up copy for the line cut of Fig. 177 very little hand work 
was required. If an outline map of suitable size is available, the only 
hand work necessary for a cut of this kind is in drawing the small 
circles and placing inside them the figures serving as key numbers 
for the shading used. The actual shading is done by the engraver 
making use of the Ben Day process. For information regarding the 
preparation of engraver's copy for plates on which Ben Day shading 
is desired, see Fig. 233. 




HORSE 
7,000,000 — 


=OWER ^ 
9,000,000 


4,000,000 — 


7,000,000 


2,000,OCX3 — 


4,000,000 


l,CX)O,0CXD — 


2,000,000 


500,000 - 


1,000,000 


E 50,000 - 


500,000 


100,000 — 


250,000 


50,000 — 


100,000 



I ® I LESS THAN IS,000 

Fig. 177. Potential Water Power in the Different States of the United States 

This is a splendid example of the contrasts in shading made possible by the Ben Day mechanical processes 
of engraving. Nine contrasting shades increasing in darkness are used here with absolute distinctness. 
The small number in the circle used to identify the shading is of great advantage 

There is one serious error which should be avoided in the inter- 
pretation of any shaded map like Fig. 177. The key scale at the 
lower left-hand corner of the illustration shows that the different 
shades do not become darker by any uniform increase in horse power. 
The range included in shade number eight is 50,000 — from 50,000 
to 100,000. For shading number two, however, the range is 3,000,000 — 
from 4,000,000 to 7,000,000. This numerical scale was badly selected, 
for the steps vary so greatly in size that the increasing degrees of shad- 



MAP PRESENTATIONS 



217 




Fig. 178. Yield of Com per Acre in the Eastern Part of the United States in 1900 

Here the data have been recorded by counties rather than by States. This chart is an example of what 
any draftsman may do by hand shading. It would have been better to use the smaller numbers to rep- 
resent the best rank, as was done in Fig. 177 



218 



GRAPHIC METHODS 




MAP PRESENTATIONS 219 

ing, as they appear to the eye, mean practically nothing. States having 
shading number two could vary from each other in the amount of 
horse power by more than the whole quantity of power in States 
having shadings from three to nine inclusive. If the steps in the 
shading scale had been so made that there were nine increasing classes 
of shading, each representing 1,000,000 horse power, it can be seen 
that all the States here numbered five to nine inclusively would have 
the same shading. Such a map made with a scale of uniform steps 
would appear so entirely different from the map shown here that no 
one would ever recognize the maps to have been made from the same 
data. The selection of scale for maps of this kind is important in order 
that the map may tell a truthful story. Wherever feasible, the nu- 
merical scale intervals for colorings or shadings should be uniform. 
Frequently the data are of such kind that there is much concen- 
tration at some portion of the scale, but with important facts to show 
at other portions of the scale above and below the point of greatest 
concentration. It may then be desirable to use uniform scale-steps 
for the shading in the portion of the scale with greatest concentra- 
tion, and to have smaller scale-steps at either end or at both ends of 
the scale. In Fig. 177 small scale-steps would seem desirable for the 
lower portion of the scale. 

It will be noticed in Fig. 177 that the numbers denoting the shadings 
are arranged with the smallest numbers to represent the largest quanti- 
ties. This arrangement was made purposely. On a map of the kind 
seen in Fig. 177 there may be any number of different shadings, from 
one to a dozen or more. In order to simplify matters for the reader it 
seems best to assign the smaller numbers to represent those conditions 
which are considered most desirable or commendable. The reader may 
then see instantly which areas are first, second, third, etc., in rank 
simply by observing the figures inside the small circles. 

In Fig. 178, if it be assumed that there is a likelihood of corn crops 
going up to 60 bushels per acre, the scale intervals are shown as uniform. 
Fig. 178 is of interest chiefly because it shows what can be done by hand 
ruling when it is necessary to produce an illustration for a report in 
which an expensive cut by the Ben Day method cannot be justified. 

Fig. 179 does not do justice to the possibiUties of the Ben Day 
method of shading. The cut was made by photographing a page of the 
Census Abstract which was printed on rather rough paper. With an 
original cut made directly by the Ben Day process the distinction 



220 



GRAPHIC METHODS 



between the different shades would be considerably clearer than it is 
in Fig. 179. A cut of this size and complexity is rather expensive 
when the Ben Day shading is used. Anyone wishing a cut made with 
Ben Day work would do well to get a rough cost-estimate from his 
engraver before actually giving the order. 

It will be noticed in Fig. 179 that the numerical scale-steps for 
different degrees of shading are uniform except at the smaller end of 
the scale. It would probably not be wise to show as white area all 
of the land valued at from $10 to $25 an acre, since such land makes 



Nombre 

de maisons 




Bertillon's "Course elementaire de StaiistiQue Administrative" 



Fig. i8o. Height of the Houses in the Different Districts of Paris 

The scale for this illustration should have been indicated on the chart so that actual numbers of houses 
could be read. The vertical dimension of the group of bars for each district shows the relative total num- 
ber of houses. The horizontal dimension shows the relative number of houses of each height by stories 

up about half of the whole United States. A uniform scale varying 
by $25 per acre would give an erroneous impression regarding those 
important areas which contain land valued at less than $25 per acre 
but in which there is a large amount of farming. 

Map diagrams of the type shown in Fig. 180 are sometimes useful. 
There is danger, however, of making a chart of this kind so popular 
in character that it loses in accuracy. The utility of Fig. 180 is at once 



MAP PRESENTATIONS 

Population Density per Acre. 



221 







• 


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• 








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e 


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e © 

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0-50 



50-75 



75-100 



100-1 50 



150-200 



200-E50 








250-300 300-350 350^400 



400-45O Over 450 

Courtesy of GTaham Romeyn Taylor 



Fig. i8i. Methods of Marking Maps When an Increased Density of Population 
May be Expected in Following Years 

Each shading can be made by adding with a pen to the shading used for the next lower density. Pins of 
different colors placed in a map have an advantage over this scheme in that pins can be removed if 
population density should happen to decrease 

limited by the fact that there is no key scale shown from which an 
exact numerical interpretation may be obtained. 

The scheme for indicating population density shown in Fig. 181 
is necessary only when very large and valuable maps are used. For 
ordinary purposes it would be better to have a new map for each Census, 
and then to use colored crayons on the different areas of the map, 
rather than to attempt the complicated scheme of Fig. 181. If, how- 
ever, a photograph must be taken periodically to produce line cuts 
showing the map in printed form on a reduced scale, colored crayons 
cannot be used and the scheme of Fig. 181 may be of great assistance. 
The result obtained by the method of Fig. 181 may be obtained by using 
map pins with spherical heads and pushing the pins in until the heads 
touch the map. The number of pins in any city block or district would 
indicate the population according to some simple scale. If it is not 
necessary to photograph the map, pins with different colors of heads 
may be used to show density of population. There is one very great 
advantage in using pins instead of crayons or the pen-and-ink system 
, of Fig. 181. It sometimes happens that an error is made which may 
spoil a very valuable map because of the impossibility of erasure. When 
short pins are used instead of crayon or ink, an error can be instantly 



222 



GRAPHIC METHODS 




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tr'\j^>~~- ,...-i-r-; ^ ' / 

W'-'' '■•■ '; ' J \ '^ I 

los*v<e<io;^^»i-^ creek; ; ^ pvE*^* I u— -' — V \ Ji 

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Wm. Plerrepcmt White, of Utica, N. Y., in the New York Tlrnea 

Fig. 182. Map Showing 3,500 Miles of Completed and Proposed State Roads, in 
New York's Proposed 12,000-Mile System. The Shaded Portion Shows a 
Strip Ten Miles Wide which Contains 90 Per Cent of the Taxable Valuation and 
80 Per Cent of the Population 

The object of the illustration is to show the necessity of a road system that will feed from the farms to the 
densely settled portion, permit the quick and easy transportation of farm products to the cities, lessen 
the cost of living, and thus justify the taxing of the State as a whole for the construction of this system 

corrected by pulling out pins. Also, if there should be a reduction in 
the density of the population, pins can be pulled out, whereas with the 
pen-and-ink method of Fig. 181 it is not possible to proceed backward 
on the scale of marking and a decrease can never be shown without 
making another map or marring the old one. 

In Fig. 182 is seen a good example of the graphic method applied 
to newspaper writing designed to convince the reader by specific 
argument. The presentation is very effective. The shaded portion 
of the map shows a strip which contains 90 per cent of the taxable 
valuations and 80 per cent of the population. The possibilities for the 
use of maps in arguments of political or economic nature are almost 



MAP PRESENTATIONS 



223 



without limit. It is rather surprising that maps for such purposes 
have not been more generally employed. 

Though the map record sheet shown in Fig. 183 may appeal to 
some business men, there would seem to be little advantage in that type 
of sheet over tabulated figures in a column. The column arrangement 
would have a desirable feature in that different entries could more 
easily be compared for size by judging the number of digits contained 
in each entry. 

The method shown in Fig. 184 can be widely used in map problems 
relating to any kind of travel over specific routes. In this particular 
case the map concerns the movement of freight. Maps of this type 
are very commonly used to show the number of passengers carried on 
different city transit lines. To make an illustration on the plan of 
Fig. 184, the width of each broad strip is carefully drawn to some scale 
representing the total quantity movement. A map like this is easily 
drawn yet it is very effective, particularly if colors are used for the broad 
strips while the route itself is marked by nieans of a black line in the 
center. ' ' 



SHIPMENTS TO CONSI .\1CRS AND OEALCRS 
ron THE ^ENDINQ 19 




By Permission of " Si/stem" 

Fig. 183. Blank for Recording Sales to Consumers and to Dealers, Abbreviated 
by the Letters "C" and "D" for Each State 

A blank like this can be filled out daily, weekly, or monthly as desired 



224> 



GRAPHIC METHODS 



Maps on the scheme of Fig. 184 are made entirely in the plane of 
the paper itself. In Fig. 185 we have a map presentation in which 
quantities are represented by building verticallj" above the various 
routes laid out on the map. For the map of Fig. 185, the vertical 
representation was made by strips of wood, alternately black and white, 
glued carefully above each one of the street-car routes. Each of the 
strips of wood represents 4,000 passengers carried on the street-car lines 
in 24 hours. The model gives the whole transit situation with sur- 
prisingly great clearness, and a better presentation than this could 
scarcely be imagined. 




Railway Age Gazette 

Fig. 184. Map Diagram Showing Freight-traffic Density and Direction on the St. 
Louis and San Francisco Railroad for the Fiscal Year 1912-13 

The figures are in terms of 100,000 net tons hauled one mile per mile of road. 

A map of this kind is easilj' made and is often of very great utility. The method can also be used to show 
the number of passengers carried on railroad, subway, or street-car lines, etc. Compare Fig. 185 

The method used in the construction of the model shown in Fig. 185 
gives magnificent results, but wooden strips are not practicable except 
on a very spacious map. The wood-strip method also involves a large 
amount of time on the part of a skilled workman, and workmen to 




CouTicsv of Dr. Ewerbeck, Internationale Baufach-Aiisstellvnti. Leipzig, Germany , 1913 

Fig. 185. Passengers Carried in Twenty-four Hours on the Street-car Lines of 
Frankfurt a M., Germany. Each Vertical Strip Represents 4,000 Passengers 

The map is about eight feet square. Strips of wood are glued above each street having a car line. This 

is an excellent presentation of facts 

225 



226 GRAPHIC METHODS 

do this class of work are not so easily found in the United States as 
in Germany. 

An excellent map of this general type can be made by using sheet 
metal, as aluminum or zinc, ruled or painted with lines or colored 
stripes representing the vertical scale to which the information is to be 
shown. Where two transit lines intersect the strips of metal can be 
riveted or soldered together. As aluminum is not easily soldered it is 
best to use zinc or tinned iron if solder is to be the means of holding the 
vertical strips to each other. In many cases solder is unnecessary, for 
the strips may be held vertically by notching each strip halfway through 
so that the strips can be interlocked in the manner shown in Fig. 236. 
By using sheet metal a much cheaper construction can be obtained than 
by wood strips. The sheet-metal method also permits the use of a 
map of much smaller size and finer scale than would be feasible if wood 
strips were the means of obtaining the necessary vertical height. 



;■!'' 



Chapteb XII 
MAPS AND PINS 

PIN MAPS have not been much used in the past, chiefly because 
a map pin which would give satisfactory service has not been 
available for common use. Until recently the map markers 
obtainable have been little more than old-fashioned carpet tacks having 
chisel-shaped points which cut the surface of any map into which they 
were pushed. Tacks with rough steel shanks cannot be pushed far 
into a map if the tacks are to be pulled out again. Also, rough steel is 
likely to rust so as to cause the whole tack to deteriorate rapidly. 

Cloth heads on the map tacks make it possible to have tacks in dis- 
tinct colors and plaids. The cloth tops, however, fade in the sunlight 
and collect dust so that in a short time the different colors of tacks on 
any map, exposed as a wall map must be, cannot be easily distinguished. 
The crudeness of the cloth-covered tack makes it unsatisfactory for 
many kinds of map work. Cloth-covered tacks are long, and long tacks 
which can be pushed only a short distance into the surface of a map are 
not satisfactory, for they are likely to drop out or be knocked off by 
any slight disturbance. 

Wall maps with long projecting tacks are not practical for office 
use unless protected by an expensive frame with a glass cover. As it 
is usually necessary to open up such a glass map-case to change the 
position of the tacks frecjuently, the construction of the case becomes 
unduly expensive. Without a glass cover a wall map with long pro- 
jecting tacks is likely to be damaged by the feather duster of the janitor. 

Even when maps with long projecting tacks are safeguarded by 
being placed in separate drawers of a cabinet made for that purpose, 
there is still a probability that some of the tacks will come loose from 
the mounting and rattle around inside of the map drawers. This is 
a point not realized by most men who install map and tack systems, 
but it usually sooner or later sounds the death-knell of the tack system. 

227 



228 GRAPHIC METHODS 

Generally the tacks are placed in the maps one by one as agencies are 
established or as data are obtained from correspondence. After the 
correspondence by which each tack was located has gone to the cor- 
respondence files, there is ordinarily no list showing the geographical 
location of the tacks. If a single tack is found loose in the bottom of 

a drawer of a cabinet system, or on 
the floor of an office where there is a 
wall map, it causes distrust of the 
whole tack installation. When 
there is no list showing the geo- 
graphical location of different 




I 



b 



Fig. i86. A Contrast Between Long, tacks, the one tack which is 

SrrFSou{'.InfGra"3,e"d <"" "' ?'='« -""»' b-= P"' b-'' 
Map Pins Made with Short Needle- without checking over corre- 
pointssothatthePinsMaybe Pushed gpondence and records which 
ui until the Heads Touch the Map . i i i r- -o 

may extend back tor years, jbven 

when a list of tack locations is at hand, the loose tack cannot be replaced 
without checking the location of all the tacks on the map one by one 
to determine by a process of elimination where the loose tack came from. 
In the ordinary course of human events it is not likely that a tack falling 
out of a map would be found to give warning that the map record is 
no longer accurate. The tack system using long projecting tacks may 
therefore contain unsuspected inaccuracies just because tacks may have 
come loose. The unpleasant suspicion that a map record may be inac- 
curate, because of the long tacks falling out, sometimes causes a man to 
abandon the tack system entirely, believing that it is not reliable 
enough to give data on which important decisions must be based. 

Map and pin systems are of such tremendous assistance that they 
should not be condemned simply because the map pin itself has not 
been satisfactory. By using a short pin with a needle point and by 
having a backing for the map such that the needle point can be pushed 
in until the spherical head touches the map, we can secure a map 
system which is absolutely trustworthy. Since the pin is pushed in to 
its full length, a blow cannot dislodge it. The spherical head in contact 
with the map gives a very neat appearance, yet the spherical shape per- 
mits the fingers to remove the pin by straight pulling without any diffi- 
culty whatever. The smooth needle-point of good quality steel does not 
rust easily and it does not cut the surface of the map. When a pin 
must be removed, the hole is so small that it is scarcely noticeable. 



MAPS AND PINS 



229 



Pins having spherical glass heads may be used on wall maps with- 
out any danger of the heads fading from sunlight. The glass surface 
is so smooth that dust cannot collect sufficiently to affect the color 
appearance of the pin head. Even if the map does get dusty, it is 
perfectly safe to use the feather duster on a wall map having pins which 
are pushed in so far that the spherical heads are in contact with the 
map surface Dustmg of such a map ^MlI not loosen the pms ui any 




Review of Reviews 



Fig. 187. Location of the Plants Affiliated with the University of Cincinnati, College 
of Engineering. Every Star Represents a Plant Where Co-operative Engineer- 
ing Students are Employed 

A wall exhibit like this is easily made by using a red legal seal and red stars such as can be purchased at 

many good stationery stores 

way. A wall map on which pins with spherical glass heads are used can 
be very cheaply mounted, it needs no glass cover, and the pins can be 
put in or taken out instantly, thus giving a location record which is at 
all times in plain view, yet thoroughly accurate. 

Another great advantage of the pins with spherical glass heads is 
that they may be obtained with small-diameter heads, which permit 
the use of numerous pins on maps of small size. In portraying many 



230 GRAPHIC METHODS 

classes of information, it is impracticable to use the cloth-head tacks 
because the heads are so large that the tacks touch each other in all 
thickly populated regions. 

Photographs taken of a map containing tall pins or tacks give an 
inaccurate effect, since the angle of the lens causes the head of the 
tack to appear at one side of the point in which the tack itself is lo- 
cated. Thus, in a photograph of a map of the United States the head 
of a long pin or tack set at Providence, R. I., might well show near 
Boston, Mass. There is no way of avoiding this error if projecting 
pins and tacks are used. The only safe plan is to use the spherical pin 
head which is in contact with the map surface itself. Photographic 
views of a sphere are the same from all directions, thus causing all 
pins to appear exactly the same size and shape on the photograph. 
Photographs taken of a large map with flat-headed tacks show the 
heads in the center of the picture as circles, while the heads towards 
the edge of the picture look of much smaller size, because they appear 
flattened out as ellipses. The visual effect for points toward the edge 
of the map is lessened when the tacks are flat headed, and an un- 
necessary visual error is brought into the picture. 

A very cheap yet satisfactory mounting for a wall map to be used 
with glass-head map pins is made with three or more layers of corru- 
gated straw-board. The straw-board used should be about 7i6-inch 
thick with a facing on either side of the corrugated portion. Three 
thicknesses of straw-board are sufficient to give strength for any map 
up to one yard long. The two outside layers of straw-board should 
be so arranged that the corrugations will run with the length of the 
map, thus giving the greater strength in that direction. The middle 
layer should have the ribs running crosswise of the map so that the 
map mounting will be safeguarded from bending in either of the two 
different directions. Where very large wall maps are desired, six or 
more layers of straw-board may be used to give sufficient strength. If 
single sheets of straw-board cannot be found as large as the map 
itself, the map mounting can easily be built up of small sheets of 
straw-board, provided the joints in the straw-board are so placed 
that they will not be over each other to weaken the finished structure. 

The straw-board backing for a map to be used with pins is not 
the best obtainable if the pins must be put in and taken out frequently. 
When, however, the pins are to be placed in the map and left there, 
the straw-board is just as satisfactory as any other backing for a 



MAPS AND PINS 



231 



map. A layer of the cheapest kind of mushn placed over the face of 
the straw-board will prevent the pins from tearing the surface of the 
map if they happen not to be pushed in exactly straight. The use of 
cloth over the straw-board also permits of changing the pins many more 
times than would be feasible with straw-board without the cloth 
reinforcing. 



.'• /.■ 








Reoiew 0/ Reiyttws 



Fig. i88. Every Pin Dot on this Map Marks the Home of a Student of the University 

of Cincinnati 

By using a map printed in colors which do not photograph as black, the pins show up distinctly on the map 

as a background 

Before mounting a map the colors should be tested to make sure 
that they will not run in water. The map should then be wet all 
over, preferably by laying it flat for a time in a large tray. Use a 
flour-and-water starch paste, paper-hanger's paste, or library paste 
of the kind used in mounting photographic prints. Carefully remove 



232 



GRAPHIC METHODS 



all wrinkles and press the excess paste out from under the edge of 
the map. Shrinkage of the map and of the moistened straw-board 
surface will almost certainly cause the straw-board mounting to warp 
unless care is taken to prevent warping. At the same time the map 
is pasted on the front of the straw-board, paste a sheet of wet wrapping 
paper on the back of the straw-board mount. The shrinkage of the 
wrapping paper on the back will eciualize the shrinkage of the map 
on the front of the mount. Place the mounted map on a flat table 
surface or on a smooth floor, and stack books or other heavy articles 
upon the mount over night or until thoroughly dry so that any ten- 
dency to warp in the drying may be overcome by the weights. 

Finish the four edges of the corrugated straw-board by using 
gummed cloth tape or paper tape neatly folded over the edges in the 
manner ordinarily used with passe-partout pictures. To hang up the 

finished map use two com- 



c»^ffr /^D/c^r/jvG c/srA'/Bi/r/o/v or r^r f/£ld ^£/7y/cc 




bination clamps and rings 
such as may sometimes be 
obtained in stores selling 
window shades. These 
metal-clamp fixtures are of 
neat appearance and of 
strength sufficient to hold 
a map of any size. If two 
nails or hooks are used in 
the wall to support the 
map, the ring hangers allow 
the map to be instantly re- 
moved to a desk when addi- 
tional pins must be put in. 
If pins are to be put in and taken out of a map repeatedly, it 
should be mounted on good cjuality cork composition. Exhibition- 
board, compo-board, wall-board, or any of the various boards gener- 
ally used for wall surfaces may be used as a backing to give strength 
to the cork. Care should be taken to get a good quality of board 
which will not warp seriously. The cork composition can be glued 
to the wall-board and then the map pasted on the cork. A piece 
of wrapping paper should be pasted on the back of the wall-board 
at the time the map is mounted so that the shrinkage of the map 
may be equalized. The edge of the cork mounting may be bound 



Country (Jtnileinan 

Fig. 189. Distribution of the Field Service of 
the Department of Agriculture, February i, 
1912 

A pin map cannot be excelled for conveying information like 
this. Note the great activity of the Agricultural Depart- 
ment in the South 



MAPS AND PINS 



233 




llw) _ . . Alily Shoes 

Fig. 190. The Use of Pin Maps in Advertising 

A large shoe manufacturing company used this illustration in an advertisement announcing that 3,800 

merchants were ready to show the latest fall and winter models of shoes 
In order to make the dots stand out distinctly it would appear that agencies in any State have been sho-mi 

as uniformly distributed over the State. Actual exact locations would be almost impossible to show 

unless a much larger map were used 

with a cloth tape as suggested for straw-board mounts, or the whole 
built up combination may be framed with picture framing but without 
using any glass covering. The cork composition used should be Vs-inch 
thick. Maps backed with cork composition and used with glass-head 
pins having needle points will permit almost unlimited puncturing 
from frequently moved pins. If the map is mounted on cork composition 
the sharp-pointed pins are easily pushed in and removed, yet the record 
is always accurate because the pins cannot be knocked out. 

Numerous wall maps can be very conveniently used if they are 
mounted on vertical swinging-leaf display fixtures similar to those 
shown in Fig. 219. The two surfaces of each swinging leaf should be 
covered with corrugated straw-board and muslin, or preferably with 
cork composition in order to get a good surface into which to insert 
the pins. As adjacent leaves are likely to strike and break the glass 
heads of the pins, projecting bumpers should be placed on every 
other leaf to allow enovigh clearance for opposite pins when the leaves 
come in contact. The rubber-covered bumpers used to prevent door 



234 GRAPHIC METHODS 

knobs from striking plastered walls can be placed at the top or bottom 
of alternate leaf surfaces. If these rubber bumpers are not available, 
a narrow strip of wood at the top and bottom of each leaf will serve. 

When employed with glass-head pins having needle points, the 
drawer cabinets for maps used to route salesman, etc., can have a 
layer of cork composition fastened in the bottom of each drawer. 
The maps are then glued to the surface of the cork composition. The 
drawer cabinets regularly found on the market have sufficient drawer 
depth to permit placing a ^^g-inch layer of cork composition in the 
bottom of each of the regular drawers and still allow room for the 
pins. Map pins may be pushed into the cork composition so se- 
curely that no pin will ever be misplaced even if a book or other heavy 
object should happen to drop upon the map and the map pins. Pins 
in cork composition are so easily inserted and removed that they can 
be handled more rapidly than if stuck into any kind of a board sur- 
face. When ordering maps from any map manufacturer or map store 
for use with glass-head pins care must be taken to specify either a 
cork-composition backing or a corrugated straw-board backing, else 
the map will probably be shipped mounted on compo-board or some 
other surface entirely too dense to permit of pushing the map pins 
in until the heads touch the surface of the map. 

If numerous glass-head pins are to be put into a map at one time, 
the eraser in the end of a lead-pencil should be used to push the pins 
down until the heads touch the map. Pins can be very quickly lo- 
cated if only their points are pushed into the map by hand, leaving 
the main pressure to be applied by the lead-pencil eraser after a num- 
ber of pins have been located. The pencil-eraser method saves time 
and it also eliminates the discomfort which may be caused if thousands 
of pins are pushed into a map by using the thumb and forefinger only. 

Line cuts, sometimes called zinc cuts, may be made directly from 
pin maps if glass-head map pins of suitable color are used. At the 
point on the map where each pin head is located there will be a black 
dot on the print made from the zinc cut. As light is reflected from 
the surface of the glass heads of the pins, there are sometimes shown 
in a photograph high lights which must be retouched with a pen or 
a fine brush so that the whole spot shall be black, rather than black 
with a white center, as seen in Fig. 191. Anybody can do this re- 
touching very quickly. It is mentioned here only as a caution that 
the photograph be inspected before the zinc engraving is made from it. 



MAPS AND PINS 



235 



Photographs for hne cuts must have a good contrast of white and 
black, or colors which photograph as black. Photographs or original 
drawings containing shades of gray will not produce good line cuts 
and frequently cannot be used at all for the zinc engraving process. 
When line cuts are to be made from pin maps it is best to be certain 
that the glass-head pins are selected in colors which will photograph 
as black. Red, orange, and black pins can be used without any ques- 
tion, since negatives made from these colors give a dead black on 
the photographic print. Line cuts can also be made from dark green 
and some of the other colors. Where it is necessary to make photo- 
graphs and line cuts from a very expensive and elaborate pin map, 
it is wise to consult the engraver before the pin colors for the map are 
finally decided upon. The color blue should be carefully avoided if 
photographs or line cuts are to be made, since blue almost totally fails 
to show up on a photograph. 

If half-tone engravings can be used to illustrate the pin map, 
many more different colors of pins may be used on the original map than 
when zinc cuts are the means of printing. Another advantage of 
half-tones is that different colors of pin heads are represented in the 
half-tone by different shades of gray, as can be seen in Fig. 191. On 
the left half of Fig. 191, fourteen different colors of glass-head map 
pins were used. The photograph Avas not retouched in any way. 
Fig. 191 thus represents about what can be expected of different 
colored pin heads for contrast in half-tone illustration. Note the 
high lights which give white spots on the circles of the darker pin heads. 
It is spots like these which should be retouched by hand on any photo- 
graph from which a line cut is to be made. 

Tacks and pins have been used on maps to locate agencies, sales- 
men, customers, etc., more than for any other one purpose. The 
various possibilities in applying tacks and pins to sales-department 
work cannot be thoroughly covered here, but if a few general methods 
are known, each sales manager can work out for himself the pin scheme 
which best suits his own conditions. 

Fig. 191 was photographed, without any retouching, direct from 
a section of the United States Geological Survey topographical maps. 
These contour maps, having a scale of about one inch to the mile, 
may be obtained from the Geological Survey at Washington, for most 
of these sections of the country which are thickly settled. The maps 
are very low in cost and yet are remarkably accurate. Fig. 191 was 



236 



GRAPHIC METHODS 




MAPS AND PINS 237 

purposely photographed at an angle of about 45 degrees. As the 
upper part of the illustration is out of focus because of the angle, 
the illustration does not do justice to the Government maps. Another 
reason why the map does not come out clearly is that brown ink is 
used to print the contour lines and these lines accordingly show only 
faintly in the half-tone. 

When it is necessary to show the routing to various points on a 
map the best method is to use a fine red string or thread between 
map pins as seen in Fig. 191. If the routing must be changed the 
thread can be almost instantly moved to connect the pins in some 
new order. Lines could be drawn on a map in ink to show routing, 
but the map would be ruined if any change in routing should ever be 
necessary. 

In the preparation of illustrations for reports, advertising, etc., 
whether maps with or without pins are used, great care must be taken 
in the selection of the map itself. Map manufacturers have a very 
annoying custom of purposely making maps in such manner that the 
maps cannot easily be duplicated by photographic processes. Maps 
printed in blue ink are almost hopeless for use in making zinc cuts. 
Maps on which large areas as States, or counties, are differentiated by 
the use of colors red, orange, green, etc., do not produce either good 
line cuts or good half-tones since the colored areas on the original maps 
are likely to show as solid black areas and blot out all detail on the 
photograph. If an illustration must be made from a map it is well to 
be sure that the map is printed in black, red, or orange outline so that 
the resulting photograph will have distinct contrast. Maps should 
contain as little detail as practicable, to make certain that the pin heads 
or other representations of specific data will show up as distinctly as 
possible. Fig. 192 is a good example of the kind of map to use for 
reproduction when pins are employed. Notice in Fig. 192 a heavy 
border for the country as a whole, and the outlines for each State. 
Towns and rivers are not shown. Each dot on the map may thus be 
seen with great clearness. 

As maps are very carefully copyrighted by most map publishers, 
maps which are copyrighted should not be reproduced without con- 
sideration of the copyright. For maps which are photographed down 
with comparatively little change, permission should be requested from 
the map publisher, to make certain that unpleasant complications such 
as damage suits or the holding up of a publication may be avoided. 



238 



GRAPHIC METHODS 



The 228 Principal Trading Centers 




Saturday Emning Post, Curtis Publishing Co. 



Fig. 192. The 228 Principal Trading Centers in the United States 

This illustration was taken from an advertisement proclaiming that a certain magazines circulation was 
mainly in the 228 chief trading centers of the country, and that, accordingly, the magazine must be 
effective as an advertising medium for merchandise 

Note that in the east the dots are so numerous they are shown as crescents. The crescent scheme is a good 
one as it permits the use of a much larger dot than would otherwise be possible 

The amount of detail which may be permitted on any map in which 
pins are used depends on the size of the resulting illustration and the 
size of the pin heads. If the pins are so numerous that the map must 
be very large, there is danger of reducing the map so much in size be- 
tween photograph and final illustration that the pin heads will appear as 
indistinct dots on the complex surface of the map. In Fig. 193 a map 
was used in which there was more detail than really necessary or desir- 
able for a clear illustration. In justice to the General Electric Review it 
must, however, be said that the map shown in Fig. 193 has been reduced 
in size and made smaller than it was in the original print. This map 
could not be reduced further without danger of completely losing the 
pin heads in the gray background resulting from so many lines on the 
map. 

In producing an illustration like Fig. 193 considerable ingenuity 
must be used to make two or more classes of pins show out distinctly 
in zinc cuts which can be printed in only one color. The pins on the 




LOCATION OF 

■r V OF 1000 HP. AND OVER 

AMD 

Ss POWER 

SECTIONS OF STREAMS 

ijgi*- IN THE 

: • Commercial Developments 
:-; ■ Manufacturing Developments 
2 Heavy line {-y^for Stream. indicates 
T^Vyou^hly'Sectian having power. 

General Electric Review 

Fig. 193. Location of Water-Power Developments of 1,000 Horse Power, and Over, 
and Power Sections of Streams in the United States 

The original of this map would have pins in two different colors. The photograph taken from the map 
would be retouched by the use of a pen so that squares would replace dots for one of the two colors 
of pins. The illustration shows a contrast of dots of two shapes rather than dots of two colors 

239 



240 



GRAPHIC METHODS 




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MAPS AND PINS 241 

original map can be in different colors. After a photograph has been 
made of the pin map it is best to compare the photograph with the 
original, and then to make squares out of those circles which represent 
a certain color of pin on the original map. Squares are easily made by 
using a fine pen on a photograph considerably larger than the cut itself 
will be. When the final dots are not too small in size it is possible to 
make shapes with the pen such as triangles, outline circles, etc., which 
can be distinguished from one another. 

If a great reduction in size is necessary between the original material 
and the finished illustration, extreme care must be used to have all 
the lines on any original drawing wide enough to stand the reduction 
in line thickness due to the decrease in size. If a drawing one foot 
wide is photographed down to an illustration three inches wide the 
lines will be only one-quarter as thick as in the original drawing. Lines 
on the original drawing must therefore be made very wide — in fact, 
much wider than is ordinarily considered desirable until experience has 
been gained from several disappointments in the appearance of finished 
illustrations. It is not easy to find maps with lines sufficiently heavy 
to permit of the great photographic reduction usually necessary in 
making illustrations from pin maps or other map representations. 
Quite often it is necessary for the person making a map chart to go 
over by hand all outlines such as borders and the divisions between 
States, counties, etc., to make those particular lines very much heavier 
than on any map which can be purchased. 

A reducing glass which makes everything seen through it appear 
smaller is almost essential when many maps or charts must be repro- 
duced. A convenient size of reducing glass has a single lens, about 
1^ inches in diameter, and causes objects to appear from one-half to 
one-quarter the size of the original. The amount of reduction can be 
varied by holding the glass at different distances from the original 
drawing. In order to tell how much reduction in size is made by the 
glass at any given distance, it is possible to look at the original object 
with one eye and through the reducing glass with the other eye so that 
by superimposing the two images their length may be compared. When 
a chart has ruled lines, as co-ordinate lines, it is a simple matter to 
superimpose the images from the two eyes so that one square of the 
original equals two, three, or four squares of the image seen through the 
reducing glass. When the two images are thus superimposed, study 
can be made of the thickness of lines or other details in the reduced 



242 GRAPHIC METHODS 

size so that a decision may be had as to whether the drawing will safely 
stand the proposed reduction without having the lines made heavier. 

Fig. 194 shows about the extreme limit of what can be done in the 
making of pin maps. The original map here was 40 inches wide and 
66 inches long. Nevertheless, the map shows up satisfactorily in the 
greatly reduced size of the half-tone because care was taken to have 
very wide lines and little detail on the original map. Each of the 19,500 
pins of five different colors had a head diameter of V32 inch. It must be 
remembered, that most of these pins were in the characteristic blue 
colors commonly associated with the Bell Telephone System, and, 
because blue is almost impossible to photograph, the pins do not show 
out as strikingly as they would if other colors were used. The black 
splotches on the map were caused by the predominance in those areas 
of pins with dark blue heads. When this pin map was made there was 
no intention of taking a photograph of it. A much more distinct 
photograph would have been secured if pins in the contrasting colors 
of red, orange, black, green, purple, etc., had been chosen. All of these 
would have shown dark in the photograph, instead of white or light 
gray like the pale blue pins which in Fig. 194 were used in the greatest 
number. 

Fig. 194 was photographed at an angle. The eastern half of the 
United States appears smaller than true scale because of the perspective 
in the picture. The perspective view shows that the glass-head pins 
had long shanks. This map, costing several hundred dollars to pro- 
duce, could be injured severely by a few strokes of a janitor's feather 
duster. If short pins were used with spherical heads in contact with 
the map there would be no danger of the pins being misplaced. An- 
other disadvantage of the long steel pins is that the steel portion exposed 
to the atmosphere is likely to rust, especially in cities near salt water. 
Pins with short needle-points pushed entirely into cork composition 
or corrugated straw-board have little opportunity to rust. 

Fig. 195 shows a convenient map scheme by which different places 
on the map are numbered so that detailed information regarding each 
may be obtained from the annexed tabulation numbered to correspond 
with the pin numbers. In this scheme we have all the advantages of 
a pin map without the confusion of too many data on the surface of the 
map itself. The illustration of Fig. 195 was evidently prepared by 
hand. Such an illustration can, however, be made by using pins like 
those shown in Fig. 196, or like pin No. 20 in Fig. 199. This latter 



MAPS AND PINS 



243 




No 






R-R. 


Cap. Bbls. 
per day 

1,BOO 


?. 


H«LDEaBERa Cem. Co 


. . . Howo Can, N. Y . 


., D. A H.R R 


T 


AJfloo.N. Y . 


N. Y. C 4H. R 

N. Y. C. 4 H. R. 

N. Y. C & H. R. 

L. V. R R 


4,300 


4 




. Hudaon. N. Y 










fj 




. . . Portlaad Poial, N. V 


1£00 


f 




Wayland, N. Y 


lP-.^„*^- ^ 








N. YC 

Penn. R. R 




9. 


VnoiEJt Port- Cem. Co 

AuxrrrowN Port. Cem. Co 


. . , MoUtorfn. Pa 

. . . EvanaviUe. Pa 


750 




P * L E 


2£00 
1,200 
3,500 
1.500 






CementoD. N. Y 


N. Y.C &H. R.. 

Penn.R.R 

Penn. R.R 

. West MiTR. R 


1 




YorktOWD, Pa 






York, Pa 


s 




Security. Ud. 


f 


UNivEBaAL Port. Cem. Co 










... Newcastle, R.' 

...Wampum, Pa 

^..Maaheim,W.V8.... 

..Middle Branch. Ohio » 

.BayRidjcOnio 

..Wdhton.Oliio 

..Wdliton.Ohio... 

. . Portsmouth, Ohio 

..Siroh.lod 


P.ALE 

P.4L.E.. ...... 

B.40.a.B.... 

Penn.R. R 

L.S.iM.S. . . 

C, H. V. 4 T . . . . 

C.H.V.iT 

N & W 


•36,600 
3,600 

1500 


18. 


Chesceht Port. Cem. Co 

JBncKBORN Poet. Cem. Co 

Diamond Port. Cem. Co ^ ., 


23 

?4 


AlmaCi.me.vtCo 

Lehiok Port. Cem. Co 

YohkPort Cem Co 

Wabash Port. Cem Co 


2.000 
•3S.60O 


23- 


L.S.& M.S..;. 

Penn. R. R ._... 

C. I. &L 

B.iO.R.R..., 

.. B. 4 0. R R 


1500 










28. 


Lehigh Port. Cem. Co 

LoLiiflviLLE Cement Co 

KosMos Port. Cem. Co 

ViRGmA Port. Cem. Co 

Norfolk Port, Cem. Corp 

Dixie Port. Ceji. Co 


. . MitclicU. Ind 

.Specdfi. Ind 


•36.600 
2,000 




, . Fordwick. Va 

-. Norfolk. Va 

.. Richard City, Tenn 






31. 
32. 
33. 
34 


SoufernR. R... 

.Southern R. R... 

A.G.S. R.R... 

Southern R. R... 

Southern R. R. . . 

L. S. 4M. S 


3.300 
3.000 
4,000 


35. 
.'V 


Standard Port. Cem. Co 

Castalia Port. Cem. Co 

StrpERioH Port. Cem. Co 


..Leeda.Ala 

..Caatalia, Ohio... 

..Superior, Ohio 


1.200 
2,000 


,m 


C.40 

Data. Ch 






•Includes all mills owajd by company. 




icago 



Fig. 195. Location of the Portland Cement 
Plants of the Eastern Portion of the United 
States in 191 1. Below the Map Is a Tabula- 
tion Giving the Name, Address, Capacity and 
Shipping Raihoad for Each Plant 

A pin map like this can be quickly made up by using pins 
such as are pictured in number 20 of Fig. 199 or pins such 
as are used in Fig. 196. An outline map with the pins can 
illustration like the above 



pin has black figures on a 
white background, and does 
not give as striking an effect 
as white figures on a black 
ground. 

Fig. 196 gives a hint of 
what may be done to pre- 
pare advertising copy with 
almost no expense. The 
illustration was made direct 
from a map on which pins 
were used having black 
areas lettered in white. The 
only hand drawing neces- 
sary for this illustration 
was about one minuie's 
work in darkening the high 
lights where there were re- 
flections from the surface 
of the black pins. An illus- 
tration of this type to show 
the location of agencies, 
branches, etc., makes effec- 
tive advertising because the 
black spots are so large in 
comparison with the size of 
the map that the whole 
territory of the United 
States appears to be well 
covered by agencies. 

Lettered or numbered 
pins like those in Fig. 196 
and in Fig. 199 are fre- 
quently desirable to show 
the daily whereabouts of 
salesmen, repair men, etc., 
in order that the nearest man 
may be telegraphed to in 

be photographed directly to produce an 



244 



GRAPHIC METHODS 



case of emergencj\ One prominent manufacturer of locks for bank 
vaults uses a map Avhich shows at all times the location of each of some 
fifty bank-lock experts who are routed from city to city each day by 
telegraph. The locations of the pins, and the railroad lines repre- 
sented on the map, show instantly which man can best be sent to any 
bank which reports trouble regarding the door of its safe-deposit vault. 
Letters or numbers on th^ pins indicate the name of each man so that 
there is no danger of an error such as might occur if the pins were 
colored uniformly without specific letters or numbers. 




Fig. 196. Map to Show the Location of the Selling Branches of a Large Manufacturing 

Company 

This line cut was made directly by photographing a standard map in which standard map pins had been 
inserted. Black pins 'with white letters or numbers give excellent advertising copy with absolutely 
no drafting work required 

The argument of Fig. 197 would have been brought out better if 
the railroad tracks had been drawn in heavy black lines across the city 
map. Unless one is familiar with the city of Indianapolis, there would 
be no way of explaining the heavy soot deposits in that section shown 
on the lower portion of the map. Even the mention of railroad tracks 
in the title does not make up for not showing them on the chart. 

In preparing Fig. 198 a scale was very carefully selected to use one 
dot to represent a definite number of people so as to avoid having dots 
crowd each other too closely on the map. A map of this kind could be 
made in a very large size, and then be reduced photographically to a 



MAPS AND PINS 



245 



-JlS'l 



' i * • 



'yf^ 



lU 



• ' •i«J'i''« 



•••••• 



.;.i 



••••• 

• • • • 

• • • • 

• •••• 



• • • I • • • 



• •••• 
•••••• 

• •••• 



• • • • 

:• • • 
• • • 

• •••• 






••••• 

•••• 



size which could be used in 
a report or magazine article. 
The reduction must ordi- 
narily be so great for such a 
map that considerable fore- 
thought and care must be 
used or the dots will not 
show up distinctly enough 
in the final illustration. 
Anyone wishing to see many 
maps of this type shown in 
very excellent manner 
should consult Volume II of 
the Report of the Transit 
Commissioner, of the City of 
Philadelphia, published in 
July, 1913. 

In placing dots for out- 
lying districts on maps made 
by the method of Fig. 198, 
judgment must be used to 
have each dot placed at ex- 
actly the right point to locate accurately the people represented. In Fig. 
198 each dot represents two hundred people. A dot in the suburbs 
may therefore represent all the people in one square mile of territory. 
If a map were first made with two hundred dots for the two hundred 
people, the one dot actually used on the final map would have to be 
placed not at the geographical center of the area represented, but at 
the center of gravity of the two hundred dots which it replaces. 

In Fig. 199 various combinations are shown of pins, beads, etc., 
of use in map work. Data for map presentation are frequently so 
complex that ingenuity is taxed to show the facts on any map of a 
size commercially available. A great variety of effects may be se- 
cured, however, by means of the devices shown in Fig. 199. The 
exhibits given in the illustration are as follows: 

1. Long pin with small size glass head, available in many colors. 

2. Long pin of brass wire for use with beads as shown in No. 9. 

3. Long pin with glass head used in conjunction with a piece 
of sheet celluloid cut into the shape of a flag. 



William D. McAbee in the Survey 

Fig. 197. Relative Soot Deposits in Indianapolis, 
March, 1912 

The greatest soot tall is in the vicinity of railroad tracks 
Carefully selected samples of snow were melted and the soot 
of twenty-four hours weighed after the water was evapora- 
rated. Spot maps of this kind can be quickly made by 
using short map pins pushed in till the pin heads touch 
the map 



246 



GRAPHIC METHODS 




The Engineering Magazine 

Fig. 198. Proposed Routes for a Comprehensive System of Passenger Subways for 

the City of Chicago 

On this map each dot is carefully located to represent 200 of the population. A spot map of this kind, made 
to some scale whereby one dot represents several people, is essential to any reliable study of transit 
facilities. After the spot map is made, the transit routes can be laid out to give the best service possible. 
Short map pins with heads touching the paper can be used for dots on the original map 



MAPS AND PINS 



247 




Fig. 199. A Full-size Illustration Showing Some of the Different Arrangements of 
Map Pins and of Beads Which Can be Used for Map Work 

The size of the various beads and pins can be determined by measuring on the above picture with an ordi- 
nary ruler, as the articles are shown in their exact size 

4. A celluloid flag, with beads above the flag to represent quan- 
tity, or beads in different colors to denote various characteristics 
for the data portrayed. The grip of the sheet celluloid on the pin 
is sufficient to hold both the beads and the flag at the upper part 
of the pin. 

5. Long pin with large size glass head, obtainable in different 
colors. 

6. Pin like that shown in No. 5 used with beads strung upon it. 

7. A brass tack large enough to receive gummed labels which 
may be written upon with a pen. 



248 GRAPHIC METHODS 

8. Map pins having sharp points and small spherical glass heads 
in contact with the map. These pins are available in many dif- 
ferent colors; the upper one in No. 8 is red and the lower one blue. 

9. Beads in various colors of a size to correspond with the map 
pins in No. 8. Here the beads were red. White beads, used for 
every tenth position, show at a glance that there are 22 beads on 
the pin. Note that the color red photographs as black. 

10. Map pins having sharp needle points and spherical glass 
heads in contact with the map. The pin is of the same general 
style as No. 8 but it has a head of larger diameter. This pin is ob- 
tainable in many colors. 

11. Cloth-covered map tacks available in plain colors and in 
plaids. 

12. Single bead used with an ordinary pin as a crude substitute 
for a regular map pin. 

13. Beads in different colors corresponding in size with the map 
pin of No. 10. 

14. Beads of two different sizes representing different things 
but at the same location. 

15. Beads of two different sizes and three different colors. Since 
both sizes and colors may be varied, and almost any number of 
beads used on one pin, there are practically unlimited possibilities 
for the showing of complex data. 

16. Beads on a pin which holds down on the map a sheet of 
colored celluloid cut to the exact shape of a small land area to which 
attention is directed. 

17. A sheet-celluloid marker held by a map pin like that seen 
in No. 8. 

18. Celluloid-covered tack, available in different colors. 

19. Celluloid-covered tack with stripes of different colors. 

20. Celluloid-covered tack with printed numbers from 1 to 99 
inclusive. 

21. Celluloid-covered tack having a rough surface so made that 
the surface may be written upon with pencil or pen, yet erased 
afterwards or rubbed off with a moist cloth. Lettering may be 
made permanent by means of a coat of varnish. 

22. Large size celluloid-covered tack available in different colors. 

23. Large size celluloid-covered tack with stripes of different 
colors. 



MAPS AND PINS 249 

24. Very large size celluloid-covered tack. 

It will be seen from the foregoing list that the possibilities for 
ingenuity in map and pin presentations are almost unlimited. The 
celluloid-covered tacks having large flat heads, shown in Nos. 18 to 24 
inclusive, are not as generally used as they might be for map work. 
Map pins and tacks of this sort placed upon the surface of a map 
can give a spot map with any desired diameter of spots, no matter 
what size of map is used or what the amount of photographic reduc- 
tion may be. It is simply a question of selecting from the spherical 
heads, 8 or 10, and the flat heads 18, 22, and 24, to determine which 
size head is best suited to the size of the original map and to the size 
of dot desired in the finished illustration. Large celluloid-covered 
tacks 18, 22, and 24 are also valuable to show the location of main 
offices and different factories, or the locations of particularly im- 
portant distributing points. The pins numbered 8, 10, 18, 22, or 24, 
are five different sizes of pins which may be used simultaneously on 
the same map to show different degrees of importance in the things 
represented. 

When used for photographing to produce an illustration such as 
is shown in Fig. 196, lettered or numbered pins should have a black 
background so that the black circle outlining the tack head will show 
out in clear contrast against the map itself. This requires white 
figures on a black or red background. Pins having red letters on a 
black background cannot be used for photographing, as the red letters 
would photograph black and disappear entirely, leaving a solid black 
circle instead of a circle with figures. Since pins with a black back- 
ground and white figures are not commonly obtainable, it may occa- 
sionally be necessary to use pins like No. 20 in Fig. 199 having black 
figures on a white background. Sometimes it may be feasible to 
draw an ink-line circle around each number which appears in the photo- 
graph so that the circles will be on the copy sent to the engraver who 
makes the zinc plate. 

When pins must be used to locate agencies, stores, or other things 
which are usually concentrated in cities, the limitations are rigid 
because all pins should be located on the map immediately above the 
point representing the city. Crowded pins usually have to be spread 
horizontally over a wide area, and when so spread out it is impossible 
to tell which of several adjacent cities the various pins may represent. 
Fig. 200 depicts what was done in one case to get over this difficulty. 



250 



GRAPHIC METHODS 




"Modern PMlarUliropy" , W. H. Allen, Dodd, Mead & Cu. 

Fig. 200. Sources of the First 3,000 Letters of Appeal Sent to Mrs. E. H. Harriman. 
These 3,000 Letters Asked for $70,000,000 

Eight different kinds of pins were used on this map to represent different kinds of appeals. Long pins like 
those seen here are apt to fall out of the map, and thus destroy the accuracy of the record. Note the 
area around New York shown on a larger scale at the right 

as far as possible, by showing the more thickly crowded district as a 
separate area on a larger scale placed at one side of the map. 

The use of beads in conjunction with pins overcomes the main diffi- 
culties encountered when pins alone are used. Beads may be placed 
one above each other on long pins or wires so that each pin will be 
exactly in the point on the map for each city, and thus portray nu- 
merical data by map location more accurately than possible with other 
methods. The adjoining cities can be clearly discerned by means of 
separate columns of beads, whereas if pins alone are used the dif- 
ferent groups of pins frequently blend so as to be indistinguishable. 
If there is only one item to be represented in a town, single glass-head 
pins may, of course, be used in conjunction with the beads. 

When there are several units in a town, the beads strung on a 
long pin or wire can be counted quickly if a bead of a different color 
is used for every tenth bead, so the whole column may be counted by 
tens as possible in Fig. 201. A bead map like Fig. 201 should be 
mounted on several layers of corrugated straw-board to allow the 
long pins sufficient depth in the mounting to hold fast. For this 



MAPS AND PINS 



£51 



particular map six layers of straw-board were used, giving a total 
thickness of about l3<t inches. Though this mounting made out of 
corrugated straw-board was thick, it was extremely light and very 
convenient to handlco 




Fig. 201. Residence of the Men of the Class of 1907, Harvard University, Six Years 
After Graduation. The Bead Wire for Boston Includes All Men Living within 
Twenty-five Miles of the City Hall 

Beads on long pins and wires were used here when there was more than one man in a town. A white bead 
was used on the wire for every tenth man. Counting from the top by tens, the exact number in any 
city can be seen from the illustration. 711 men are represented in this illustration less than 5 inches 
wide, yet the number in each city can be counted accurately 

If long columns of beads must be used as in Fig. 201 for New 
York and Boston, the beads may be strung on piano wire such as 
may be secured in any good hardware store. The piano wire should 
be heated in a gas flame so as to remove some of the spring temper. 
After the wire has been heated it can be straightened and it will re- 
main straight without continually springing back into coil form. 



252 GRAPHIC METHODS 

Brass wire should be used if the holes in the beads are large enough 
to take wire of a diameter sufficient to give the required amount 
of stiffness. Brass wire is not as stiff as steel wire. When small beads 
must be used having small holes, the combination of wire and beads 
may be given several coats of varnish, if necessary, to make a tall 
bead column stand up straight. The columns for Boston and New 
York in Fig. 201 had to be varnished as the wire was very small on 
account of the fact that the diameter of the beads was only about 
-i^ inch. 

The bead map in Fig. 201 gives a great quantity of information 
in a small amount of space. The illustration depicts the whole United 
States on a page width of only 5}/^ inches, yet all the facts represented 
by the beads are brought out clearly. The men of the group por- 
trayed who reside in foreign countries are indicated by pins near 
the seacoast with arrows pointing toward the country of residence. 
The fact that there were large numbers of the men in Massachusetts 
made necessary an extremely long wire for the beads of the Boston 
district. Because of the small size of the finished illustration and the 
size of map available, large diameter beads could not be used, and the 
bead wire for the Boston district was necessarily very tall and slender. 
The Boston bead column was about as tall as could be used without 
the column of beads bending under its own weight, even with the 
bead column varnished. ^ 

Another difficulty in having very tall columns of beads is due 
to the fact that the bead map must be photographed at an angle of 
about 45 degrees in order to show a good picture of the map. 

If the bead column projects more than a reasonable distance 
from the map it is impossible to find a camera lens which will keep 
in focus the whole map and the full length of the bead columns. Either 
the map or the top of the bead column will be out of focus and there 
is no way of overcoming the difficulty. When Fig. 201 was photo- 
graphed the image on the ground glass of the camera showed at once 
that the tops of the bead columns were out of focus. The bead wires 
for New York and for Boston were accordingly pulled entirely out of 
the map and the map was photographed without these two bead 
wires. The two bead columns were drawn in by hand on the surface 
of a photograph measuring 8 inches across the base of the map. With 
a little care, using a fine-pointed pen, bead columns such as these can 
be drawn in so that the ordinary observer would jiever notice that 



MAPS AND PINS . 253 

they were put on after the photograph itself had been taken. The 
angle at which the tall bead columns should slant can be determined 
by observing other bead columns in the same vicinity. In the case 
of Fig. 201, the angle was obtained by observing the bead column 
for Philadelphia. The reduction in size from the photograph on which 
the hand drawing was done, to the half-tone (in this case, a final re- 
duction of from 8 inches to i^i inches) was sufficient to eliminate 
most of the imperfections due to hand work. 

The use of beads opens up a whole new field for map presentation 
of statistical data. The Board of Sanitary Control for the Cloak 
and Suit and the Dress and Waist Industries of New York city made 
up two bead maps showing the fire risks and the sanitary condition 
in all the twenty-five hundred factories which come under the super- 
vision of that Board. One bead on the map represents the condition 
for each factory. On the fire map the height of the multi-story loft 
buildings in which the difi^erent factories may be found is indicated 
by using one bead for each floor. Thus, in some of the taller build- 
ings, twenty stories are indicated. Different colors of beads according 
to the fire risk or the sanitary defect to be shown mark the stories 
very plainly, and the heights of the bead columns show the heights 
of the buildings so that the bead map itself represents in miniature 
the sky line so typical of Manhattan Island. 

Bead maps carefully made up should be of great use in preparing 
illustrations for advertising purposes. The accuracy of a bead map, 
when data for different cities must be shown, is much greater than that 
of a map on which only pins are used. The bead map makes possible 
the giving of information in condensed form with that great clearness 
and accuracy necessary to good advertising. It can safely be pre- 
dicted that pictures. of bead maps will in the future be a common 
thing in the advertising pages of magazines. 



Chapter XIII 
CURVES FOR THE EXECUTIVE 

WITH the exception of the railroads, there are relatively few 
businesses which make a practice of plotting curves to show 
operating records in convenient form for the use of executives. 
Railroad accounting is more highly standardized than accounting in 
industrial corporation work. The standardized method of accounting 
has made it rather easy to compare the operating records of different 
railroad divisions and of different railroad systems. It is probably for 
this reason that railroads have adopted the use of curves for operating 
records so much more extensively than have industrial or mercantile 
businesses. 

The upper curve in Fig. 202 is plotted according to the method used 
on many railroad systems. In this form of plotting a month may be 
said to be represented in the middle of a space between the vertical 
lines. Horizontal lines are drawn in the space for each month to a scale 
representing the figures which it is desired to chart. Lines are then 
drawn vertically to coincide with the vertical lines of the co-ordinate 
paper, and they join the horizontal lines of different months in such a 
way as to give an effect like that of a stairway. 

Curves for the same data plotted by the method shown at the bottom 
of Fig. 202 are much easier to read than those plotted by the step method 
shown in the upper portion of the illustration. By the method in the 
lower part of the illustration the plotted line more closely approaches a 
true curve, there is much less variation in the direction of the lines from 
month to month, and the general trend of the curve line is easier for 
the eye to grasp. Compare the two curves for the summer months of 
the year 1909-10. In the upper curve a series of steps, and in the lower 
curve an almost straight line from April to September inclusive, indi- 
cate an increase by fairly equal increments during those months. 
Certainly equal increments are more easily represented by the straight 

254 



CURVES FOR THE EXECUTIVE 



255 



200 OOO 

160000 

160 000 

140 000 

1 20 OOO 

100000 

80000 

60000 

40 000 

20000 

O 



200000 

180000 

160000 

140 000 

120000 

100 000 

80 000 

6 0000 

40 000 

20000 

O 




1908-09 



1909-10 



19tO-ll 



Fig. 202. Total Sales of the "Metropolis" Branch House of the "R.S.T." Automobile 

Company for Three Years 

These two curves are plotted from exactly the same figures. The upper curve is drawn by the method 
still used by some railroads, but generally going out of use. The lower curve is plotted by a simpler 
method which should be universally used 

line as in the bottom curve than by the ragged series of steps shown 
in the upper curve. 

Another disadvantage of the method of steps with flat tops as 
compared with the method using slanting lines and peak tops, is seen 
when two or more curves are so drawn that they intersect on the same 
sheet of co-ordinate paper. Curves plotted with peak tops can be 
drawn very close together and yet be fairly distinct from each other, as 
will be noticed in many of the illustrations in this book. If, however, 
two curves with flat tops hke those shown in the upper portion of Fig. 
202 are plotted in such manner that they intersect each other, the re- 



256 



GRAPHIC METHODS 



/<?o^ 


JAN 


FEB 


MAR 


APR 


MAY 


JUNE 


JULY 


AUG. 


SEPT 


OCT. 


NOV. 


DEC. 


TOTAL COST 


3*^ 77 


<yy- 31 


^h ts 


66 88 


8-^ f/ 


77 29 


7S 5J 


82 /S 


60 7 7 


JJ 3Z 


V-S.7S 


soke 


NO.OF TONS 


.2.16 


^J? 


W-Otf 


1^33 


JZiS 


n-JZ 


J 70 


V-9S 


i^v-S 


JS-o 


J8i> 


S-T^ 


COST PER TON 


.yjj 


Z/5 


2oh 


. /S'^ 


.ZS9 


./78 


Z'Z 


/i,^ 


/JV 


09^ 


//8 


ass 


K -275 

O .250 

gg .225 

gtt .200 

Z fe i50 

o ,o ,oo 

^ liJ .050 
-'°- .025 


















































































































/ 


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Courtesy of Factory 

Fig. 203. Lubrication Cost per Ton of Product for a Factory in the Year 1908 

The figures at the top of the co-ordinate ruling give the data from which the curve was plotted. Though 
data should be put on all charts, figures arranged in the direction here shown are not in convenient form 
for addition. See the later illustrations in this chapter for methods of placing figures above each point 



on a curve 



suit is very confusing on account of the fact that the vertical lines con- 
necting the flat tops may coincide. When one line falls directly on top 
of the other, there is no way for the reader to judge which curve is 
which beyond the point of intersection. Unless the curves are very 
carefully colored or dotted there is great danger that the reader will 
jump from one curve to the other in his interpretation of curves which 
happen to meet. This weak point in the flat-top method is particularly 
noticeable if blue prints must be made from original charts in which the 
flat-top method is used. On the original chart the curves can be fairly 
well distinguished by using difl^erent colored inks, but as the colors are 
lost in blue-printing, each blue print must be colored by hand, using 
the original chart as a key to show what the colors should be. If a peak- 
top method of plotting is used, numerous curves may be run across the 
same sheet and yet be distinct enough for identification even when all 
are reduced to uniform white fines on the blue print. It would be easy 
to name fifteen reasons why the method of plotting with peak tops is 
superior to the method of plotting with flat tops. The advantages of 
the peak-top method seem so obvious that it is believed the reader 
will agree to its desirability, without further argument being given here. 
The man who plots a curve has before him the data showing the 
actual value for each point plotted on the curve. If any questions 
arise in his mind regarding the comparative figures at difl^erent points 
on the curve, he can refer to the data from which the curve was plotted. 



CURVES FOR THE EXECrTIVE 



257 



:z 03 QJ o; >- _ 



The man who reads the curve, how- 
ever, must ordinarily get the value 
of any point on the cur-^ e by refer- 
ring to the scale on tlie left-hand 
margin of the chart. As most points 
on curves do not fall exactly on the 
horizontal co-ordinate lines, the only 
way in which the actual value at 
any point can be determined is by 
careful estimate of the fractional 
distance betVeen horizontal lines, 
according to the scale shown on the 
margin. The resulting value for 
the point is ordinarily more or less 
inaccurate, depending upon the scale 
to which the curve is drawn. Not, 
only is the reader's time taken in 
estimating the value for any point 
on the curve, but when he gets his 
result he is dissatisfied, for he cannot 
feel that the figure obtained is really 
accurate. There is a great advan- 
tage in showing on a chart the figures 
from which the curve was plotted. 
When only one curve is shown on a 
chart it is very easy to give the 
figures immediately above each point. 
The method used to show the figures 
in Fig. 203 is not, however, satis- 
factory, as the figures do not fall 
in a column. The method of indi- 
cating figures shown in the illus- 
trations later in this chapter is much 
superior to the method of Fig. 203, and 
should be adopted as general prac- 
tice by anyone preparing curves for 
Million Dollars or More record purposes, or for executive use. 

This illustration shows one of the diiBculties encountered when curves for successive years are plotted on 
the same co-ordinate ruling. Here the data of .January, 1913, are indicated by a dot rather than by a 
line. The change occurring from December to .January is not easily seen. This difficulty can be 
easily overcome by allowing an extra space for one month as in the following illustrations 




CALENDAR YEAR !|I3 ° 

Bureau of Railway Economics, Washington, D. C. 

Fig. 204. Monthly Revenue, Expense, 
and Net Revenue per Mile of Line 
for Railroads in the United States 
Having a Yearly Revenue of One 



258 GRAPHIC METHODS 

In Fig. 205 a curve is shown drawn upon a carefully designed four-by- 
six-inch card form. This card is designed for the plotting of data for 
one year by months. Thus, the fiscal year of a business can be shown 
on one card. Succeeding years are entered on different cards, so that 
by arranging the cards chronologically variations from year to year 
may easily be seen. In order to avoid the difficulties pointed out for 
Fig. 204, and Fig. 104, thirteen vertical lines are used on this four-by- 
six-inch card. At the beginning of each card the last month of the 
previous fiscal year is repeated. In Fig. 205 the fiscal year begins in 
August. At the beginning of the card we repeat the line for July, so 
that instead of showing a dot when the August figures are plotted w^e 
are able to draw a line showing the change which has occurred from 
July to August. In general, it is good practice to use one more vertical 
line than there are points to be plotted, so that the last point on one 
curve, sheet or card may be repeated on the next curve sheet or card. 

Figures representing the value for each point on the curve are given 
immediately above each point, in the case of Fig. 205 to the nearest 
dollar. Figures for cents could, of course, be given if desired, but for 
executive purposes it is usually better to neglect the cents in all large 
numbers. The arrangement of the figures shown in Fig. 205 is such 
that at the end of the year the figures can be added cj[uickly and the 
total given on the card. Cards for different years can easily be looked 
over and the yearly total figures compared instantly, to the great ad- 
vantage of the executive who has these additions made for him and 
recorded where they are always in plain sight. Curves as they were 
used in the past gave the values of single points only, without any 
summation for a series of points. In Fig. 205 we have not only the 
yearly total, but also totals for every three months, so that the total 
for any ciuarter of the fiscal year can be compared with the total for 
any other quarter. 

Fig. 206 represents a four-by-twelve-inch card used to plot data for 
fifty-two weeks in one fiscal year, the last point of the preceding year 
being repeated at the left-hand margin. Figures for the repeated week 
are not given above the co-ordinate ruling, as the repeated figures might 
then be included in the additions and cause serious error. By repeating 
the point, however, and not repeating the figures, the curve is made 
continuous without any danger of adding too many items into the total. 

In the right-hand margin of Fig. 206 a vertical green line may be 
seen. This line may be used as the shank of an arrow to indicate, as 



CURVES FOR THE EXECUTIVE 



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CURVES FOR THE EXECUTIVE 261 

in Fig. 205, in which direction the executive desires that the curve should 
trend. In Fig. 205, which represents total sales, the head of the arrow 
of course points upward. If the curve is to show expenses per 
unit of output, the head must be placed on the vertical line so that the 
arrow will point downward. In Fig. 206 no head is placed on the arrow, 
as fluctuations in a payroll mean nothing unless we know the output of 
work. An increasing payroll may result either from increasing sales 
or from inefficient production. A decrease in payroll may result 
from increased efficiency of production or because sales have fallen 
off undesirably. Accordingly, no head is placed on the arrow and the 
curve must be interpreted by conditions other than those shown on the 
face of the card itself. In general, all curves relating to total money 
expenditures may trend either up or down, without meaning anything 
unless other conditions are considered. It is only when we express 
expenditures as expenditure per unit that we really get a curve for 
which it is safe to say that we should always desire a downward trend 
as long as quality is maintained. 

The insert page on which Fig. 205 and Fig. 206 are printed is made 
of an especially high grade of paper. Most paper in use to-day contains 
sulphite pulp and chemicals which cause more or less rapid deterioration. 
The paper commonly used becomes brown and brittle within five or 
ten years, so that records on such paper are likely to be useless in a com- 
paratively short time. The high-grade paper used for record cards as 
are shown in Fig. 205 and Fig. 206, contains only the finest selected 
linen stock and is guaranteed absolutely against any deterioration for 
twenty years. The chief advantage of this paper, however, is that it 
can be used in card form, yet be transparent enough to allow of blue- 
printing. 

The time required to blue-print this paper may best be compared 
with the time necessary when ordinary tracing cloth is used. Blue 
prints are also frequently made from bond paper. Bond paper requires 
an exposure of, roughly, three times as long as tracing cloth. This 
special card requires an exposure of about six times as long as tracing 
cloth, or twice as long as bond paper. 

When sunlight is used for blue-printing, there is no difficulty in 
getting a sufficiently long exposure to make good blue prints from the 
card forms shown in Fig. 205 and Fig. 206, if the forms are printed on 
special paper. Should electric blue-print machines be used, however, 
it may be found that certain of the older types of continuous printing 



262 GRAPHIC METHODS 

machines cannot be run slowly enough to give the required length of 
exposure. Some of the older machines can be changed at rather slight 
expense so as to have an extra belt-pulley reduction between the motor 
and the blue-printing machine itself. The newer types of machine 
can usually be run slowly enough to give the exposure necessary for 
this special paper. If a new blue-printing machine is to be ordered, 
however, it is well to make some preliminary tests with the cards. 

The cost is not great for blue-printing a whole set of record cards 
once each month after the last data have been plotted. Blue-print 
paper of heavy weight should be carried on hand, already sensitized 
and cut to size, four by six inches and four by twelve inches. The 
original curve cards, each backed by a sensitized card of the same size, 
are simply fed into the blue-print machine as rapidly as the operator can 
put the two cards together in pairs. 

There is a tremendous advantage in having all curve records made 
on the high-grade transparent card so that any card may be duplicated 
by blue-printing whenever desired. It is impossible for anyone to 
predict what conditions will come up in the future of a business, and 
the only safe plan is to install from the start such a curve-record system 
that any card may be duplicated by blue-printing in future years if 
desired. It frequently happens that an executive wishes to have a blue 
print made of a recent year's curve card to compare with the curve 
card of an earlier year, in order that the blue prints may be mailed to 
some higher official or to some branch -house manager to point out certain 
conditions which it would be difficult to describe fully if copies of the 
curve cards could not be sent. Unless, however, the curves for the 
earlier years are made on cardboard from which blue prints can be 
taken, it is impossible afterward to make duplicates of these cards 
except by hand copying or photographing. In many cases it will be found 
desirable to take a blue print of every record card once each month, so 
that blue prints may be sent each department head to show him the 
exact condition of his department as a guide for the next month. 

The space toward the left-hand side of the cards shown in Fig. 205 
is for remarks which may be necessary to explain different fluctuations 
in the curves. In Fig. 206 full circles along the curve show those weeks 
in which a full holiday reduces the amount of the payroll. In the month 
of x4pril there was, for this particular plant, a half-holidaj' on the nine- 
teenth. This is shown by a half circle. At the end of the fiscal year we 
see in Fig. 206 stars to explain why the curve showed a drop to less than 



CURVES FOR THE EXECUTIVE 263 

one-half in the normal size of the payroll. The plant was shut down at 
the end of the fiscal year in order that an inventory might be taken. 

The notes at the left-hand side of the card are absolutely essential to 
explain unusual conditions affecting the curves. In two years after an 
event, most managers are entirely unable to explain certain peaks or 
valleys in a curve, though these extreme fluctuations may be due to 
such events as fires, floods, or strikes. Unless the causes of unusual 
fluctuations are recorded, the curves would have far less than their 
possible utility to any new man who must take up the manager's task 
as his assistant or as his successor. An example of the kind of informa- 
tion which should be noted on the curve-card margin came up in a large 
public-service company, where the manager was for several minutes 
unable to explain a very great fluctuation which had affected the earn- 
ings of a trolley company some two years before. After careful study 
to explain the drop in the curve, he finallj^ recalled that this trolley 
line was in a city where all cars must pass over a drawbridge between 
two sections of the town. At the time in question a steamer had col- 
lided with the drawbridge, making it impossible for about two weeks 
for any street car to cross. This accident caused the earnings of the 
trolley line to drop greatly during the whole of the two-weeks period. 
The cause of the unusual condition for the curve should have been 
recorded for future reference. 

In Fig. 207 we have the curves for three succeeding years placed one 
above the other, so the eye can glance up and down the vertical lines 
for months and see instantly the changes which have occurred during 
the entire period. As, automobile sales are very greatly affected by 
the weather conditions of different seasons of the year, these curves are 
important. Though weather conditions have affected the curves quite 
largely, we can see, by comparing the curves for 1910 and 1911, that 
probably conditions of management as well as weather conditions 
caused smaller shipments in November and December, 1911, than in 
those same months of 1910, when shipments were quite good. The card 
for 1912 is shown with the curve incomplete, just as the manager might 
have seen it early in the month of February, 1912, after the January 
reports had been received, tabulated and plotted. As Fig. 207 shows 
curves which are true records of the real happenings in an automobile 
plant, they are worthy of study for practice in curve interpretation. 
Notice that the changes from July to August, in 1911 and 1912, are 
readily seen because each curve card begins by repeating the record 



264 



GRAPHIC METHODS 



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Fig. 207. Sales of the "X.Y.Z." Automobile Plant for Three Consecutive Years 

The three -l-by-e-inch cards are arranged one above the other so that the curves for different years may be 
easily compared. Note that November and December were good months in 1910, but poor months in 
1911 and 1912. The 1911 card above is the same as in Fig. 205, but here it is printed in one color 
only. Observe at the right the arrows showing that it is desired that the trend of the curve should be 
upward. Arrows like this save about two-thirds of the executive's time in looking over a large number 
of curves 



CURVES FOR THE EXECUTIVE 



265 



for the last month of the 
preceding fiscal year in- 
stead of using a dot as 
shown in Fig. 204. 

The separate cards for 
different years, which in 
Fig. 207 are arranged ver- 
tically one above the other, 
may be laid horizontally as 
in Fig. 208. Here the cards 
are superposed on a black 
background, the left-hand 
and middle cards each over- 
lying the card to the right, 
so that the curve appears 
continuous. The vertical 
arrangement allows of a 
very accurate analysis of 
changes which have oc- 
curred from month to 
month of each year. With 
the horizontal arrangement 
it is not so easy to compare 
any month of one year with 
the corresponding month of 
another year, but it is easier 
to see the changes which 
have occurred in a curve as 
a whole throughout a period 
of years. Thus in Fig. 208 
it is much easier than in 
Fig. 207 to see that sales 
dropped seriously in the 
first half of 1911, and that 
they increased far beyond 
any previous record during 
the last half of 1911. The 
vertical arrangement is use- 
ful for one purpose : the hori- 



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266 GRAPHIC METHODS 

zontal arrangement, is useful for another purpose. By having loose 
cards, we can arrange the cards either horizontally or vertically and 
get all the advantages of either position. Curves plotted in loose-leaf 
books, or on large sheets of paper, cannot have this flexibility of arrange- 
ment, and they accordingly handicap the executive in the analysis 
of data which may be vital to the success of his business. 

When the cards are arranged horizontally the figures for the curve 
over a series of years are in plain sight, while in the vertical arrange- 
ment one card hides the figures on another card. Figures are essen- 
tial to the true interpretation of curves like those seen in Fig. 208. 
In looking at Fig. 208 most readers are likely to feel that the business 
of the year 1911 was much better than the business of the year 1910. 
When we look at the total figures, however, we see that the sales 
for the year 1911 were only $1,435,041, while the sales for 1910 were 
$1,575,298. Not only were the total sales for 1911 much less than the 
sales for 1910, but there was a very great fluctuation in sales from 
month to month which created a very difficult problem in the opera- 
tion of the manufacturing plant. In the early half of the fiscal year 
ending in 1911, men were not needed because of the small volume 
of sales, and a large portion of the working force had to be discharged. 
In the latter half of the fiscal year, sales increased so rapidly that men 
had to be hired in large numbers. Inevitably, therefore, many un- 
skilled men were obtained who were sure to spoil a large volume of 
any output requiring the great accuracy needed by automobile parts. 
The record for the fiscal year ending 1911 was in every way bad, as 
compared with that for the fiscal year 1910. The company eventually 
ended in a receivership. 

Cards only four inches by six are of sufficient height to hold the 
co-ordinate ruling needed for curve plotting, and yet have room above 
the ruled field for two separate columns of figures of seven digits 
each, as well as space across the top for a title which may run the whole 
length of the card. In Fig. 208 we have two sets of figures, one set 
for months and the other set for quarters. Each set of figvires con- 
tains six numerals. Although the illustration in Fig. 208 is only 
about one half the natural size of the card, the figures themselves are 
clearly legible and the title at the top of the card is easily read. 

One of the chief advantages in the use of loose cards lies in the 
fact that any set of cards may be laid out on a table and compared 
with any other set of cards in the manner shown in Fig. 209. It is 



CURVES FOR THE EXECUTIVE 267 

difficult with a loose-leaf book to arrange a system for keeping hun- 
dreds of curves in such a way that quick comparisons between any 
of them can be made. When loose cards are used any card can be 
compared with any other card instantly, and, if desired, cards for any 
curve for a series of years may be laid out for comparison with cards 
for any other curve for any series of years. Anyone without experi- 
ence in the analysis of curve records for large corporations may take 
it as a fact that no system of curve records should be installed which 
does not permit the instantaneous comparison of any curve with any 
other curve in the whole system. 

Fig. 207 and Fig. 208 show the shipments from an automobile 
manufacturing plant as sales. Many of the automobiles recorded 
as sold were shipped to branch houses owned by the same company, 
to be stored there during the winter months when the branch-house 
sales are very small, for the reason that people do not wish to buy 
touring cars in winter. In Fig. 209 and 210 more curve records from 
an automobile business are given. In these cuts also, as in Fig. 207 and 
208, cards are shown in groups of three, photographed against a black 
background. In Fig. 209 we have in the upper curve the actual 
sales of an automobile branch house selling direct to the auto- 
mobile user. Notice that the sales in the spring months greatly ex- 
ceed the sales at any other time of the year. In the first two fiscal 
years sales were at a maximum in May, while in the third fiscal year 
sales reached the maximum in April and were fairly large in both 
March and May. 

In the lower curve we have the expenses of this same branch 
house. A very noticeable increase in the expenses occurred in the 
fall months at the beginning of the fiscal year, once in October and 
twice in September. This increase was due to local advertising an- 
nouncing the new-model automobile for the next season. It was 
customary for all manufacturers of automobiles to announce their 
next season's models in the fall months, and the peaks in the expense 
curve shown here came as they did simply because of this custom 
of the trade. 

It is quite easily seen from the upper curves that the sales for the 
second fiscal year were much greater than those for the first fiscal 
year. The total figures, however, show much more clearly the extent 
of the increase. Because of the excellent sales during the spring months, 
the curve for the third fiscal year at the right gives the impres- 



268 



GRAPHIC METHODS 



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sion of a prosperous year. 
Reference to the figures for 
the total yearly sales, how- 
ever, shows that the sales 
for the third year increased 
only very slightly over the 
preceding j^ear. When we 
compare the sales of this 
branch house with the ex- 
penses, we get quite a dif- 
ferent story from that read 
from sales curves alone. 
The increase in sales from 
the first year to the second 
year was very great and 
without a correspondingly 
great increase of expenses. 
Putting the figures for the 
first and second years into a 
ratio, sales increased 64 per 
cent, while expenses in- 
creased only 10 per cent. 
In the third year, however, 
the sales hardly increased 
at all, while the shape of 
the curve for expenses 
shows an almost constant 
increase. A little mental 
arithmetic will show further 
that with almost stationary 
sales the expenses were per- 
mitted to increase about 
one-seventh or, roughly, 14 
per cent. 

Notice that in Fig. 209 
arrow-heads mark a desire 
that sales should go up. No 
arrow was used in connection 
with the curve for expenses. 



270 GRAPHIC METHODS 

It was permissible that expenses should go up in the second fiscal 
year, for the volume of sales increased very rapidly. The cost per 
unit of sales or the ratio of expenses to total sales had decreased greatly. 
An arrow pointing downward would have given a wrong impression 
as the total expenses had increased justifiably. It is better, therefore, 
to avoid using arrows than to use arrows which would mean nothing. 

The real story of this automobile branch house is seen in Fig. 210 
which gives the profit-and-loss curve corresponding to the sales and 
expense curves of Fig. 209. Expenses of the branch house were fairly 
large throughout the whole year, because of fixed charges, while the 
great fluctuation in sales caused a loss during the many months in 
which the volume of sales was small. Note how much better the 
profits were in the second year than in the first year, because the 
business had been established long enough to have a fairly good vol- 
ume of sales during the fall months. There was a profit in all the 
months of the second year except two, with a total profit of very 
considerable size, though not a tremendous one compared with the 
volume of sales, since the profit was only 5.9 per cent of the sales. 
In the third year the profits were on the ragged edge throughout 
the whole year except in the three spring months of March, April, 
and May when sales were exceptionally large. The total profits for 
the year, even with a slightly increased volume of sales, were less than 
one-third of what they had been for the preceding year. 

Just to show what complex conditions enter into the comparison 
of business curves of this sort, it is mentioned here that the small 
volume of sales, the large expenses, and the negligible profits in the 
first half of the third fiscal year were not the fault of the manager of 
this branch house. The trouble went back to the factory engineering 
department which failed to get its next season's models designed early 
enough. Consequently the car could not be manufactured in suf- 
ficient quantities to give the bi'anch manager enough cars to make 
a satisfactory volume of sales. The branch manager blamed the factory 
because the factory could not deliver a sufficient C][uantity of cars. The 
factory manager was not to blame, however, as the engineering depart- 
ment (reporting direct to the president instead of to the factory man- 
ager) had delayed the design for the new car, and the factory manager 
was, of course, unable to build a car until he had the drawings. This 
example will perhaps give a fair idea of the uses which can be made of 
curves plotted from the operating figures of a complex business. 



CURVES FOR THE EXECUTIVE , . . 271 

A person who has not tried plotting curves on cards only four inches 
high is likely to say that the card is not of sufficient height to permit 
satisfactory curve plotting when there is a great fluctuation in the curve. 
Such a person would argue that the card is not high enough to allow 
the plotting of curves on a scale sufficiently large for easy reading, and 
that any curve for a constantly increasing business is likely to run off 
the top of the co-ordinate ruling within a few years. The curves as 
shown in this chapter certainly vary enough to allow the eye to see all 
the changes clearly. As the curves are in each case accompanied by 
the actual figures for the value of each point on the curves, it is not 
necessary that one should be able to measure accurately for points 
falling between horizontal co-ordinate lines. Instead of consulting the 
vertical scale to get the value at any point, reference is made to the 
actual figures above the various points. These figures indicate a finer 
fluctuation in the curve than it is possible for the eye to appreciate 
even in curves plotted on very large sheets of paper. Figures, then, in 
conjunction with curves like those shown here, make it unnecessary to 
plot lines of such fine width or great accuracy as would be necessary 
if the figures were not shown above the curve. 

In Fig. 207 the bottom card shows the zero line extended to the left 
over the figure seven at the lower left-hand corner of the ruled field. 
On the middle card the zero line has been extended to the right. This 
right-and-left extension of the zero line is not made until a card has 
been completely filled out. The extension of the zero line indicates 
the point at which cards are to be joined when laid in the horizontal 
position shown in Fig. 208. It will be noticed, in Fig. 208, that the 
cards are overlapped in such a way that the right-hand edge of the 
uppermost card coincides with the left-hand edge of the ruled field 
of the lower card, and that the zero line is continuous. The extension 
line drawn at the left of any lower card shows where the extension 
drawn across the right margin of the upper card is to be joined. Cards 
may be laid together in a horizontal position almost instantly, and cor- 
rectly, when these joint lines are present as a guide. 

If, as in Fig. 211, a curve should rise with such rapidity as to be 
dangerously near the upper limit of the ruled portion of the card, the 
joint lines may be so drawn as to allow more vertical space on the suc- 
ceeding cards. In Fig. 211 the curve for 1910 indicated that the curve 
for 1911 might go higher than the 1,400 line. Consequently, when 
the new card was made out for the year 1911, the joint lines were so 



272 



GRAPHIC METHODS 





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drawn that the line 
at the right of the 

1910 card was above , 
zero, and the joint 
hne at the left of the 

1911 card at the bot- 
tom of the ruled 
field. Thus, when 
the two cards are 
overlapped so that 
the joint lines match, 
it is seen that there 
is enough space in 
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right for the curve to 
rise to the scale line 
for 1,600. Two more 
spaces were again 
allowed in 1912 in 
anticipation of even 
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gress in the curve. 
As joint lines may be 
drawn in continua- 
tion of any horizontal 
line on either the 
upper or the lower 
card, any amount of 
expansion in future 
years may be pro- 
vided for. The curve 
cards are small 
enough to be very 
convenient to handle 
and yet they may 
be joined together in 
such a way as to 
provide for unlimited 
future growth. 



CURVES FOR THE EXECUTIVE 273 

The card for 1910 in Fig. 211 has a broad hne drawn by hand to 
show the zero hne. On the card for 1911 the scale begins at 400, and, 
because the scale does not begin at zero, the bottom of the co-ordinate 
field is marked with a wavy line. This wavy line is made very rapidly 
with a pen and serves the very useful purpose of safeguarding the 
reader from interpreting the curve as if the lower line on the field were 
zero. Whenever zero is not shown at the bottom of the ruled field, 
this wavy line should be used. Any card can thus be read independent- 
ly, with safety so far as its interpretation from the zero point is con- 
cerned. When several cards are laid out together, and the zero line is 
shown on the left-hand card, as in Fig. 211, it is a simple matter for 
the eye to imagine the zero line extended to the right below the other 
cards, thus permitting easy interpretation of all cards. 

It sometimes happens, especially in plotting costs, that the desired 
direction of the curve will be downward instead of upward. In such a 
case, and to show small fluctuations from month to month, the scale on 
the curve cards may be so selected that the zero line does not appear 
even on the first card plotted. Should the costs be reduced so rapidly 
that the curve tends to run off the bottom of any card, the card for the 
succeeding year may have the joint line drawn in such a way as to 
allow an extension of the scale downward, exactly as Fig. 211 shows an 
extension of the scale upward. By drawing the left-hand joint line 
on the later cards above the bottom of the ruled space, and by putting 
the right-hand joint lines for the first cards at the bottom of the ruled 
curve field, the series of curves can be made to progress downward to 
any desired extent in exactly the same manner as the curves in Fig. 211 
progress upward year by year. By the use of these joint lines a 
thoroughly universal arrangement of cards may be secured, allowing 
extra space for movement either up or down. 

Joint lines were devised chiefly to permit of showing a large up- 
ward or downward progress in the curves for succeeding years with- 
out the necessity of laboriously replotting the curves for the earlier 
years. The desired result has been very satisfactorily attained. Should 
anyone, however, object to the presenting of a series of cards in steps 
as in Fig. 211, he need only replot the curve for the earlier years to 
some smaller scale. In general, however, it will be found that prac- 
tically no replotting is necessary or desirable. By connecting the cards 
with joint lines and by using a wavy base line when the scale does not 
extend to zero, all necessary convenience and accuracy may be secured. 



274 GRAPHIC METHODS 

When plotting curves on large sheets of co-ordinate paper it fre- 
quently happens that the scale desired cannot be placed upon the 
kind of ruled paper available. Scales must usually be made in full 
size, one-half size, one-quarter size, etc., and it is usually too big a 
jump to change from one of these sizes to another. The ideal arrange- 
ment is to have a supply of co-ordinate paper with different rulings 
so that when one ruling does not suit, some other ruling may be used. 
On the curve cards shown in this chapter the horizontal scale is fixed, 
as the cards are designed for use with definite units of time, such as 
one year by months, one year by weeks, five years by months, etc. 
For the vertical scale, however, two different rulings are provided. 
One of these rulings has seven i-inch spaces as may be seen in Fig. 
211. The other ruling has ten vertical spaces of t inch each as seen 
in Fig. 209. The ratio of the two scales is seven to ten or, roughly, 
one scale may be said to be two-thirds of the other. This is the most 
desirable arrangement that it is possible to get, as these two rulings 
afford a great range of scales to choose from. If by using one ruling 
the curve comes too high on the card, simply change over to the other 
ruling and the peak will come lower down on the card. The two 
rulings, either in full size or in some fractional size, give every pos- 
sible combination of scale that need be desired. 

The ruling having vertical spaces of one-sixth of an inch is ten 
spaces high. This ruling is very convenient for curve plotting on a 
percentage basis when 100 per cent is shown at the top of the chart 
as in Fig. 126, Fig. 128 and Fig. 129 in Chapter IX. If, on the ten- 
space card, each space is used to represent 10 per cent with zero for 
the bottom line and 100 per cent for the top line of the chart, the 
neatest possible arrangement is secured. 

In starting to plot a curve which is to be continued year after 
year, it is ordinarily best to allow plenty of room for future growth. 
In the upper curve of Fig. 209 the scale was purposely selected for 
the first year so that the curve would extend only about one-third 
of the way to the top of the ruled portion of the card. This would 
allow the sales to be trebled in volume before the curve would extend 
over the top of the ruled portion and necessitate a change in scale 
or a step upward so that the zero line could no longer be shown at 
the bottom of the card. It is well to start all curves for output or 
sales at about one-third of the height of the card so as to allow plenty 
of room for future expansion. Curves for expenses per unit, however. 



CURVES FOR THE EXECUTIVE 275 

may be started well up on the card if there is any hope whatever of 
reducing the unit expenses in future years. 

The man who plots curves on the cards described here keeps a 
supply of the printed cards in each of the two rulings of seven spaces 
high and ten spaces high. When starting any new curves he uses 
whichever of the two cards gives the scale best suited to his purpose. 
The cost of carrying two different kinds of ruled cards on hand is 
negligible compared with the great convenience resulting. 

The ruling of the cards in which the vertical spaces are either 
T-inch or ■g--inch high permits the use of an engineer's scale in forti- 
eths or sixtieths of an inch, if it should ever be desired to locate plot- 
ted points on the cards with very great accuracy. The engineers' scale 
in fortieths or sixtieths of an inch gives ten divisions to each space 
between the horizontal lines on the card and makes it possible to locate 
each plotted point with a very finely sharpened lead pencil or a needle. 
Practice, however, proves that there is no necessity for using an en- 
gineer's scale in plotting curve points on the cards here described. 
The man doing the plotting learns very quickly to locate the points 
by using only the eye and a hard lead-pencil, so that the points are 
practically as accurate as if spaced with an engineer's scale and a 
needle point. Even if the points on the curve are not located quite 
so accurately as they may be when a needle point and a scale are 
used, it makes no difference to the executive by whom the curve is 
read. The figures denoting the value of each plotted point are given 
immediately over the point in the upper margin. The executive 
reading the curve does not have to refer to the vertical scale. He 
need only glance at the figures above any point to learn the value 
for that point far more correctly than would ever be possible with 
even the most accurately plotted curve if the value of the point had 
to be interpolated from the vertical scale of the chart. The vertical 
scale of these cards on which the figures are given in the upper margin 
fulfills almost no purpose except that of giving a record of the scale 
to the man who must plot points in succeeding months, or that of 
giving the values of horizontal lines which are convenient in locating 
high points or low points on any curve. 

When another point has to be added on a large number of curves for 
a succeeding month or week, the most convenient procedure consists 
in first copying upon all curve cards, immediately above the vertical 
line for the proper month, the figures from the typewritten reports, or 



276 



GRAPHIC METHODS 



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other sources of informa- 
tion. This is straight 
clerical work and may be 
done with a pen on one 
card after another with 
great rapidity. Ordi- 
nary liquid drawing ink is 
the best for the figures, as 
the opaqueness of the 
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This is often partly trans- 
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the newly recorded fig- 
ures in the upper margin. 
When all the curve points 
have been located by 
lead-pencil marks on the 
curve cards, a drawing 
pen is used to draw the 
line on each card to show 
the change that has oc- 
curred since the previous 
point was plotted. As the 
new point has already 
been indicated in each 
case by the lead-pencil 



CURVES FOR THE EXECUTIVE 277 

mark, all the ink lines can be drawn in rapidly with a draftsman's 
ruling pen. If the suggested procedure is used, the lines may be drawn 
so rapidly that there is no chance for the ink to dry on the pen and the 
ruling operation is almost continuous. 

In Fig. 212 we have complete in black ink the same card which in 
Fig. 206 is given full scale, using two colors to make the contrast be- 
tween the green-ink background and the black-ink curve. Though Fig. 
212 shows the card in reduced size, it nevertheless gives a very good 
idea of the appearance of a card suitable for the plotting of records 
for one year by weeks, making it necessary to have fifty-two entries 
of figures in the upper part of the card. 

In Fig. 212 the arrangement to show the dates along the bottom of 
the card, with short vertical lines dividing the horizontal scale into 
months, is not put on to the card until the exact year is known for which 
the particular card is to be used. Lines dividing the year into months 
so as to show exactly how many weeks are included in each month and 
at just which portion of the week the beginning or end of each month 
may occur are then put in by hand. In Fig. 212 the card has been used 
for a fiscal year beginning August 1. The card is marked 1911, 
meaning the fiscal year ending July 31, 1911. By referring to the 
calendar for the year 1911 one may see how the short lines for months 
are put in. As the pay weeks ended on Thursday, there were only four 
pay weeks ending in July, but there were five pay weeks ending in 
March. March 1 came on Wednesday. The last day of March was on 
Friday. The vertical co-ordinate lines for March show clearly that 
there were five Thursdays, and they also show the exact time relation 
of the Thursdays to the beginning and to the end of the month. 

After the month scale for any fiscal year has been marked by hand 
on one card, any office boy can quickly copy the scale to other cards by 
superimposing the first card on the next card and copying the pen 
strokes from the first onto the second card. A supply of cards for any 
year can thus be made up at small expense, without having to have 
cards printed differently each year just because mankind has not yet 
made a calendar which always has the same relation between days of 
the week and days of the month. The scheme of indicating the rela- 
tion of weeks and months by the short vertical pen marks permits the 
carrying on hand of a supply of printed cards which can be used for 
absolutely any fiscal year without danger of having to send the supply 
of cards to the scrap basket, as calendars are sent to the scrap basket 



278 



GRAPHIC METHODS 



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just because last year s 
calendar is of no use 
after December 31. 
This assurance of a 
perennial form instead 
of one which must be 
renewed or replaced 
every year is no small 
advantage. Figures 
designating the months 
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ly card if desired. In 
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10, etc., indicating the 
months, can be printed 
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Fig. 213 shows the 
weekly curve card 
used in the records 
of a dairy farm. The 
particular curve shown 
is for a prize Jersey 
cow which was being 
very carefully tested 
in the hope of break- 
ing the world's record 
for milk production. 
The milk production 
each week is indi- 
cated here, in pounds, 
together with the but- 
ter-fat analysis taken 
at various intervals. 



CURVES FOR THE EXECUTIVE 



279 



The days on which the 
butter-fat analysis were 
made are quite accurate- 
ly indicated by the dots 
on the butter-fat curve. 
Figures for the milk pro- 
duction each week are 
given to hundredths of 
a pound in the appro- 
priate column above, 
and the butter-fat anal- 
ysis is given to one one- 
hundredth of one per 
cent for each date on 
which the analysis was 
made. The grand total 
milk production for the 
year of the test is given 
at the foot of the col- 
umn. Note the diag- 
onal arrangement of the 
two headings, "Pounds" 
and "Per cent Butter 
Fat". This diagonal 
arrangement is a con- 
venient one as it is easy 
to read and refers to 
each of two columns of 
figures, one column ver- 
tical and the other hori- 
zontal. 

A card for each cow 
as indicated above is 
worth while in a modern 
dairy. Individual rec- 
ords are fundamentally 
necessary to efficient 
operation. There is such 
a wide variation in cows 
that unless they are care- 



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GRAPHIC METHODS 



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fully watched tliere 
are certain to be in 
every herd cows whose 
milk production is far 
below the average. 
Individual records of 
each cow are now be- 
ing kept regularly by 
up-to-date dairies, 
and any cow that fails 
to give a definite mini- 
mum of milk with a 
definite per cent of 
butter-fat is sent to 
the butcher. Curve 
cards are a conven- 
ient means of record- 
ing the output of each 
cow in such form that 
instant comparison 
between cows is pos- 
sible. 

In Fig. 214 a rec- 
ord for one cow for a 
period of five years is 
shown on a 4-by-12- 
inch card. As the 
card 12 inches long is 
necessary for weekly 
records, a card of the 
same size can be used 
conveniently to show 
five years by months 
instead of using five 
separate 4-by-6-inch 
cards, one for each 
year. In Fig. 214, 
the figures at the top 
of the card show the 



CURVES FOR THE EXECUTIVE 281 

milk production each month and the total milk production for each 
calendar year. The notes in the left-hand margin show the dates on 
which calves were born. 

In Fig. 215, also, curves are plotted on a card for five years by 
months. In this case there was no hope of getting the cost per ton 
below 50 cents, and the scale was accordingly so chosen that it began 
at 50 cents instead of at zero in order that fluctuations from month 
to month might be more carefully observed. As the zero line was not 
shown on the card, the wavy line was drawn at the bottom of the 
ruled portion, indicating clearly to the reader that he must not inter- 
pret the curve as though the bottom were at zero. 

When using an arrangement showing five years by months on one 
card, considerable mental effort is necessary to get a clear interpreta- 
tion of the fluctuations in the curve from year to year. In Fig. 215 
certain peaks in the curve appear to have somewhat similar shape. 
Thus the peak for 1908 looks like the peak for 1907 until closer ex- 
amination shows clearly that the low point for 1908 was in July, 
while the low point following the peak of 1907 came not in July, 1907, 
but in January, 1908. The waves themselves, although of somewhat 
similar shape, have peaks at entirely different times, the peak for 1908 
being in February and the peak for 1907 in April. The foregoing 
examples may serve to point out the mental effort necessary in read- 
ing horizontally if the danger of misinterpretation is to be avoided. 
If the curves for these same years 1907 and 1908 were plotted on 
4-by-6-inch cards, and one card placed above the other as in Fig. 207, 
there would be no possibility of error on the part of the reader. The 
eye would follow the vertical lines and see at once that there was no 
great similarity in the two waves. Having five separate cards causes 
the reader to take more time in handling cards in order that he may 
save mental effort and avoid error in interpreting the yearly waves. 
Having five years on one card saves handling the cards, but it takes 
more mental effort to be accurate in reading the curve horizontally. 
The choice between five cards of one fiscal year each and one card 
for five years must rest with the judgment or the habit of mind of 
each individual person. 

It sometimes happens that the seasonal wave in a curve is almost 
completely obscured by the tendency toward a very great increase 
or decrease in the business. Conditions may give so large an increase 
in volume of business in any one year as to more than offset any de- 



282 GRAPHIC METHODS 

crease due to a seasonal period of slackness. The manager may think, 
therefore, that his business is not affected by seasons, when in reaHty 
the seasonal changes are very great. The extent of these might be 
very evident if, for instance, a panic year should come along and 
suddenly stop the upward tendencies in the curve resulting from 
the rapid increase in the size of the business. This is an important 
point for any small business to watch, for it may involve bankruptcy 
to assume that the particular business is not affected by slack seasons 
of the year such as affect most businesses. Fig. 211 gives an example 
of a curve in which a large amount of seasonal fluctuation might be 
easily seen if the rapid increase in the business did not make the up- 
ward trend from increased sales greater than the possible downward 
trend due to seasonal changes. 

It is often necessary to compare curves for entirely different things. 
For instance, it is desirable to compare expenses with sales. When 
sales increase expenses per unit should decrease, and vice versa. Tre- 
mendous saving can be made in most large manufacturing plants by 
carefully watching the curves for the unit expenses and the output. 
Something is usually wrong in any department in which expenses 
per unit increase at the same time that the output curve goes upward. 
When the amount of work done is fluctuating greatly, as during 
periods of business depression, the executive may often get many vital 
hints for the operation of his plant if he will simply make periodic 
examinations to see whether th^ overhead-expense curves for each 
department react in the manner which would be indicated by fluctua- 
tions in the curves for direct labor or for quantity of output. 

In making comparisons between separate curves there is a great 
advantage in having a standard arrangement of the five-year cards 
so that there may be no danger of comparing two curves for different 
years when it is intended to compare for the same year. It is desirable, 
as seen in Fig. 215, that all five-year cards should have the years 
arranged by half-decades. One arrangement includes those years 
ending in one to five inclusive, and the other arrangement takes those 
years ending in six to ten inclusive. The person reading the curves 
can then pick up any two cards relating to the same half-decade and 
compare the curves instantly and correctly, simply by placing the 
cards so that the edges coincide. If this half-decade arrangement 
were not followed there would be five different positions in making 
curve comparisons, and there would be grave possibility of frequent 



CURVES FOR THE EXECUTIVE 283 

error in that different years might be compared without the reader's 
noticing that he was making an error. In starting a new curve on a 
five-year card the curve should be started in the middle of the card 
if the first year plotted happens to fall in the middle of a half-decade. 
The half -decade arrangement should be carefully followed even though 
it does not leave a portion of a card unfilled. 

The fine-line curve running through Fig. 215 represents a twelve- 
months moving average of the points on the heavy curve. If the 
executive wishes to know the general trend of his costs, he refers at 
once to this fine line and sees what the cost has been for the last twelve 
months for which costs are known. In making up this moving average 
(as explained in Chapter VI), one month is dropped from the addition 
and another month is included in the addition, so that the twelve 
months added are always the most recent months for which figures are 
available. Note in Fig. 215 the degree of accuracy used in recording 
the figures for the curves. Costs are known quite accurately in this 
case and are recorded here to one one-hundredth of a cent. The moving- 
average line shown above is a much simpler line than the curve line, for 
the reason that the violent fluctuations in the heavy curve are largely 
eliminated by the method of moving averages. The general rule for 
smoothing a curve is that the number of points included in the moving 
average should be the number ordinarily found in one complete cycle 
or wave on the curve. This principle also was more fully discussed 
in Chapter VI. In Fig. 215 the length of the wave is approximately 
one year. It is accordingly good practice to have twelve points in- 
cluded here in making up the moving average, so as to give as smooth a 
curve as possible. If there had been a complete wave or cycle every 
six months instead of once a year, it would have been desirable to use 
six points in the moving average, rather than twelve points. The prac- 
tice in many offices is to use the last twelve months in making up a 
moving average, though it frequently occurs that a smoother curve 
would be obtained if some other number of months were used. 

As will be seen by reference to Fig. 91, points for a moving-average 
curve are usually plotted in the middle of the horizontal space covered 
by those points included in the moving average. In executive-control 
curves such as are seen here, it seems desirable to make an exception 
to the general rule and plot the last point on the moving-average curve 
so that it falls on the same vertical co-ordinate line as the last point 
included in the average. If the moving-average curve were made as 



284 GRAPHIC METHODS 

in Fig. 91 it would be following so far behind the periodic record curve 
that the ordinary reader would not realize that the moving-average 
curve is really up-to-date. For executive work, the object of a moving- 
average curve is not so much to get a smooth curve as to show the aver- 
age for the preceding year or other period of time considered. Under 
these circumstances it seems permissible to plot the moving-average 
curve as done in Fig. 215 instead of following the accepted method 
shown in Fig. 91. 

In the last portion of Chapter VII some of the disadvantages of plot- 
ting curves on ordinary ruled co-ordinate paper were discussed. One of 
these disadvantages is due to the great difference in fluctuation with 
curves of small and of large numerical quantities placed near the bottom 
and near the top of a chart. In order to overcome this disadvantage, 
curves are often plotted on logarithmic paper. It seems desirable to 
point out that curves plotted on the curve cards described here are 
usually compared so that the disadvantages commonly found with 
curves plotted on ordinary co-ordinate paper are largely overcome. 
If only single curves are plotted on each curve card, and the zero line 
appears at the bottom of each card, then curves on different cards have 
approximately the same percentage scale. If two curve cards with 
different numerical scales are compared the comparison is much more 
accurate than would be the case if the two curves were plotted on a 
large sheet of paper to the same numerical vertical scale. The fact 
that the curves are all put into the same size of space on the curve cards 
causes them to have somewhere near the same percentage scale of 
height, even though the actual numerical scales may be widely different. 
Having all curves on the curve cards thus gives more accuracy and ease 
of reading than would be obtained if several curves were shown on 
large sheets of arithmetically ruled co-ordinate paper with one curve 
above the other to the same scale. 

On the left-hand edge of each curve card shown in this chapter will 
be noticed the word "Authorized" with a space for a date and initials. 
When a new curve is added to the list of those curves which are regularly 
plotted in any organization, the man who desires to see the curve periodi- 
cally must put his initials and the date of signing on the left-hand 
margin of the card. This is to show his approval of the general form 
in which the information is given, and to authorize the expense neces- 
sary in collecting data and plotting the curve week by week or month 
by month. A definite authorization, by which some one must sign his 



CURVES FOR THE EXECUTIVE 285 

initials in the manner described, assists greatly in preventing unneces- 
sary clerical work, as it eliminates any curves which are not used 
somewhere in the organization. The man who approves the curve 
can be told just about what it costs to plot each curve. For instance, 
if three thousand dollars a year is expended for the labor, materials, 
etc., necessary in plotting all the curves in an organization, and there 
are three thousand curves kept regularly, it can be seen that the ex- 
pense per curve per year will be about one dollar. Therefore, if the 
man should wish one hundred curves plotted for different data relating 
to his department, he would be approving an expenditure of about 
one hundred dollars per year. 

At odd times before the end of any year the person who does the 
curve plotting should begin to get titles and scales in place upon the 
new cards, which will be necessary at the end of the year when the cur- 
rent curves have reached the right-hand edge of the cards. As most 
curves continue on the same basis as before, the man who has charge 
of the plotting would take the new cards to those different men who had 
approved the curves in the preceding year. If, during that year, any 
change in departmental organization had occurred which would affect 
the manner of plotting a curve or the facts which should be shown in 
any curve, the change would automatically be brought to light by the 
man who must authorize the continuance of the curve. In large cor- 
porations, department heads and officials change so rapidly that con- 
tinual vigilance is necessary to weed out those records and clerical 
procedures which are no longer of any use. The authorization plan 
here outlined, if any man leaves a corporation, would automatically 
give his successor an opportunity to consider how much of the curve 
plotting should be continued on the basis formerly used. There is 
always a great personal difference in the manner in which executives 
desire reports prepared. The authorizing of curves periodically gives 
each executive an opportunity to think the matter over and to have 
data prepared in the manner which is most effective for his individual 
use. In most organizations the president or the general manager would 
be likely to have certain standard ways of assembling data and plotting 
curves, since the chief executive officer must usually refer at some time 
to each of the records of the different departments. The standards 
of the chief executive would thus tend to prevent any freak methods 
being introduced into the general curve-plotting scheme by any depart- 
ment head further down the line. 



286 



GRAPHIC METHODS 



Each curve plotted regularly is assigned a serial number for con- 
venient identification. This serial number remains the same year after 
year, even though changes are made in the manner of assembling data 
or in any other minor details affecting the curve. The serial number 
is placed at the upper left-hand corner of the card, where it can easily 
be seen when the cards are filed in card-index fifing cabinets. The cards 
are identified by the number and year, as may be seen in Fig. 211 where 



aCTft 



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<a\c.s. 



c. • i\V ft ._0._ o k • -o -4- (i^"?V "^ 



Ji^ 



the three cards are tlio ml till. When two curves appear on the same 
card, as in Fig. 215, they may be identified by the letters "A", "B", 

"C", etc., placed on 
the chart near each 
curve, and any refer- 
ence to the several 
curves may be made 
as4323A-1910,4323B 
-1910, etc. When 
five years are placed 
on one card the last 
year given is marked 
in the upper left- 




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^^^ '^'^'^^'^• ■ ^'^"^^'f"^ '' P^ hand corner of the 



Fig. 2 1 6. Each Curve Card Plotted Periodically Has a 
Serial Number. A 4-incli by 6-uicli Record Card is 
Filed by the Curve Serial Number to Give the Com- 
plete Information Necessary so that Anyone May 
Know How to Collect the Data and Plot the Curve. 
The Card, Shown Above, Refers to Curve 2678 Shown 
for Three Years in Fig. 207 and in Fig. 208 



card, as in Fig. 215, 
to identify the card 
and show that it 
represents all the 
data for the half- 
decade ending in 
that year. 



It is not feasible or desirable to place on each curve card a title so 
complete that it gives all the information concerning the source of the 
data used in plotting the curve. It is better to use a fairly short title, 
and then have all supplementary information given on a separate card 
to which reference, if necessary, can easily be made. Fig. 216 shows a 
4-by-6-inch card such as is used in conjunction with each curve card 
regularly plotted. The number on this card corresponds with the serial 
number on the curve card as will be seen by referring to Fig. 205 and 
Fig. 207. If two or more curves appear on the curve card, a card like 
that in Fig. 216 would have subheadings such as 2678A, 2678B, etc., 
all shown on the same card No. 2678. It will be seen that the informa- 



CURVES FOR THE EXECUTIVE 287 

tion given on the card in Fig. 216 is much too lengthy to be included 
as a portion of the title of any curve card. The information on the 
record card is so specific that a new man in an organization should be 
able to follow the card instructions and assemble all the data necessary 
to plot each curve in the whole set. 

Information cards such as are shown in Fig. 216 can sometimes be 
simplified by expressing the information as a formula. Curve numbers 
used in a formula may greatly simplify the method of expressing the 
fact that several sets of data must be added and one total divided into 
another total to obtain a desired ratio. Though information cards like 
that depicted in Fig. 216 are used principally by the man who plots 
the curves, they are filed in such convenient location that they may be 
referred to by any executive who wishes to know the source of the data 
plotted on any curve card, or who wishes to see just what figures are 
included and what are excluded in making up any grand totals. The 
use of the serial numbered information card gives full information in 
condensed and easily accessible form. 



Chapter XIV 
RECORDS FOR THE EXECUTIVE 

A GOOD executive has been described as a man who decides 
cjuickly and who is sometimes right. Probably ninety per 
cent of the answers "Yes" or "No" given by a business 
man are based on opinion rather than on fact. The trouble is that 
the average executive cannot obtain and analyze facts quickly enough 
to base his decision on them. He is forced to decide quickly and his 
one hope is that he will guess "right". 

The problems confronting the executives have grown, in the last 
few years, to such an extent in volume and in complexity that it is 
increasingly difficult to find men with endurance and capacity great 
enough to match the jobs. The executives of our corporations, the men 
who are mayors of our cities, and the men in active charge of the govern- 
ment of our country are, without exception, the hardest worked men in 
the world. The stoker heaving coal into the furnaces of an express 
steamer has a better chance for long life than the man who accepts the 
presidency of even our best managed railroads and industrial corpora- 
tions. The stoker can at least sleep soundly at the end of his day's 
work. The railroad president is likely to be kept awake wondering 
whether his guess was a good one, whether his decision was "right". 

The men now steering the courses of our big corporations are men 
who have come up the line, step by step, through each department. 
They know accurately the relation of every department to every other 
department in their own company. They have available, also, a tre- 
mendous fund of information as to what has been accomplished by their 
competitors. The present executives of corporations are fortunate, 
in that they have seen, in their own business experience, each of the 
steps toward the greater division of labor and the consolidation of 
executive control which have done so much to make economic produc- 
tion possible by large-scale production. 

288 



RECORDS FOR THE EXECUTIVE 289 

The present executives are extremely fortunate in that they had 
an opportunity to develop themselves at the same time that their 
jobs grew bigger. What are we going to do ten years hence, when execu- 
tives who have had such thorough training have all retired or have been 
killed off by the strain of the job? Where shall we find men with broad 
enough knowledge and experience to decide, instantly and correctly, 
each problem placed before them? 

The answer is that the executive of the future will be forced to 
depend on the analysis of facts which have been collected and arranged 
for his instantaneous and continuous use. The executive of the future 
will decide quickly, and he will be more than '"sometimes" right, be- 
cause he will base his decisions on the analysis of actual facts. His 
value as an executive will depend chiefly upon his powers of accurate 
analysis. 

Corporation directors are changing rapidly these days. Suppose 
a new director were to come into your corporation, what could you show 
him of the history and present standing of your business that would 
permit him to give an intelligent director's vote within a year of his 
election to the board? 

It is perfectly feasible to focus a whole business into records so 
simple that a trained- man could see, in half a day, all the important 
tendencies well enough to give an intelligent director's vote. This, 
too, without a spoken word of explanation from anyone. The records 
themselves could tell the complete story in every detail if placed in 
proper graphic form. It is the purpose of this chapter to show how 
such a thing may be done. 

Fig. 217 shows a standard 4-by-6-inch filing case used to file curve 
cards and information cards. The right-hand drawer shows the 4-by- 
6-inch cards filed with appropriate guide cards. In this particular 
case, the guides give the names of brandi houses by cities. The left- 
hand drawer shows the 4-by-12-inch cards filed according to the loca- 
tion of factories. As factory payrolls must be watched closely, weekly 
records of the payrolls were kept for this corporation, though monthly 
curves were found to be sufficient for the sales. There is no difficulty 
in filing the 4-by-12-inch cards in a standard 4-by-6-inch filing cabinet. 
The follow-up block in the drawer is placed 12 inches from the end of 
the drawer, then the cards are filed lengthwise with a sufficient quantity 
of blank cards at the back to keep all the cards in an upright position. 
Of course a special filing cabinet 12 inches wide can be made if desired. 



290 GRAPHIC METHODS 

but it is not really necessary. In a cabinet like that shown in Fig. 217, 
the original curve cards would ordinarily be filed behind the guide cards 
showing the factory or selling-house locations, or behind guide cards 
showing the names of departments in any large business. All the cards 
for succeeding years would be filed behind the proper guide cards, with 
the curve card for the earlier year at the front. Having the card for 
the earlier year at the front instead of at the back permits comparison 
of curves for different years with a very slight lifting of the cards, 
and without any danger of the cards being put back in the drawer in 
mixed order. 

Information cards like those shown in Fig. 216 would be filed in 
the same filing cabinet. These 4-by-6-inch information cards are filed 
by curve serial numbers, with appropriate numbered guide cards so 
that any information card may be quickly located by its serial number., 
As the numbered information cards are needed only for occasional 
reference, they can be put in the back portion of a file drawer, leaving 
the front portion of the drawer available for the curve cards more fre- 
quently needed. 

In checking up the condition of his business, the executive usually 
considers it department by department. For this reason the original 
curve cards should be filed by departments so that the complete history 
of any department may be had from the cards behind the guide card for 
that department. A large portion of the executive's work, however, in- 
volves the study of his general business not by departments but by 
functions. For instance, the executive may wish to know how many 
employees he has in his whole business, and how many employees there 
are in each department, if he is considering the departmental increases 
or decreases which afl^ect the total payroll. It is therefore desirable 
that the executive should have available for instant reference a cross- 
index of information which will show his whole business by function 
instead of by department. Such a cross-index can easily be provided, 
when curve cards are used, by taking a blue print of each curve card 
and then filing the blue print by function, instead of by department. 
In such an arrangement, there would be a complete set of guide cards 
giving different headings, such as "Number of Employees", "Total 
Sales", "Total Expenses", etc., with guide cards having suitable sub- 
headings placed behind each one of the main guide cards. A blue 
print of the curve showing the total number of employees in the corpora- 
tion would be filed at the front of the division for employees. Back of 



RECORDS FOR THE EXECUTIVE 



291 



this total card would be filed blue prints showing the employees in each 
department of the whole plant. Thus, if a total card at the front 
showed that the employees were increasing, the manager could refer 
to each one of the department cards filed immediately back of the total 
card to see in just which departments there had been an increase during 
the last month, and in which department there had been a decrease. 




Fig. 217. A Standard 4-inch by 6-inch Filing Case Is Used for the Curve Ceirds. 
Cards Twelve Inches Long Can Be Filed Lengthwise in a Drawer without In- 
convenience 

Guide cards separate the curve cards by departments. If desired, blue prints can be made from each curve 
card and the blue prints filed by expense-account numbers, as a cross-index of the data on the white 
cards which are filed by departments 

In a similar manner, the blue print showing total expenses would have 
filed back of it cards showing the detailed expenses by departments 
or by account numbers. If expenses had increased the manager could 
refer to the departmental or account-number cards and see just which 
departments or accounts were responsible for an increase or decrease 
in the curve giving the total. The cards in a large business would 
be filed by expense-account numbers, with the total card referring to 
any expense account for the whole business filed at the front of each 
group of cards giving the figures for that expense account by depart- 
ments. Thus, in a manufacturing plant, the card showing the loss 



292 GRAPHIC METHODS 

from spoiled work as a percentage of the total payroll could have filed 
back of it cards showing the percentage loss in each department. If 
the spoiled-work curve for the whole business should go up in any month, 
the manager could see instantly in which departments the percentage 
of loss had increased and in which the percentage had decreased. Let- 
ters could be sent to the foremen of the departments having bad records, 
calling their attention to the bad showing made. 

The cross-index of curves, obtained by filing the cards according to 
function or by expense-account number instead of by department, is 
of tremendous importance to the busy executive. This feature alone 
may save a large amount of his time by making necessary information 
more accessible, and by afi^ording information which may show leaks 
in his business that he would otherwise never know to exist. In a 
business of any size the cost of making one blue print each month from 
each original curve card is almost insignificant. The guide cards 
showing functions or account numbers remain useful year after year, and 
it is necessary only to discard a blue print for each card each month and 
to substitute the latest blue print made from the original curve card 
after a new point has been added. Having the original cards filed 
by departments and the blue prints filed by function or account number, 
the manager may instantly consider his business from whichever point 
of view he desires. He may study the whole operation of a given 
department, or he may study one function or expense account in its 
effect upon his business as a whole. 

Practically every company which does an annual business of 
$1,000,000 or more would find it a paying proposition to have a room 
reserved in the office as a general record or information department 
regarding all the facts of the business. Though such a room might 
be combined with a technical library for books relating to the particular 
art or industry in which the company finds its field of operation, it is 
advisable to have the amount of furnishings in the room limited so 
that there may be no likelihood of valuable confidential papers being 
lost or misplaced. Such a room really needs to have no more furniture 
than filing cases like those shown in Fig. 217, a large table, and a draw- 
ing table or a flat desk for the man who plots curves. 

It would be the function of a man having an office like that described 
to collect for the business all the data and facts which would be of any 
assistance to the executive, the officers, or the department heads. 
Most of his work would relate, of course, to getting data and plotting 



RECORDS FOR THE EXECUTIVE 293 

curves for all the operating reports of different departments of the busi- 
ness. The operating reports regularly furnished by the accounting 
departments of the business would be gone through carefully, and 
figures transcribed from these reports to the curve cards mentioned 
previously. There could also be in the record room a series of maps, 
large wall charts in the form of curves, and perhaps loose-leaf books 
or large vertical card files for cumulative curves such as are shown in 
Fig. 134. Since the information contained in this room is practically 
a history of every phase of the business, it would be desirable to have 
the room enclosed with fire-proof walls and fire-proof doors and equip- 
ped with fire-proof file cases and furniture so that the destruction of 
the records by fire would be absolutely impossible. As good light is 
essential in such a room, large windows are necessary. The windows 
can ordinarily be sufficiently protected against fire by using polished 
plate glass reinforced with wire to prevent breaking of the glass from 
fire in adjoining buildings. 

The title given the man who does the work described is really not 
important. Ordinarily, in a large corporation, he would be ranked as 
assistant to the president, as he should report only to the chief executive 
ofiicer in the particular office in which he is located. He could, if 
desired, be given the title of chief of the record department, or, in a 
larger business where much specialized information is sought from 
outside sources, the title of "statistician" might be justified. In the 
work of most corporations it would soon be found desirable to have a 
man of the type described collect and record, for convenient use, data 
from sources entirely outside of the business itself. Most companies 
have to buy large quantities of raw material which fluctuates greatly 
in price. To assist in making decisions relating to purchases, it would 
usually be found desirable to have curves plotted for the chief materials 
entering into the finished product, such as pig iron, copper, tin, zinc, 
cotton, lumber, coal, etc. Very desirable information could also be 
obtained concerning the business conditions of the country as a whole. 
Since practically every business is affected by the general waves of 
financial prosperity and depression, a good man in this position could 
be of great assistance to the chief executive, by carefully studying 
some series of curves (which might, after long experience, prove to be 
the best barometer available) to indicate changes for better or worse 
in the general financial conditions affecting the particular business in 
question. 



294 GRAPHIC METHODS 

In a business of ordinary size, the yearly outlay for an office like 
that described and a man to run it would be comparatively small. It 
would probably be best to get a young man graduated within a few 
years from one of the technical schools, or from one of the schools of 
business administration now established as separate departments in 
several of the large universities. If a man of the right type were told 
that he would report directly to the chief executive, and that he would 
have a confidential position with complete access to the records of every 
department of the whole business including both manufacturing and 
selling, he would be quite willing to start the work at a reasonable 
salary, knowing full well that the opportunities given would soon per- 
mit him to demonstrate his ability. A recent college graduate could 
be obtained for $20 or $25 per week, as he would see for himself that 
there would be chances for him to make himself worth much more inside 
of the first year or so. 

A man starting a record department of the type described would 
at first find his chief work in getting records for a series of years so 
that comparisons would be possible. In most corporations it is extreme- 
ly difficult to get any kind of good records further than two years back, 
because of constant changes in personnel and changes in accounting 
systems without any reliable notes to tell just what these changes were 
and when they were made. In large manufacturing companies, sub- 
divisions and changes in the expense accounts are likely to occur as 
new departments are added or as new men of different training in ac- 
counting come into control of the accounting procedure of the company. 
After the back records have been fairly well tabulated and plotted in 
the form of curves, the work of keeping the curves up to date would 
be comparatively simple. One man can add one more point monthly to 
several thousand difi^erent curves, and do also a certain amount of 
the clerical work involved in making up ratios, grand totals, etc. If 
a record file of curves like that shown in Fig. 217 is once made thorough- 
ly up to date, for any business, it is easy to keep it up to date with only 
routine work such as any man of even ordinary mental caliber can do. 
Information cards 4-by-6-inch, such as are shown in Fig. 216, explain 
every step of the work required in plotting any curve, and even a new 
man just out of college would be able to follow the instructions well 
enough to take charge of a record system which some one else started. 
Thus, if it is desired after a j^ear or two to promote a man who has built 
up a record system of this kind, it would be quite easy to have him break 



RECORDS FOR THE EXECUTIVE W5 

in a successor so that there would be no change in the methods of col- 
lecting data and plotting curves. This possibility of taking on a new 
college graduate every few years permits having an excellent record 
department, even for a small-size business in which it would be thought 
undesirable to spend more than $3,000 or $4,000 a year to cover the 
total yearly departmental cost. 

It should be a strict rule for a record department of the type de- 
scribed that no original papers shall be taken from the room. The rec- 
ord department should be in a quiet place to which the president or 
any other official may retreat to get completely away from the distrac- 
tions which are common in his own office because of the telephone and 
constant visitors. In the record room the executive would be free to 
concentrate his whole attention on the records of what his business 
has been doing in the last weeks or months, so that he may be able to 
formulate plans for the future. Though the arrangement of the files 
in the record room would be well known to the executive, so that he 
could lay his fingers instantly on any desired curve or other record, 
the chief of the record department would be at hand most of the time 
so the executive could send word ahead to have certain curves or other 
records laid out for instant reference when he arrived. To save time 
the executive should not be required to put back into the card files 
the curve cards which he has taken from any file drawer. By using a 
large table the executive could simply push to the other side of the 
table any cards which he may have laid out for careful comparison. 
The man who has charge of the room can later put the cards back in 
the files. There is an advantage in having one man put all the cards 
back in the files, as in this way there is less chance of the cards being 
misplaced in the file than if several different executive officers were to 
use the cards and themselves put the cards back. It should be stated 
here that in the ordinary use of curve files such as are shown in Fig. 217 
an executive would not need to remove the cards from the drawer. He 
would simply turn the cards over one at a time, raising any card of 
special interest about three inches to look at it, but not removing it 
sufficiently to cause any danger of restoring the card in a wrong position. 
It is only when cards for a series of years are taken out and laid down for 
comparison with some other series of cards that there is any necessity 
for removing the cards from the drawer. 

The Westinghouse Electric and Manufacturing Company of Pitts- 
burgh regularly plot about four thousand curves which record the 



296 GRAPHIC METHODS 

activities of all departments of the business. The majority of the curves 
have one more point added each month, but some of the curves are 
on a weekly basis. Day and Zimmermann, of Philadelphia, are plotting 
a total of about eight thousand curves, most of the curves on a 
cumulative basis somewhat as shown in Fig. 134. In order to allow 
space enough for a cumulative curve (which naturally takes up more 
room than a curve plotted on a non-cumulative basis), the curves are 
plotted on cards 8}^ inches by 11 inches, and these cards are filed ver- 
tically in a tray desk so that a man sitting at the desk can instantly 
lay his hand on the proper card for any one of the eight thousand curves. 
Guide cards are of course used to make card location easier. To pre- 
vent cards being replaced at some wrong position in the file, Day 
and Zimmermann have worked out the clever scheme of notching in a 
similar manner the tops of all cards which are filed in any one division 
of the file. When cards are filed one after another the notches of indi- 
vidual cards form a groove in the group of cards. If any card should 
be filed out of place it would break the continuity of the groove and 
would instantly be noticed. In using the notched-card scheme two 
notches may, if desired, be placed in the top of each card, thus permit- 
ting many more group combinations than would be possible if only one 
notch were used. The notches may be cut with a special instrument of 
rather simple construction so as to insure their uniform spacing right 
or left from the upper corners of the card. A notch in the form of a 
segment of a circle is the most satisfactory. 

In order to keep the general rule that original curve cards shall 
not be taken out of the record room, it is well to provide means by 
which blue prints can be made quickly from any curve card. In a 
business of reasonable size, blue prints may easily be made with a 
small-size printing frame and sunlight printing, if the record room is 
located on the southern side of the building where there is sunlight most 
of the time. In large businesses electric blue-printing machines are a 
part of the regular equipment of the drafting office. If the drafting 
office is not near the record room, however, it may be well to equip the 
record room with an electric blue-printing machine and a small washing 
tank, so that blue prints of each card may be made without the neces- 
sity of taking confidential record cards out of the room. Photographic 
processes for copying records have recently been much improved. A 
machine called the photostat makes black and white copies quickly 
without the expense of glass negatives. With a blue-print machine or 



RECORDS FOR THE EXECUTIVE • 297 

a photostat in the record room, it would be a very simple matter to 
copy periodically the complete current set of curves so that the cross- 
index of cards by function or account may be provided for the execu- 
tive, as described in the preceding paragraphs. 

The plan suggested for a record department sounds much more com- 
plex than it really is. In considering the space and expense necessary 
for such a department it must be borne in mind that the time of the chief 
executive of a modern corporation is of a great value — almost beyond 
computation. The value of the president's time in a large corporation 
cannot be figured out on the basis of his salary, for it is certainly true 
that the executives of large corporations receive salaries much less 
than the value of their services to their corporation. A single "yes" 
or "no" decision of the corporation executive usually involves a gain or 
loss in the earnings of the corporation greater than the executive's 
salary for a whole year. Anything that can be done to give the presi- 
dent and the other executives better and more cjuickly available in- 
formation on which to base decisions is justifiable and should be in- 
stalled practically without regard to cost. 

In a large office it will be found desirable to give a number of 
department heads access to the record room. As no one would ever be 
admitted to this room except the chief executive, and department heads 
who were given written permission by the chief executive, there would be 
no danger of confidential information coming into the hands of outside 
parties. As it may not be desirable to have department heads in a 
business know anything about the finances of the company as a whole, 
or anything regarding the records of departments other than their 
own, it may be best to have the curve cards filed in several drawers with 
a separate drawer for the cards relating to the work of each department 
head. If the drawers are equipped with spring locks, each department 
head could have a key to his own drawer, yet it would be impossible 
for him to go through the records of departments other than his own. 
The chief executive would, of course, have a master key to all the draw- 
ers, so that he could compare the records of one department with the 
records of any other department whenever he desired. The presence of 
the man in charge of the record department would in itself tend to 
keep minor officials from going through the cards relating to bank 
deposits, earnings, etc., for the corporation as a whole. There would 
necessarily be times when the head of the information department would 
not be in the room while minor officials were there, and the expedient 



298 GRAPHIC METHODS 

of locking up the summarized control curves for the whole corporation 
is therefore mentioned here as a possible safeguard. 

Directors and executives change quite frequently in large corpora- 
tions. When a new man comes into a corporation as an executive or a 
director, the value of his service to the corporation is at first practically 
nothing, and he may even for a while be considered a handicap to the 
corporation in that it is necessary for men who have been associated 
longer with the corporation to spend a great deal of their time in explain- 
ing to the new member the facts relating to the various departments and 
to the present scope of the business. This information is generally 
passed on from man to man by word of mouth. Usually there is no 
written statement giving in condensed form a bird's-eye view of the 
whole history and present field of the corporation. Broadly, it is now 
almost impossible for any new director in a corporation to give an 
intelligent director's vote on any proposition brought up within a year 
after he has joined the directorate. 

It will not be long before every man holding the position of a corpora- 
tion director or a corporation executive will be able to readj quickly 
and intelligently, simple curves and figures like those combined on the 
curve cards here. With a card-index file of curves and a record depart- 
ment like that described in this chapter, it should be possible for any 
trained man coming into a corporation as a new director or new official 
to give a fairly intelligent vote after only half a day's study of the 
curves, and this too without having spoken a single word to anyone. 
If the record department and the curves are properly kept, the whole 
situation would be shown on the face of the cards with far more clearness 
than it would ordinarily be possible to give by words alone, even if 
the whole history and present status of the corporation were told. 

Consider the value of a record department like that suggested, if 
such a department were part of the equipment of the mayor's office of 
any city. The department could be maintained continuously by civil- 
service employees who could keep the records in standardized form year 
after year, no matter what shake-ups there might be in political parties 
and in spite of the numerous changes in personnel usual when one set of 
city officers follow another with great rapidity. In mvmicipal work 
there would be no necessity for keeping any except the original curve 
cards under lock and key, as all the information would be public 
property and, of course, available to properly authorized persons. It 
would certainly make a great difference to any new mayor if he could 



RECORDS FOR THE EXECUTIVE 299 

go to a record room and study a set of curves showing, for instance, the 
total number of men in the employ of the city year after year under 
different administrations. He would be able to see over a period of 
years the number of men in each city department such as fire, police, 
street-cleaning, etc., together with the average rate of pay. He would 
also have complete information over a long series of years regarding 
taxable property in the city, tax rates, total population, death rates, 
etc. All this information would be available instantly, not only to the 
mayor but to each member of the council, who might apply to the record 
department very much as he would apply to any good reference library 
when in search of information. The only rule necessary would be 
that no curve cards should leave the room. To safeguard information 
files to which numerous councilmen have access, it would be wise to use 
only blue prints in the open files, keeping the original cards in separate 
locked files, available only to the man who plots the data on each card, 
point by point, as information is received. Councilmen, civic organiza- 
tions, newspapers, etc., wanting copies of any record card should 
be able to get blue prints or photographs at a nominal charge of say 
ten cents per card copy. The New York Public Library is successfully 
working a plan by which photographs of any page of any book in the 
library can be provided to readers in a few hours at a cost of only 
twenty-five cents per page. A similar plan could be used for the sug- 
gested copies of official curve records. 

Progress in the government of the world, and especially in the 
government of cities and of industrial corporations, has been greatly 
retarded by the fact that the only information available to executive 
officers has been provided to the executive in the form which is most 
convenient for the use of the accountant. It is, of course, necessary 
that records should be kept accurately from the standpoint of good 
accounting, and the author has no complaint to make of accounting 
methods in so far as accuracy is concerned. It is not, however, right 
that executive officers who must determine pohcies and who must make 
instant decisions should be forced to base all their decisions on 
information provided to them only in the form of the accovmtant's 
standard arrangement of balance sheet and operating statement. 

The accountant must necessarily take a bird's-eye view of the 
whole business from time to time, so that he may see how all the com- 
ponent parts add together, to make certain that he gets a balance. 
The result is that the accounting officer usually makes up a periodic 



300 GRAPHIC METHODS 

report, in which he gives at the end of any month or at the end of any 
year a complete bird's-eye statement of the status of the business 
at that particular time. Because of the nature of his problems, the 
executive's mind must necessarily work in a manner absolutely dif- 
ferent from that of the mind of the accountant. The executive does 
not often want a bird's-eye view of his whole business at any one 
period of time. What the executive must have is a cross-index of the 
accountant's information, so that he may see over a long period of 
time the whole history of any portion of his business. Most managers 
are forced to work from the accountants' monthly statement, and 
their procedure is accordingly to go through the separate operating 
statements for several months and take off on scratch pads the figures 
for the items in which they may be particularly interested at the 
moment. These figures may have to be added together in order to 
compare a certain number of months this year with the same months 
of last year. This work not only takes the time of the highest paid 
man in the organization, but the hasty scratch-pad figures are likely 
to contain errors. It is absurd that executive officers should be forced 
to make their own cross-indexes of the accountant's statement, and 
not only make these cross-indexes but make them while holding the 
long-distance telephone or at other rush times when seconds are 
important. 

The information as it comes from the accountant's office should be 
passed to the man in the executive department whose function it is 
to provide information for the executive by cross-indexing all in- 
formation from the accountant's reports and putting this information 
in the form of curves. The accountant's report would, of course, be 
filed carefully for future reference purposes if reference is ever neces- 
sary, but for the purposes of the executive the curve cards with the 
figures they contain are sufficient. Not only is the information for 
any subject shown on the cards as a curve over a long period of time, 
but the actual figures of the accountant's report are visible in such 
manner that they may be found instantly and quoted directly from the 
curve cards without having to refer back month by month to the 
original figures in the accountant's report. 

The manager or chief executive of any business using curves in 
order to keep in close touch with all departments will find that he 
needs a liberal education in logic to enable him to draw the correct 
conclusions quickly from the large number of facts available. There 



RECORDS FOR THE EXECUTIVE 301 

are certain general principles which are gradually being recognized, 
and which within the next few years will doubtless be well enough known 
to classify and make available for the executive's use. At present, 
however, each executive must work out for himself his own means 
of recording data and of determining policies in operating his business. 
An example showing some of the difficulties involved in correct inter- 
pretation is one concerning overhead-expense ratios. Some managers 
consider the ratio of indirect expenses to the direct labor in any de- 
partment of a manufacturing business as an infallible barometer by 
which each department of the business can be run. They little realize 
the absurdity of paying too much attention to overhead-expense 
ratios and the danger to the business of using overhead-expense ratios 
as a yard-stick by which to measure accomplishment. In this par- 
ticular case, that of a large manufacturing plant, a new department 
manager changed the manufacturing methods so radically that he 
was able to produce an increased output with less than half the former 
payroll for direct labor. The expenses for the foremen, clerks, sup- 
plies, etc., in the department remained about the same as before. 
Because of the reduced amount of direct labor the overhead-expense 
ratio was of course doubled, much to the astonishment of the chief 
executive, who accordingly considered this department as the worst 
managed in his whole works. This executive had been running his 
plant for so many years on the expense-ratio basis that the new de- 
partment head found it almost impossible to convince the chief ex- 
ecutive that the department was making money more rapidly than 
ever before, even though the overhead-expense ratio had doubled. 
The overhead expense itself had not increased, and the ratio was 
doubled simply because the amount of direct labor had been de- 
creased. 

It is perhaps worth while to point out here that there is danger 
in giving too much information and too many facts to executives 
of small brain capacity who do not know how to use their authority 
intelligently. Curves such as those described in this and the preceding 
chapter, placed for the first time in the hands of the executive who 
does not know the technology or the general underlying principles 
of the business which he controls, are likely to prompt such a narrow- 
minded director to send out a regular deluge of letters unjustly crit- 
icising the actions of his subordinates. There is a possibility that a 
small-caliber man in the manager's chair may send out too much 



302 GRAPHIC METHODS 

destructive criticism and not enough constructive criticism. If such 
a misfortune should occur it would cause every department head in 
the organization to withhold information and consider the whole 
curve-record system as a new form of diabolical torture. Curves are 
not intended to give any chief executive an excuse to "jump on" any de- 
partment manager or foreman. The curve records are intended only 
to point out those danger points at which construction work is needed. 
An executive of the right type will soon realize as he uses the curves 
that he must do the constructive work himself, and that the curves 
will really have more effect in changing the procedure in his own 
office than in changing the detailed routine in the departments of 
his various subordinates. 

One of the first tasks confronting any modern executive is that 
of training, on the one hand, his board of directors and executive 
committee, and on the other hand, his various department heads and 
their subordinates, to read curves accurately so that the facts pre- 
sented may be intelligently grasped and applied to the benefit of the 
business as a whole. It is unfortunate that so many men serving 
to-day on boards of directors and in executive positions of large busi- 
nesses are not able to read even the simplest curve with any real 
grasp of the facts portrayed. Engineers and other trained men who 
have real facts available are tremendously handicapped in presenting 
the facts if it is not feasible to use the graphic method of presentation. 
A man prepared to show his data in the form of curves, for example 
like Fig. 157 or Fig. 159, feels that he would have an almost hopeless 
task to convey the vital facts if only spoken words might be used. 
The writer ventures to predict that within ten years practically all 
corporation directors and executives will be able to interpret curves 
with satisfaction to themselves and with great benefit to their business. 
The executive who cannot read curves will in the near future be the 
exception rather than the rule. 

If any general manager will take the trouble to train his department 
heads to read curves and will then supply to them curves showing the 
facts of his business, he will be tremendously repaid in the interest, 
enthusiasm, and real progress toward improvement which will be 
aroused in his men. 

It is possible to use a reflecting lantern like that pictured in Fig. 
218 to show on a screen the curves from the curve cards described in 
Chapter XIII. Lantern slides are not practicable when frequent meet- 



RECORDS FOR THE EXECUTIVE 



303 



making 



ings of department heads must be held. The expense of 
lantern sHdes each time a new point is plotted on each curve would be 
too great for even the largest corporations. Another disadvantage of 
using lantern slides is the impossibiUty of getting shdes made quickly 
enough to represent always the latest points plotted on the curves. By 
using the original curve cards directly in the reflecting lantern there is 
always a certainty that the picture shown on the screen represents the 
very latest data which are available in curve form. When these curve 
cards are used in a reflecting lantern a simple slide carriage is made 




Fig. 218. Reflectoscope as Made by A. T. Thompson & Co., Boston, Mass. 

Lantern slides may be used as shown at the top of the picture. The stand holding the book may be replaced 
by a simple carriage arranged to take the 4-by-6-inch and the 4-by-12-inch curve cards. The very 
latest data from the file shown in Fig. 217 may then be instantly reflected onto a screen for use in a 
meeting of the department heads of a business. 

to replace the stand holding the book in Fig. 218. As the card is laid 
down flat in its natural position and in plain view of the operator, there 
is no likelihood of cards being put into the jnachine incorrectly. If a 
carriage about two feet long is used, the carriage may be moved 
alternately from right to left, and while one side contains the cards 
which are being reflected on the screen, the other side may be loaded 
with the cards next desired. On account of its length the carriage 
will hold curve cards for several succeeding years. By pushing the 
carriage slowly across the lantern the fluctuation in any curve may 
be shown for as long a series of years as may be desired. Simple spring 
clips on the carriage may be used to hold the overlapping cards in their 



304 GRAPHIC METHODS 

exact position. Not only are the curves themselves shown on the screen, 
but the whole face of the card is seen so that the figures for any points 
on the curve Avhich are of special interest may be read directly from 
the screen. 

If the information or record room is large enough to serve for holding 
conferences the lantern and the screen may be installed permanently 
as part of its equipment. Ordinarily, however, it will be found best 
to have the record room more private than any room used for general 
conferences can be made, and the lantern would be part of the equip- 
ment of the conference room rather than of the record room. With this 
arrangement it will be necessary to take the curve cards from the record 
room to the place where the lantern is installed. The file for the curve 
cards (see Fig. 217) had better be ecjuipped with spring locks so that 
there will be no danger, when the file is carried, of drawers slipping out 
and spilling the cards. A rod arrangement is never desirable with such 
cards as these, for the rod would spoil the bottom portion of the card 
and would also make it impossible to lift cards out for quick reference 
or comparison. Brass handles on the sides of the file case would make 
it easy to carry the case to the conference room. There, on a table 
beside the lantern, the cards in the file case would be available for use 
almost exactly as lantern slides are used with the ordinary lantern. In 
fact, the arrangement of the cards is even more convenient than the 
usual arrangement of lantern slides in that the cards have a guide index 
so that any desired card may be instantly located. 

An executive who wishes to have a meeting of his department heads 
need not make any very definite plan before the meeting begins as to 
what cards he is to show on the screen. He can start talking to his 
men, and, at pleasure, ask the lantern operator (ordinarily the statis- 
tician) for any set of curve cards which may be of interest to him at 
the moment, or which may be referred to at any time during the dis- 
cussion. The use of curves on a lantern screen in the manner suggested 
would entirely revolutionize the meetings of the department heads of 
a business, or the meetings of branch-house sales managers. In sales 
work especially, the use of the various cards would make it possible to 
show the whole assembly the recent records made by selling houses in 
the different parts of the country. The cards for those houses which 
made particularly good records could be shown, the records could be 
commended, and conclusions could be drawn as to how the success 
had been attained. Records for the less successful houses could also 



RECORDS FOR THE EXECUTIVE 



305 




Fig. 219. Curves on Swinging-leaf Display Fixtures Used for Ready Reference in 
the Office of Day and Zimmermann, Philadelphia. Each Leaf May Be Easily 
Carried to a Desk when Additional Points Are to Be Plotted on the Curves 

This same type of display fixture is often convenient for showing pin maps of different territories 

be shown, with comments by the sales manager giving his own sugges- 
tions and asking for suggestions from the other branch-house managers 
present. 

Reflecting lanterns can be used at directors' meetings as soon as 
corporation directors know how to read curves. By using the lantern, 
the president could show facts relating to the business much more 
rapidly, much more clearly, and with greater accuracy than would be 
possible with any spoken words. The showing of curves would give 
the directors a chance to check the president's statements so that there 
would be less danger than at present of a corporation president so 
choosing his words that, though the words might be strictly truthful in 
themselves, they would be over-optimistic because they did not tell 
all the truth. The presence of the whole file of curve cards immediately 
beside the lantern would enable any director to call for facts relating 
to any phase of the business on which he might desire information. The 
use of these curve cards, and a lantern, would permit a properly educa- 
ted set of directors really to direct the business for which they are 
responsible to the stockholders. 



306 GEAPHIC METHODS 

It is sometimes desirable to have the chief facts relating to a business 
plotted on wall charts which are instantly visible in a conference room. 
Fig. 219 was photographed in the record room which adjoins the direc- 
tors' room of Day and Zimmermann, of Philadelphia. On the swing- 
ing-leaf fixtures a series of curves are plotted giving all the salient 
facts relating to a group of public-service corporations. Though this 
type of wall chart is in many cases desirable, there are limitations to 
the use of wall charts because the number of charts cannot be suffi- 
ciently increased to give all the detailed information which is usually 
necessary. Wall charts are suitable chiefly to furnish summarized 
information to directors or other men whose time is limited or who come 
to an office only at rare intervals. 

Wall exhibits of curves can sometimes be used with satisfactory 
results if special care is taken to draw the curves on a very large scale 
and arrange them on all four walls of a room. A prominent financier 
of New York City is said to have a large room, on the top floor of his 
residence, where the walls are completely covered with curve charts 
on which points are plotted as rapidly as data can be obtained. This 
man is so limited for time that he keeps in touch with general financial 
conditions by referring to the charts in this room for only a brief 
time each evening. He disappears to his reference room to meet 
his private secretary immediately after dinner. In the center of the 
room is a revolving desk chair with an ash tray fastened to one arm. 
For the length of one cigar the financier sits in his chair slowly re- 
volving the chair until he has covered the information given on all 
of the wall charts, perhaps, if necessary, asking a few brief questions 
of his secretary. Though very little of the financier's time is taken, 
he is able by concentrated thought on the facts shown by his wall 
charts to keep in full touch with world finance and to map out his 
own plans for future operation. 



Chapter XV 
CORPOEATION FINANCIAL REPORTS 

THE annual report of a corporation is usually mailed to each 
stockholder. The report, as commonly gotten up, contains prac- 
tically nothing except a brief statement by the president in 
regard to the last year's business, together with the balance sheet 
and operating statement furnished by the accounting officers of the 
company, and perhaps an audit by some firm of certified public ac- 
countants. The report sent to a stockholder is essentially in that 
form necessary for the auditor to check the financial figures and to 
certify to their being in balance and correct. 

Though the balance sheet and operating statement, with the letter 
of approval by the certified public accountant, are necessary and de- 
sirable, they do not contain, in themselves, the information most 
desirable and most intelligible to the average stockholder. What the 
stockholder needs most is a report from which he can make comparison 
with preceding years. The bankers and large investors who can pre- 
serve in their files annual reports of a corporation over a long period 
of years probably number less than one per cent of the total number 
of stockholders to whom the annual reports are sent. It is only in 
very large, well managed offices that a file of corporation reports is 
made so that a complete set of reports for a long period of years is 
available for comparison with any new report which may be received. 
The average stockholder cannot preserve his annual reports from year 
to year in such manner that he can lay his hands on the earlier reports, 
and thus compare the last report with the record of preceding years. 
Even if every stockholder should have some yet uninvented type of 
filing system by which everything is preserved and everything can be 
found instantly when needed, that would not solve the problem. Stock- 
holders are changing so rapidly that, of the total number of stockholders 
to whom reports are sent in any one year, a comparatively small percent- 

307 



308 GRAPHIC METHODS 

age have been stockholders for more than two or three years. Because 
they have not been stockholders for any length of time, they cannot have 
available the annual reports of earlier years to compare with any annual 
report just received. The only way a new stockholder can possibly 
determine whether he wishes to buy some more stock or sell what 
stock he already has, is to hunt up some other stockholder or some 
banker who may happen to have a file of the annual reports over a 
period of years. Assuming that a complete file of annual reports can 
be found, most stockholders, if left to their own resources, would be 
hopelessly confused in trying to reach any correct basis for analyzing 
the figures. Each stockholder would have to take a sheet of paper 
and copy off, into different columns for various important items of 
the operating statement and balance sheet, figures for a number of 
years so that the figures for different years could all be seen at one 
time and compared. This means that each stockholder would have to 
make practically a cross-index of the most important data contained 
in a series of annual reports in order to study the different phases 
of operation independently. Even if the stockholder should know 
how to make such a cross-index properly, there are very few stock- 
holders who would be willing to give the time and the mental effort 
requisite to make a tabulated comparison of the kind necessary. 

The absorption of good securities by the public has increased in 
the last ten years at a tremendous rate. The Wall Street Journal 
has compiled statistics of the stockliolders of the larger railway and 
industrial corporations showing that the numbers have grown as 
follows : 

1901 227,000 

1906 431,000 

1911 865,000 

1913 1,250,000 

Mr. Samuel Rea, the president of the Pennsylvania Railroad, 
recently stated that there are nearly 100,000 stockliolders in the 
Pennsylvania Railroad and its affiliated companies, and that the 
number of its bondholders probably exceeded 200,000. Therefore, 
if there are 1,250,000 stockholders of the railways and industrial 
corporations, there are doubtless considerably more than 2,000,000 
bondholders. Though there are many duplications in these figures, 
the fact remains that the prosperity of probably 3,000,000 investors 
is largely dependent upon the success of these corporations. 



CORPORATION FINANCIAL REPORTS 309 

While the number of stockholders has been increasing, the average 
holdings of each stockholder have been steadily decreasing, and now 
average ninety-eight shares. The stocks of the United States Steel 
Corporation are great favorites among small investors. Taking the 
stockholders' list, it was found that among one hundred people, chosen 
at random, only nine own one hundred shares, or over, of both preferred 
and common stock, while forty-seven have less than ten shares each. 

It is highly desirable that corporations should not only keep their 
old stockholders, but should attract new ones. The surest way to 
accomplish this end is to treat stockholders with the utmost frankness. 
Although considerable publicity is already given to the affairs of the 
larger corporations, further publicity is desirable. The average stock- 
holder does not as a rule understand a balance sheet, and has only the 
vaguest idea of his company's affairs. So long as dividend payments 
are maintained, he is content. To be sure, a stockholder can always 
get an impartial and valuable opinion from an investment banker con- 
cerning the past records and future prospects of any company, but it 
would be well if the annual reports of boards of directors to stock- 
holders contained material from which the investor could judge for 
himself to a greater extent. The material included should show the 
records of the company over a period of years, for the company's 
achievement in any one year may be unnecessarily discouraging, or 
fictitiously encouraging. These records are most easily understood 
when put in graphic form. With such graphic presentations any 
stockholder can learn instantly how the fiscal year under review 
compares with the several years preceding. 

The American Telephone and Telegraph Company have for several 
years shown on the back cover of their annual report a chart like Fig. 
249 portraying the growth in their business. Fig. 2 also appeared 
in an annual report of the same corporation to give a clear conception 
of what becomes of the company's revenue. 

Though Fig. 1 has not been used in any annual report, it shows a 
type of chart which could very readily be included in a financial report 
to give complete facts to stockholders regarding complex conditions 
on which the average stockholder would gather very little information 
from the kind of corporation financial report ordinarily sent to him. 

The railroads have used charts in their annual reports to a greater 
extent than the industrial corporations. Some of the railroad charts, 
Jiowever, are not put up in such form as to be easily understood and, 



310 



GRAPHIC METHODS 



with many of the charts, there is danger of misinterpretation. For 
instance, it is not at all easy to analyze Fig. 220 so that its four dif- 
ferent subjects may be compared. 





PER CENT OF INCREASE OVER 1902 | 


YEAR 


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FROM FREIGHT 


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TONS REVENUE fREIGHT 
CARRIED ONE MILE 


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MILES RUN Br LOCOMOTIVES 
IN FREIGHT TRAIN SERVICE. 


























































































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Fig. 220. Percentage Increase in Freight Service on the 
Illinois Central Railroad Since 1902. This Illustra- 
tion Was Taken from the 1912 Annual Report of the 
Company 

Four distinct subjects are treated in this chart, but the horizontal bars 
are arranged in such manner that the reader is likely to think there 
is only one subject. Probably most readers would prefer to turn 
the chart so that it may be read from the left-hand edge as four 
separate curves. To a trained reader this information would be much 
more clear if put in the form of curves like those seen in Figs. 224, 
225, 226, 227 

Fig. 221 also shows several different subjects which should be 
compared, but for which comparison is not very feasible on the chart 
as given. In Fig. 220 the four different subjects were so widely sep- 
arated that comparisons were almost impossible, while in Fig. 221 the 
four different subjects have the bars so arranged that it is difficult 
for the eye to follow any one subject through the maze of bars. 

In Fig. 222 the method of presentation is somewhat similar to 
that used in Fig. 221. As seen in Fig. 222, however, the bars are 



CORPORATION FINANCIAL REPORTS 



311 




i| E' 3 II 01 II II illH 

1 lil-ii^ 



arranged horizontally Avith the earlier year at the bottom, while in 
Fig. 221 the bars are arranged vertically with the earlier year at the 
right. In both of these charts the arrangement for successive years 
is incorrect, for the charts give the impression that all quantities por- 
trayed are becoming less in- 
stead of greater as years go on. 
The indiscriminate mixture of 
so many different kinds of 
bars in one chart makes a 
complex diagram to interpret, 
and it is probable that the 
chart would at least be no 
more difficult to apprehend if 
made entirely in the form of 
curves instead of bars. 
Though it is true that curves 
are not understood by some 
people who can readily grasp 
the bar method of presenta- 
tion, there is no use in keeping 
to the bar method if the bar 
presentation is made as com- 
plex as a chart involving 
curves. 

Fig. 223 was not printed in 
a corporation annual report, 
but it is included here because 
it may show some possibility 
for the inclusion of curves 
in financial reports to give the 
stockholder more complete 
information than he would 
otherwise receive. The data 
of Fig. 223 are of interest 
when considered along with 



■ I M II I niiiiii 

Ililiiil'iyiJi":"! 



Fig. 221. Freight Service and Traffic on the 
Union Pacific Railroad and Auxiliary Com- 
panies 

This chart shows by years the per cent of increase over the 
year ended June 30, 1898, in the gross revenue from the 
transportation of commercial freiglit, the number of 
tons of commercial freight carried one mile, and the 
number of miles run by cars and locomotives in freight- 
train service. Locomotive miles include revenue 
freight-train miles, all mixed-train miles, and helping- 
train miles 

The illustration is reduced from the 1912 annual report 
to stocldiolders. The backward arrangement of 
years from right to left causes the first impression that 
all quantities are growing less instead of greater. 
Four subjects shown combined in one chart in this 
manner are confusing. Either four distinct groups of 
bars or four curves would be superior to the method 
used here 



the charts seen in Fig. 224, Fig. 225, Fig. 226, and Fig. 227. Fig. 
223 is, however, misleading because the vertical scale does not extend 
to zero and the chart gives the impression of a much larger per- 
centage difference between net earnings and dividends than really 



312 



GRAPHIC METHODS 



existed. Omitting the bottom of the chart makes the dividends 
appear a smaller percentage of net earnings than they really were. 
Fig. 223 could have been considerably improved, also, if the line 
showing net earnings were made much heavier than it is seen in the 
illustration. 



Year 


FEB CENT OF (NCneASE OVER 18BS 


1912 


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Union Pacific Railroad 

Fig. 222. Passenger Service and Traffic on the Union 
Pacific Railroad and Auxiliary Companies 

This chart shows by years the per cent of increase over the year ended 
June 30, 1898, in the gross revenue from the transportation of passen- 
gers, the number of passengers carried one mile, and the number of 
miles run by cars and locomotives in passenger-train service. Loco- 
motive miles include revenue passenger-train miles, all mixed-train 
miles and helping passenger-train miles, but do not include miles run 
by motor cars 

Here the reversed arrangement with the latest year at the top gives the 
erroneous impression that passenger business is decreasing. A chart 
like this does not assist greatly in conveying information to the stock- 
holder 

What figures for an annual report should always be shown in 
chart form to make comparisons most clear is hard to determine, 
but it will doubtless be agreed that, if possible, the charts should 



CORPORATION FINANCIAL REPORTS 



313 



miukin; 

001 -BR! 


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New York Times Annalist 

Fig. 223. Net Earnings and Dividends of the United States Steel Corporation 

The figures for net earnings are plotted by quarters. Dividend figures are plotted to sliow the total divi- 
dends each year. The line at the top of the shaded area shows the dividend paid. Dividends exceed 
net earnings in portions of the years 1911 and 1912, but the total earnings of those years were nevertheless 
great enough to justify maintaining the dividend rate 

Though this illustration contains some interesting information, the chart is misleading because the scale 
does not extend to zero. At first glance, the dividend of 1909 would seem to be more than four times 
the dividend of 1908 when in reality it is only about twice as large 

attempt an answer to these questions that naturally arise in the stock- 
holder's mind: 

1. Has the earning power of the company been maintained? 

2. Is the property being kept in proper physical condition? 

3. Is the financial condition sound? 

For the purpose of illustrating the advantages of the graphic 
method for annual reports, the United States Steel Corporation has 
been selected. The chart shown in Fig. 224 is designed to answer the 
first question: "Has the earning power of the company been main- 
tained?" In order to bring out more clearly the very important 
relation between the surplus for dividends and the dividends paid, 
curves Nos. 3 and 4 are redrawn on a considerably enlarged scale 
as seen in Fig. 225. Curves No. 3 and No. 5 are therefore identical, 
as are also curves No. 4 and No. 6. 

Fig. 224 and Fig. 225 show that the Steel Corporation, like a 
large number of railways and industrial companies, reached the zenith 



314 



GRAPHIC METHODS 



















































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DOLLARS 
I, OOO, OOO, OOO 
900, OOO, OOO 
800, OOO, OOO 
TOO, OOO, OOO 
600, OOO, OOO 
500, OOO, OOO 
400, OOO, OOO 
300, OOO, OOO 
200, OOO, OOO 
lOO, OOO, OOO 



'02 '03 '04 '05 '06 '07 '08 '09 'lO 'll '12 

Fig. 224. The Earning Power of the United States Steel Corporation 

Curve 1. Gross earnings 

Curve 2. Operating expenses ' 

Curve 3. Surplus earned available for dividends 

Curve 4. Preferred and common dividends paid 

This chart and the following charts relating to the United States Steel Corporation arc submitted as a sug- 
gestion to show how the annual report of a corporation could easily give comparisons over several years. 
The space required for the charts is insignificant, yet the stockholders would receive the vital facts in 
such form as to permit a full understanding of the condition of their company as compared with previous 
years 

of its earning power in the year 1907. In that year more than 15 
per cent was earned on the common stock, while only 2 per cent was 
paid. Curve No. 1 shows that the gross earnings in 1907 were $757,- 
000,000. Then follows, in 1908, the terrific slump in business due to 
the financial panic, with a gradual but uncertain recovery. By 1912, 
the corporation succeeded in bringing its gross business up to $745,- 
000,000, still somewhat under the 1907 high-water mark. 

The movement of operating expenses is depicted by curve No. 2. 
A glance at the chart shows that, during 1905-6-7, gross earnings 
tended to increase faster than operating expenses, which is again true 
in 1909 and 1910. In 1908 and 1911, it proved impossible to reduce 
operating expenses to conform to the reduction in gross earnings, 
with the result that profits were sharply reduced in both these years. 
In 1912, a unique situation occurs. Curves 1 and 2 run practically 
parallel, showing that although the gross earnings were largely in- 
creased, operating expenses kept pace. The largest factor in op- 
erating expenses is naturally labor, and the reports of the corporation 



CORPORATION FINANCIAL REPORTS 



315 



5 
@ 



Dollars 

200, OOO, OOO 

ISO, OOO, OOO 

I60, OOO, OOO 

140, OOO, OOO 

120, OOO, OOO 

lOO, OOO, OOO 

so, OOO, OOO 

60, OOO, OOO 

*40, OOO, OOO 

20, 000, 000 



'02 '03 '04 '05 '06 '07 'OS '09 '10 'II '12 

Fig. 225. The Surplus Earned and the Dividends Paid by the United States 

Steel Corporation 

Curve 5. Surplus earned available for dividends 
Curve 6. Preferred and common dividends paid 

These curves are the same as Curve 3 and Curve 4, respectively. The data are depicted here on a large 
scale so that the relation of dividends to surplus earned may be seen clearly 

throw the necessary light on this item. The average wages per man 
in 1907 were $765 per annum, and in 1912, $857. It has been shown 
that gross earnings in 1912 were less by $12,000,000 than in 1907, 
yet operating expenses in 1912 were $45,000,000 more than in 1907, 
being, as the curve shows, over $600,000,000 for the first time in the 
Corporation's history. 

Curves 3 and 5, representing the surplus for dividends, are of most 
interest to the stockholder. It will be recalled that when the Steel 
Corporation was organized in 1901, the common stock was imme- 
diately placed on a 4 per cent basis. In 1903 the disbursements to 
the common stock ceased altogether and even the 7 per cent upon 
preferred was seriously questioned. During 1906, 1907, and 1908, 
2 per cent was paid on the common, and then in 1909, the rate was 
first raised to 3 per cent, later to 4 per cent, and finally to 5 per cent. 
Conservative people have always criticised the 5 per cent dividend, 
believing that a 4 per cent rate would be more likely to be permanent. 
However, a consideration of the relation of curve No. 5 with No. 6 
will show that the Corporation has avoided the payment of unearned 
dividends throughout its career. The margin was very slim in 1903 



SI 6 GRAPHIC METHODS 



and 1904 and again in 1911 and 1912. As the balance of earnings 
for the common stock in 1911 was only 5.9 per cent and in 1912 only 
5.7 per cent, a continuance for another year of such narrow margin 
would probably have meant the reduction of the 5 per cent rate, 
especially in view of the reduced appropriations for new construction 
and betterments, as disclosed in Fig. 226. Fortunately, however, 
for the stockholders, conditions in 1913 improved enormously and 
11.17 per cent was earned for the common stock. Considering only 
the figures charted here, it is evident that the earning power of the 
Corporation during 1912 was not maintained. 

To answer the question "Is the property being kept in proper 
physical condition?" the chart shown by Fig. 226 has been constructed. 

As seen from curve 7, depreciation and repairs have shown a fairly 
constant increase, the amount in both 1910 and 1912 exceeding that 
of 1907, although the gross earnings were larger in 1907 than in either 
1910 or 1912. This is a satisfactory sign. 

Curve 8 portrays the total amount of money invested in the con- 
struction of new plants, mills, etc. This curve reaches its height 
in 1907 (running up to $67,000,000) and represents in large part the 
creation of the great plant at Gary. Curve 8 shows that even the 
panic of 1907 failed to curtail new construction to any great extent. 
But the poor profits in 1912, coupled with the higher rate of dividend 
on the common stock, did produce a sharp contraction — from $50,- 
000,000 in 1911 to less than $15,000,000 in 1912— the latter figure 
being the smallest since 1902. This, however, is not to be criticised 
too severely, since it is clear that a continuous expansion in pro- 
ductive capacity might easily outrun the normal consumptive demand. 

Curve 9 represents the extent to which surplus earnings have 
been "ploughed back" into the property. This tells how the water 
has been squeezed out of the common stock. The report of the Bureau 
of Corporations in 1912 shows that, whereas there was a capitalization 
over indicated investment amounting to $625,353,559 in 1902, such 
excess was only $281,051,222 in 1910. Furthermore the report expressly 
states that this excess is not necessarily, nor entirely, "water". Up 
to 1908, curve 9 follows curve 8 very closely, indicating that the new 
construction was largely paid out of earnings, and not capitalized. 
Since 1907, there has been a tendency to finance such additions by 
the sale of bonds. This tendency, if not carried too far, is not open 
to criticism. One may, therefore, answer the second question in the 



CORPORATION FINANCIAL REPORTS 



317 



Dollars 
lOO. OOO, OOO 

90, OOO, OOO 

SO, OOO, OOO 

70, OOO, OOO 

60, OOO, OOO 

50, OOO, OOO 

40, OOO, OOO 

30, OOO, OOO 

20, OOO, OOO 

lO, OOO, OOO 



'02 '03 '04 '05 '06 '07 '08 '09 'lO 'II '12 

Fig. 226. The Maintenance of Property by the United States Steel Corporation 

Curve 7. Depreciation, repairs, etc. 

Curve 8. Expenditure for new construction 

Curve 9. Appropriation from surplus earnings for construction and betterments 

No more lines or figures are placed on this chart than are really necessary. The intention was to make the 
chart just as simple and clear as possible. Note the large quantities expressed by the numbers in the 
vertical scale, yet the wide spacing of the groups of three figures makes interpretation very easy 





































































































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GRAPHIC METHODS 



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Fig. 227. Financial Condition of the United States Steel Corporation in Different 
Years as Shown by the Balance Sheet 

Curve 10. Current assets 

Curve 11. Cash holdings 

Curve 12. Current liabilities 

Here the numbers in the vertical scale represent larger quantities than in Fig. 226 and the spacing is closer 
in the vertical direction. Nevertheless, the numbers are easily read. To avoid any chance of error 
in interpretation it seems well to write out in full even the large numbers necessary here 

affirmative, for from the evidence given, the property has been ade- 
quately maintained . 

Fig. 227 illustrates the financial condition of the company as dis- 
closed by the balance sheet. This chart is very conclusive, for it 
shows a very large excess of current assets over current liabilities, 
while cash holdings have tended to eciual or exceed the total cur- 
rent liabilities. The balance sheet, therefore, indicates continuous 
and increasing financial strength. Current assets in 1912 reach nearly 



CORPORATION FINANCIAL REPORTS 319 

$300,000,000, compared with $275,000,000 in 1907. Current liabilities 
were $60,000,000 in 1912 and $45,000,000 in 1907, but cash increased 
from $54,000,000 to $67,000,000. The Steel stockholder has, therefore, 
good evidence that his compa-ny is being managed with great sagacity 
in all departments. 

An exhaustive study of the United Staces Steel Corporation would 
require a great many charts similar to the foregoing, but those given 
probably bring out clearly the main results in each annual report. 
The use of graphics to drive home statistics is yet in its infancy, and 
the next few years will doubtless witness a rapidly growing employ- 
ment. There seems no good reason why any management, desiring 
to tell the whole truth to its stockholders, should not adopt graphic 
methods to supplement, as well as to illuminate, the statistical tables. 

The famous economist, Stanley Jevons, wrote in 1875: 

There is much to be learnt about money before entering upon those abstruse 
questions, which barely admit of decided answers. In studying a language, we begin 
with the grammar before we try to read or write. In mathematics, we practice our- 
selves in simple arithmetic before we proceed to the subtleties of algebra and the 
differential calculus. But it is the grave misfortune of the moral and political sciences, 
as well shown by Mr. Herbert Spencer in his " Study of Sociology, " that they are 
continually discussed by those who have never labored at the elementary grammar 
or simple arithmetic of the subject. 

To-day, everyone still believes himself competent to discuss cor- 
poration finance, which is a branch of political science, in the same 
cheerful ignorance of the fundamentals of the subject. Everything, 
therefore, which will help to throw light on the dark corners of finance 
and make ignorance less excusable should be welcome. Never have 
corporation managers been more sensitive to public opinion, and if 
charts in annual reports make the truth more easily grasped (which 
they do) they will soon command an established place in corporation 
records. 
/ 

This chapter is largely hased on an article prepared at the suggestion of the author by 
Mr. Pierpont V. Davis, of New York City, and published by Mr. Davis in Moody's 
Magazine. 



320 



GRAPHIC METHODS 




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Chapter XVI 
GENERAL METHODS 

THERE are a number of comparatively little known short cuts 
and convenient methods available in the collection and record- 
ing of statistical facts. If obsolete or unsuitable methods are 
used it may make a difference between success and failure in the work 
of keeping records of any complex business. When the methods of 
tabulation are too laborious, not only are the records so extensive as 
to be in disfavor, but they may occasionally include errors, in spite of 
the greatest care that can be taken by even the highest grade of employ- 
ees. Anything which will reduce the amount of mental concentration 
necessary on the part of persons collecting and tabulating facts, will 
ordinarily assist in the production of more accurate final results. In 
large statistical studies, such as are made by the United States Census 
Office, it would be practically impossible to get all the information 
now obtained if tabulating machinery were not brought to the aid of 
the human brain and hand. 

The punched-card system now widely used in statistical work has 
made possible an almost unlimited amount of subdivision of analysis 
with very little extra expense. Fig. 228 shows the card used by the 
United States Census Office for the 1910 census. One of these cards 
was punched for each inhabitant in the United States in accordance 
with the data obtained by the Census enumerators. It will be noticed 
that the card contains different columns of names or numbers and that 
there are twelve classifications possible in each vertical column in which 
a punched hole may be made. Ordinarily the different columns are 
used for different subjects, and the position of the punched hole in each 
column records the classification of the data relating to that particular 
subject. ■' . 

The punched cards are stacked so that all are right-side up. It will 
be noticed from Fig. 228 that the lower right-hand corner of the card 

321 



322 



GRAPHIC METHODS 



Needles connected to electric wires 



is clipped off. If any card in the stack is arranged improperly, it will 
show because the card will project beyond the other cards at the clipped 
corner of the pile. The stacks of cards are run through a sorting ma- 
chine such as is seen in Fig. 229. 
make a contact through the 
holes in the card, and operate 
the sorting mechanism auto- 
matically in such manner that 
the cards are dropped into com- 
partments in accordance with 
the position of the punched hole 
on the card. Cards are sorted 
for one particular characteristic 
at a time, so that all cards 
having that characteristic are 
obtained for tabulating pur- 
poses. After the data on one 
set of cards have been tabulated, 
the cards can then be run 
through the sorting machine 
again and sorted for other char- 
acteristics. This permits using 
the punched cards over and 
over again until all of the differ- 
ent data which may be of 
interest have been taken from 
the cards by the tabulating 
machines. 

Fig. 230 shows the tabu- 
lating machine as used in the 
general commercial work 
of corporations, and for 
State or municipal departments. 
The cards are placed in the ma- 
chine at the left and are fed 




Courtesy of the Tabulating Machine Company 

Fig. 229. Hollerith Card-Sorting Machine 
Suitable for Use by Corporations for 
Statistical Work Relating to Sales, 
Costs, Etc. 

This machine will sort about 12,000 cards per hour, 
and place in the right compartment all cards having 
the hole punched in the same position in the particu- 
lar column for which the sorting is done 



through automatically, one by one, so that electric contacts are made 
wherever there are holes punched in the card. The electric contacts 
cause the counting dials to revolve by just the right amount to record 
properly the data for each punched hole. 



GENERAL METHODS 



323 



After any group of cards has been run through the machine the 
totals can be read off from the counting dials and written down by 
the operator. Then the machine is ready for some other set of cards. 
Machines are built with different numbers of counting heads to suit 
the complexity of the data in any kind of business. By having several 
counting heads on the same machine, different sets of information may 
be taken from the cards simultaneously, thus frequently permitting 
one run of the cards through a tabulating machine to give all the data 

which may be re- 
quired. 

The punched- 
card machines are 
proving to be of 
very great useful- 
ness in commercial 
work. Fig. 231 gives 
a view of a com- 
pletely equipped 
office for the use 
of the punched-card 
system by an elec- 
tric lighting com- 
pany. The data are 
transferred from the 
original records to 
the cards by very 
simple punching 
machines with keys 
somewhat similar 
to typewriter keys. The punching is usually done by girls. A little 
training and practice gives high speed. Once punched, the cards are 
always available and may be filed for record purposes. It is frequently 
a great convenience to be able to run through the machines cards for 
several years back so that comparative statistics may be made. The 
preservation of the cards makes it unnecessary to dig out the original 
records. The uniform size of the cards makes it possible to preserve 
large quantities of them with comparatively little labor. 

In punching the cards there are certain holes relating to depart- 
ments, dates, etc., which are repeated time after time for large numbers 




Courlesy of the Tabulating Machine Company 

Fig. 230. Hollerith Tabulating Machine for Totalling 
the Data Contained on Punched Cards 

The machine illustrated has four counters, permitting the simulta- 
neous taking off of the data contained under four different headings 
on the punched card. The sorted cards are placed at the left 
of the tabulating machine and run through at the rate of about 
3,000 per hour. Totals are read from the dials shown at the right 



324 GRAPHIC METHODS 

of cards. Instead of the operators punching these repeated holes one 
by one in each card, the cards are punched by a gang punch, which at a 
single stroke punches several holes in many different cards. The gang 
punch can be seen in Fig. 231 on a table near the right-hand side of the 
illustration. 

Manufacturing companies now use the tabulating machines for 
keeping track of the cost of different orders and of different classes 
of work in the factory. The data from the original time slips of the 
workmen are transferred by the punching machines to the cards day 
by day as the time slips are turned in. The punched cards can then be 
sorted by order number and department, so that when each order 
is completed the total cost of all work on that order is obtained. The 
distribution of the value of work done by different departments can be 
had also if desired. 

In keeping the records of a sales department, the facts relating 
to the various sales orders are transferred to the punched cards and the 
cards sorted and tabulated in any manner desired. A very large manu- 
facturing business having many kinds of machinery as a product, uses 
the punched-card system for each order as it is received in the plant. 
At the end of each month the records show the total sales of each branch 
house, the total sales of each salesman, the total sales of each main class 
of product, and many other kinds of information. In this particular 
plant tabulating machines are of very great assistance, because they 
can be used to make a sales analysis for any one class of product. The 
punched card for each order shows the catalogue number of the product 
called for by that order, ^^^lenever desired, cards for a definite length 
of time can be run through the machines so as to sort out all the cards 
for any catalogue number of product on which a study is to be made. 
The resorting of these cards by sales districts shows the distribution 
of the total sales of this particular product by distinct districts, or 
States, and, if desired, by different salesmen. The sales for the various 
months or seasons of the year may be had if wanted. Though the data 
relating to the many kinds of product need not be regularly tabulated, 
the facts are nevertheless preserved so that tabulation for any particular 
class of goods or any territory can be made whenever a study seems 
desirable. 

The multitudinous uses to which these card-sorting and tabulating 
machines can be put are far beyond any possibility of naming here. 
The very great flexibility, speed, and accuracy of the machines make 



GENERAL METHODS 



325 




Courtesy of the Tabulating Machine Com-pany 



Fig. 231. A Completely Equipped Office for Collecting and Tabulating the Operating 
and Sales Statistics of an Electric-Lighting Company 

The girls at the left are operating the key punches for punching the cards. A gang punch is shown on 
the table at the extreme right. In the corner is the card-sorting machine, and the tabulating machine 
is in the center. Files for punched cards are seen along the wall 

them almost indispensable in any work where there is large quantity 
of complex data to be analyzed. It has been found feasible and profit- 
able to use machines of this type in businesses of only moderate size. 
The adding machine is now so commonly used that it seems scarcely 
worth while to mention it here. There are, however, frequently times 
when special investigations must be made, but adding machines do 
not happen to be available, and the investigator feels seriously handi- 
capped because he must take from the original records only those 
items which may be of especial interest to him. In work of this kind, 
it is sometimes convenient to use one of the small-size pocket adding 
machines of which there are several different makes now on the mar- 
ket. Though these machines are not at all in the same class as the 
large key-operated machines, they are of assistance in taking off 
occasional items because they overcome the necessity for putting 



326 



GRAPHIC METHODS 



dov/n the items on a piece of paper for addition later by mental effort. 
With the portable adding machine the data are taken from the original 
work directly and added automatically as the work proceeds. 

Engineers do the greater portion of all of their computing work 
by means of the slide rule. By others than engineers, however, the 
slide rule is very little used. In the preparation of data for curves 
and charts for corporation work, or for any investigations where 
numerous percentages are necessary, the slide rule is almost indispen- 
sable. A 10-inch slide rule as shown in Fig. 232 is sufficiently accurate 
for most work, and, as it costs only a few dollars, it should be a part 
of the equipment of everyone who is doing even the simplest form of 
statistical work, or who is periodically plotting curves involving 
ratios or percentages. By using a slide rule the percentage ratios of 
numbers can be determined almost instantly and with no mental 
effort. It can be confidently predicted that anyone who has miich 
multiplication or division to do in relation to curve-plotting and chart- 
making will find the slide rule of such a great assistance that the 
rule would not be parted with under any circumstances if a new one 
could not be obtained. 



TT 



'j i Ji i ;!s^rii;jil^l])4:ll ' j;i^'^!ii i tl | iBjll^|j;^ 

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Fig. 232. A lo-inch Slide Rule 

The slide rule is of great convenience in doing work involving multiplication or division- 
It is especially valuable for obtaining ratios or percentages in statistics for industria' 
work 

Judgment must be used in the showing of figures in any chart 
or numerical presentation, so that the figures may not give an ap- 
pearance of greater accuracy than their method of collection would 
warrant. Too many otherwise excellent reports contain figures which 
give the impression of great accuracy when in reality the figures may 
be only the crudest approximations. Except in financial statements, 
it is a safe rule to use ciphers whenever possible at the right of all 
numbers of great size. The use of the ciphers greatly simplifies the 
grasping of the figures by the reader, and, at the same time, it helps 
to avoid the impression of an accuracy which is not warranted by 
the methods of collecting the data. 

A recent government report* contained this statement: "The 
cotton crop of last year (1911) aggregated 16,250,276 500-pound 

* "The Packing and Marketing of Cotton," by John M. Carson. 



GENERAL METHODS 327 

bales, the total value of which is $1,000,000,000 and, including the seed, 
$1,200,000,000." The figure for the number of bales implies that 
every single bale of cotton raised in the United States was accounted 
for and that these figures are absolutely accurate down to one bale of 
cotton. This denotes an accuracy of 1 part in 16,000,000 parts, or an 
accuracy within 0.000006 per cent. It is very doubtful indeed whether 
the figures for the cotton crop are accurate within 1,000 or even 10,000 
bales. Suppose a possible error of 10,000 bales were assumed, and the 
cotton crop put down as 16,250,000 bales, the accuracy would still 
be 1 in 1,625, or within 0.06 per cent. For most purposes it would 
be much preferable to use the round number 16,250,000 instead of the 
detailed figures which were given in the Government report. The 
particular report from which the figures are taken is not a tabulation, 
but a written report in regard to the methods used for packing cotton. 
Since the report was intended to be read by merchants and planters, 
rather than by statisticians, it is all the more important that the 
figures should be presented in round numbers so that they may be 
easily grasped. The mere fact that values for the cotton in the latter 
part of the quotation given above are in very rough estimates of such 
round numbers as "$1,000,000,000", calls special attention to the 
use of detailed figures for the "16,250,276 bales". 

Misleading figures irnplying a greater accuracy than justifiable 
are very often found as a result of the addition of different quantities 
some of which are large and some small. The small quantities may 
have a great degree of accuracy, but this does not give accuracy to 
the sum of all the quantities, for the total cannot be any more accu- 
rate than the most inaccurate item included in the total. If a very 
large item is not accurate within ten thousand, then it is useless to 
include in the grand total the three right-hand digits which may be 
obtained as the result of addition. When some of the items included 
are so small that they are in tens or hundreds, the addition should be 
made to include all the digits. After the sum is known then all those 
digits whose accuracy is doubtful in the total should be replaced by 
ciphers. 

Fictitious accuracy is quite often implied in the results of com- 
putations where a shde rule has been used. The ordinary 10-inch 
slide rule can give an accuracy of only three significant figures, and, 
on the right-hand portion of the scale, the third figure is often some- 
what in doubt unless very great care is used in manipulating the 



328 GRAPHIC METHODS 

rule. This means that with the 10-inch sHde rule the accuracy is 
ordinarily no greater than 1 in 1,000, or one-tenth of one per cent. 
Though two quantities each running into five figures may be multi- 
plied on the slide rule, the product would not be accurate beyond three 
significant figures, and ciphers must be put down to express the re- 
mainder of the number for the product. 

If very large quantities obtained by slide-rule computation are 
added together with a number of small quantities, the total cannot, 
of course, be accurate beyond the third or fourth digit toward the right 
of the largest ciuantity included in the total. The fourth digit may be 
fairly accurate in the total, because in the process of addition the 
various figures added would tend to give a close approximation of the 
fourth digit and that digit might accordingly be put down in the total 
because it has at least a fair possibility of accuracy. 

It must not be assumed from the preceding paragraph that the slide 
rule gives figures too crude for ordinary use. There are comparatively 
few sets of data relating to costs, output, or other records of industrial 
work which have an accuracy greater than one-ten.th of one per cent. 
For the great majority of ordinary problems, the data are so crude that 
the 10-inch rule has more than sufficient accuracy. The use of the 
slide rule on many classes of work has a desirable psychological effect, 
in that it calls attention to the accuracy of the data and assists in pre- 
venting unnecessary detail work which it is very easy to drift into if 
any assumptions of great accuracy are permitted to creep in. 

The question of significant figures in statistical work and even in 
ordinary commercial reports is an important one which should have 
greater attention than it ordinarily receives. Unfortunately the sub- 
ject can be only briefly touched upon here and the reader would do well 
to look the matter up in some of the books on statistical theory.* 

It sometimes happens that a few blue prints are required from 
some complex chart made on heavy paper or cardboard. Instead of 
making a tracing from the drawing by means of tracing cloth and with 
great expenditure of labor and time, it is sometimes feasible to treat 
the original drawing with a transparentizing solution so that blue 
prints can be obtained directly. The transparentizing solution is put on 
the paper with a brush or sponge and then blue prints are made in the 
ordinary manner. There are several different makes of the trans- 

* A chapter on " Approximation and Accuracy " will be found in " The Elements of Statistical Method," by Willford I. King 
published by the MacmiUan Company, New York City. 



GENERAL METHODS 329 

parentizing solution on the market and a supply can be obtained from 
most shops selling drafting materials. 

During the last few years very convenient photographic machines 
have been put on the market which photograph directly on sensitized 
paper without the use of any negative. With this type of machine, 
copies of drawings can be made very cheaply and clearly. One of the 
convenient features in doing work by this machine is that drawings 
can be enlarged or reduced within a wide range of sizes. The machine 
most commonly used for this work is called the photostat. In most 
large cities there are companies equipped with the photostat appara- 
tus who will at reasonable cost make copies of drawings sent to them, 
much as the blue-printing companies make copies from tracings. Some 
of the best equipped libraries have now installed photostat machines 
as a convenience to their patrons. In a library so equipped it is pos- 
sible to have a copy made from any page in any book or periodical in 
the library. In the New York Public Library, the reader need only 
fill out an order form giving the exact page and the name of the publica- 
tion from which the copy is to be made, and state the size desired in the 
reproduction. Usually the copy is available within a few hours, but, 
if desired, it may be mailed, thus avoiding any necessitj^ for waiting 
on the part of the person ordering the copy. In case of rare books or 
manuscripts, copies may be made page by page so that a complete copy 
of the book is obtained without prohibitive expenditure. 

Charts from which plates must be made for printing are nearly 
always drawn considerably larger in size than the completed illustration. 
Most of the charts in this book were drawn two or three times as large 
as seen here. A photographic reduction in the size of the chart tends to 
eliminate minor irregularities and gives a much better result than can 
possibly be obtained from drawings in the exact finished size. In 
making the original large-size drawings it is almost essential that a 
reducing glass should be used to make certain that the finished drawing 
will have the desired appearance. With complex drawings it is often 
difficult to tell whether the lettering and figures are of large enough size 
to be read easily after they are reduced to the size to be used for print- 
ing. By looking through a reducing glass it can be determined at 
once whether the drawing is in correct proportions. A reducing glass 
is similar in appearance to the ordinary magnifying glass, but the lens 
is ground concave instead of convex so that everything seen through 
the glass appears of smaller size. The ordinary reducing glass can be 



330 GRAPHIC METHODS 

used for a reduction through quite a range of different sizes by holding 
the glass at different distances from the drawing which is being con- 
sidered. 

One of the commonest errors made by the beginner in preparing 
charts from which printing plates are to be made is that he does not 
allow for the reduction in widths of the various lines. If the printing 
plate is to be made one-third the lineal dimension of the original draw- 
ing, it is essential that the lines on the original drawing should be made 
three times as wide as they are to appear when printed. The novice 
will find that even though he uses a reducing glass with great care, his 
heavy lines will at first nearly always appear less wide and black than 
he had expected and hoped that they would be. 

Quite often it is desired to change the proportions of some chart 
so that the ratio between height and width may be different from that 
of the original drawing. Though the photographic process used in 
the photostat machine or by the engraver (in making plates for print- 
ing) permits a change in size, the same proportions remain between 
width and height. There would seem to be enough demand to justify 
an engraver making a combination of lenses by which one dimension 
of a drawing may be changed more than the other dimension. By 
using two lenses having cylindrical surfaces and having the axes at 
right angles, there might be a possibility of changing the proportions 
of drawings which are copied without any great amount of expense 
after the apparatus has once been designed. 

Very often persons owning cameras do not know that the camera 
manufacturers are in many cases able to supply auxiliary lenses by 
which pictures and copies of drawings may be made practically full- 
size with ordinary cameras. Though the arrangement is not as con- 
venient to use as a regular copying camera, it may be of great service 
to supplement the work of a camera already owned. 

It is not generally known that line plates may be made from charts 
drawn on co-ordinate paper ruled with green ink. Such charts sent 
to many zinc engravers are returned with the statement that it is 
impossible to make a line cut from green-ink copy. The statement 
is made in most cases by the engraver without even attempting to 
make the cut. There is no difficulty in making excellent zinc cuts 
from copy using the ordinary green ink, and many of the cuts in this 
book have been so made, as, for instance, Fig. 156, Fig. 207, and 
Fig. 215. 



GENERAL METHODS 331 

Of course, when line cuts are made from charts having a green-ink 
background, the printed illustration shows both the black and green- 
ink lines as black, and there is no distinction between the different 
lines. On this account, it is necessary for the person ordering the 
charts made from paper having green-ink lines to make certain that 
the main features of the chart stand out with prominent broad lines, 
so that there may certainly be a contrast in the width of the Ijnes 
when printed, to make up for the contrast obtained in the original 
drawing by the difference in color of the two inks used. 

Color printing is not yet ordinarily available unless a very large 
number of copies are to be made. In order to make areas stand out 
in contrast, different kinds of cross-hatching put on by hand ruling 
have been used very commonly. One trouble with the hand ruling 
is that it lacks uniformity unless done with very great care and to a 
scale considerably larger than the finished illustration, so that there 
may be enough photographic reduction to eliminate many of the de- 
fects which would otherwise appear. It is not widely known that 
there is a method available in the form of Ben Day mechanical shading, 
which is far superior to cross-hatching for line-plate work. Most 
good engravers can do Ben Day work, and it is just a matter of speci- 
fying what kind of shading is desired on the different portions of the 
drawing. With the Ben Day shading, more degrees of shading from 
light to dark are feasible than with hand work, and, in addition, there 
are many varieties of lines and patterns which may be used. 

Since Ben Day work must be applied on each area separately by 
means of a transfer process, it is necessary for the engraver to make 
certain that the Ben Day shading shall not appear on some portion 
of the zinc plate where it is not desired. This requires that the en- 
graver must protect the different portions of the zinc plate by a paint- 
like covering, and this must be done for each of the different kinds of 
shading used. It is almost impossible to make any square-inch price 
rate for Ben Day work because each new plate is a problem in itself. 
The work is ordinarily charged for on a time basis, the usual rates 
being from $1.00 to $1.50 per hour. 

When copy to receive Ben Day work is sent to the engraver it 
is marked somewhat as shown in Fig. 233, so that the instructions 
to the engraver may be explicit. Crayon marks specify by number 
the kind of Ben Day shading desired, and arrows point to the different 
areas to be shaded. This marking of instruction is done with a blue 



332 



GRAPHIC METHODS 



pencil because blue does not photograph easily and has such a small 
eflfect on a photographic plate that it does not spoil the copy for making 
a good zinc plate. In order to make the zinc plate from which Fig. 
233 was actually printed, a red pencil was used for the bottom portion 
of the illustration referring to Ben Day work. Red photographs as 
black, and a zinc plate was obtained which shows the marking such 
as would be used with a blue pencil when Ben Day work is ordered 
from an engraver. Ben Day work has been used on a great many illus- 
trations in this book, and it is believed that the reader will have no 
difficulty in distinguishing the cuts with Ben Day work from those 
cuts for which hand shading was used. 



(0 

N 
N 



CO 



O 
(0 



to <o 
w 2 



O 05 r- r» ^ lO 

«) lO 0) (0 jv» (0 

(0 o cu <o — ro 



,0 o 

IS 



cs^x^M 





? 

§ 



'^ ^ 1ft 






Fig- 233. Copy from Which a Zmc Plate Is to Be Made with Ben Day Mechanical 

Shading 

This is the copy from which the plate for Fig. 1 was made. The areas to receive the Ben Day work are 
designated by arrows and numbers naming the particular kind of shading desired. Sample books give 
a wide choice of shadings. The markings on the face of the copy regarding the Ben Day work are made 
with blue pencil, since blue does not photograph dark enough to affect the line engraving 



GENERAL METHODS 



333 






There are a great many problems in graphic work which puzzle 
the person getting up a chart if there are three different variables 
to deal with. The problem, as ordinarily found, involves two differ- 
ent independent variables, and a dependent variable depending upon 
each of the two independent variables. Isometric drawings like Fig. 
235, or solid models such 
as are seen in Fig. 236 
and Fig. 237, can be 
used, but they require a 
great deal of labor and 
care to make and are 
accordingly not often 
seen. There is another 
method not perhaps so 
obvious as a solid model 
but nevertheless of great 
value. When the data 
follow any definite nat- 
ural laws a chart on the 
style of Fig. 234 is often 
simple to make and easy 
to interpret. By such 
charts many computa- 
tions may be made with 
accuracy and ease. 




UmmjH //m/a 

Courtesy of Data. Cfiicago 

Fig. 234. Chart for Obtaining the Weight of Steel 
Plates 3 s-inch Thick and of Various Widths and 
Lengths 

A chart of this general type permits using three variables. The two 
independent variables here are length and width. Weight is the 
dependent variable. This kind of chart is much simpler to 
construct than an isometric drawing like Fig. 167, or a model like 
Fig. 236 or Fig. 237 



In obtaining curves like those shown in Fig. 234 one of the variables 
is made some constant quantity, and the other two variables are then 
used to work out the data from which the curve is drawn. It can be 
seen, for instance, that if a definite weight and length of steel plate 
Vs inch thick is assumed, the width is absolutely fixed. To obtain a 
curve like that seen for 5 pounds in Fig. 234, it is necessary only to 
assume a weight of 5 pounds, then choose separate lengths one by one, 
and compute the widths which would correspond with the lengths 
selected to give a weight of 5 pounds. The various figures of width 
obtained are then plotted as points for the 5-pound curve, and a smooth 
curve is drawn through all of the points, giving the result seen in the 
illustration. After one curve has been plotted another weight is 
assumed in a similar manner, and new computations are made for 
various lengths on the horizontal scale. Though this method of chart- 



334 



GRAPHIC METHODS 



ing requires some little labor in making the various computations, it is 
a very excellent one where the chart must be used for frequent reference. 
The information from such a chart as seen in Fig. 234 may be read from 
any portion of the chart, even though the intersection of the length and 
width lines for the size of the plate under consideration does not fall on 
one of the curve lines drawn. It can be seen for the example stated in 
the lower left-hand corner of the chart that the intersection of the ver- 
tical and horizontal lines of the independent variables falls halfway 
between the curve for 20 pounds and the curve for 25 pounds. 

The weight is accord- 
ingly taken as 223^ 
pounds. 

Though the sub- 
ject cannot be fully 
gone into here, it may 
be suggested for those 
who care to consider 
further the general 
type of charts repre- 
sented by Fig. 234, 
that much work may 
be saved by making 
such charts on loga- 
rithmic paper. This 
subject has been dis- 
cussed at greater length 
in a preceding chapter. 
There are many classes 
of data which, when 
plotted on ordinary 
squared co-ordinate 
paper, involve plotting 
many points to produce curves like those seen in Fig. 234, but 
for which the same data shown on paper with logarithmic ruling 
would give straight lines. When the curve lines are straight lines, it 
is necessary to plot only two points for each cvu've and then draw a 
line connecting those two points. This permits a very rapid construc- 
tion of the chart. A little practice in the making of charts is necessary 
before one can determine clearly the best method to use so as to produce 




Data of Guido H. Marx. Courtesy of the Standard Corporation. Philadelphia 

Fig. 235. Relations Between Arc of Action in Inches, 
Pitch Speed in Fee. per Minute, and Breaking 
Load in Pounds, for Cut Cast-iron Gears of Ten 
Diametral Pitch 

This illustration is drawn on isometric ruling, with the ruling itself 
seen only as a background so as to give the appearance of a solid 
model in three dimensions 



GENERAL METHODS 



335 



a simple chart. Paper having logarithmic ruling in both directions is 
the kind most frequently used for mathematical charts. Such paper 
can be purchased from almost any good store selling engineering sup- 
plies. Readers wishing to go further into the preparation of charts of 
this rather highly specialized character are referred to the excellent 
work of Mr. John B. Peddle, 
entitled "The Construction 
of Graphical Charts", pub- 
lished by the McGraw-Hill 
Book Company of New York 
City. 

The use of isometric pa- 
per for drawing charts repre- 
senting three dimensions 
was mentioned for Fig. 167. 
In Fig. 235 we have another 
application of this same iso- 
metric ruling. Instead of 
"showing the whole sheet of 
isometrically ruled paper as 
a background. Fig. 235 shows 
only enough of the 
metric ruling to give the im- 
pression of three planes meet- 
ing like one corner of a box. 
The chart illustrating the 
data is drawn on the isomet- 
ric ruling so that it appears 




Data of E. 5. Farwell. Courtesy of the American Machinist 

iso- Fig. 236. Tests of a Direct-connected Fan and 
Engine. The Model Shows the Effect on the 
Efficiency of the Fan of Different Outlet Open- 
ings and of Different Speeds oif Operation 

Curves are plotted on cardboard by assuming constant values 
for one of the three variables, and then plotting the rela- 
tions for the other- two variables. Each of the curves is 
cut from the cardboard and slit halfway up or down the 
line for intersection with the cards at right angles to it. 
Cards are fitted together to give the effect seen above 



as though placed in a corner 

made by the three planes. Parallel ruled lines then permit reading the 
chart from any one of the three different scales. The dependent 
variable is made the vertical scale here, just as in most charts where 
there is only one independent variable instead of two. The use of the 
isometric ruling is not as common as it would be if it were more widelv 
realized how easily charts may be prepared to give the effect of solid 
models without the great labor which a solid model necessarily involves. 
Fig. 236 shows another method which may be used instead of the 
more laborious and costly solid model. Different curves are plotted 
by assuming at frequent intervals constant values for one of the vari- 



336 GRAPHIC METHODS 

ables of the data, and then plotting curves for the other two variables. 
These curves are made to the same scale on sheets of cardboard, and 
then the outline of the curve is cut out with shears so as to give 
a series of different cardboard curve sheets. The several sheets are 
carefully marked for their intersecting points, and are then cut half- 
way through in the upward and downward direction on the intersection 
lines so that the curve sheets may be fitted together to give an effect 
like that seen in Fig. 236. A cardboard exhibit on the scheme of Fig. 
236 is, in many cases, just as satisfactory as a solid model and it has 
the advantage of being quite easy to prepare without any special 
apparatus or materials being required. 

Fig. 237 shows a solid model of the type which may be considered 
the acme of graphic work when there are two independent variables. 
A model of this kind is ordinarily made of plaster of Paris, as that is a 
material easily handled and capable of being made into any shape 
desired. In making such a model the usual procedure would be to 
rule a flat board with lines at properly spaced intervals for each of the 
two horizontal scales. Computations made by methods similar to 
those described for Fig. 236 would give the value, on the vertical scale, 
for each set of conditions corresponding to the intersection of each two 
lines ruled for the base and showing the horizontal scales. In Fig. 237 
the cost computations can be considered to give points on curves drawn 
on the surface of the solid model. These curves correspond exactly 
with the curves drawn on cardboard in Fig. 236. In order to locate 
the curve points which determine the surface of a solid model like Fig. 
237, wires are driven into the bottom board at the intersection of the 
ruled lines of the two horizontal scales, and these wires are made just 
the proper length to represent the figures computed for the dependent 
variable. When all the wires are in position on the board, a box is 
made the right size for the base of the finished solid model, and with 
sides as high as the solid model is to be made. This box serves as a mold 
into which the wet plaster of Paris is poured. Care must be taken to 
have the bottom edges of the box fit well on the board so that the liquid 
plaster of Paris may not leak out. 

The powdered plaster of Paris may be obtained from any store 
selling building supplies, or from a drug store. Water is added and 
the mixture carefully stirred until it is free from lumps and of about 
the consistency of very thick cream. The fluid is poured into the 
box up to the desired height and allowed to stand for several hours 



GENERAL METHODS 



337 



or over night until it becomes thoroughly hard. The box is then 
removed. In order to get the shape of the model as seen in Fig. 237, 
the plaster of Paris is very carefully scraped away with a piece of 
tin or some other simple tool until the ends of the vertical wires just 
show through. Before the plaster of Paris is poured in, care should 
be taken to mark the different sides of the board so that it will be 



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R. E. Scott, in Harvard Engineering Journal 

Fig. 237. Three-dimensional Model Showing Cost of Light in 
Cents per 1,000 Candle-hours with 40-watt "Mazda" Lamps 
for Any Practicable Combination of Efficiency and Smashing 
Point. Price of the Lamp is 50 Cents and Cost of Electric 
Current is Assumed at 10 Cents per Kilowatt Hour 

Three variables are considered here. The two independent variables are repre- 
sented at the base of the model and the dependent variable, "cost", is read from 
the vertical scale. A model of this kind can be made from plaster of Paris 
by following the methods described in detail in this chapter 

known in which portions of the plaster of Paris block the greatest 
amount must be removed before the wires come in sight. Knowledge 
of the position of the wires in the block of plaster of Paris permits 
removing the plaster rapidly without danger of taking off too much. 
After the wires do come into sight, the model must be carefully scraped 
so that the surfaces will have uniform curves without any humps or 



338 GRAPHIC METHODS 

hollows. If all the surfaces are concave, as they are seen to be in 
Fig. 237, the scraping is rather a simple matter since the surfaces 
between the two wires are lower than the wires themselves. If a 
solid model were made for data such as that of Fig. 236, much care 
would be necessary, for in that case some of the surfaces are convex 
and it would be essential that enough material should be left between 
the different wires to permit giving the nicely rounded smooth surfaces 
which would correctly represent the data. When the surfaces have 
been scraped as nearly as possible to the proper shape they maj^ be 
smoothed by rubbing with fine sandpaper. The external flat faces 
of the model may also be sandpapered advantageously to remove 
any marks which niay remain from the surface of the box used as a 
mold. Lines such as are seen in Fig. 237 can be ruled on the surface 
and the different scales can be lettered by hand. A few coats of boiled 
linseed oil will harden the surface and give an attractive finish. 

In Fig. 237 the lines giving oval figures represent certain oper- 
ating conditions which, from experiment and from study of the model 
itself, have been found to be most desirable in practice. The oval 
lines show the limiting conditions best for actual practical operation, 
and give the real conclusions which the model itself greatly assists 
in portraying. Solid models and three-dimension charts like those 
shown are of supreme value in studies of complex data. It is to be 
regretted that these methods of presentation involve so much labor 
that they cannot be used as frequently as might be desired. 

In political campaigns frequent use is made of statistical informa- 
tion. Campaign orators use figures which sound impressive when 
combined with a certain amount of eloquence. Too many of the state- 
ments, however, tell only a portion of the whole truth, and that por- 
tion is, of course, assumed to be the portion which the speaker most 
desires to have put forward. It is not ordinarily feasible in a speech 
to give all the facts over a series of years so that the hearer may draw 
any conclusions for himself. The whole system is weak in that the 
audience are forced to depend too largely on the statements made 
by the orator, rather than to draw conclusions of their own from data 
which are warranted to be authentic. When we have a larger number 
of people who know how to read curves, it will be a simple matter 
to present the arguments of a political campaign by means of a pro- 
jecting lantern with properly prepared charts thrown on a screen. 
Even now the charts could probably be so made as to be understood 



GENERAL METHODS 339 

and correctly interpreted by the average person attending a political 
meeting, with resultant increase in the effectiveness of the arguments 
they support. 

In municipal campaigns, especially, the lantern talk could be of 
very great interest to the voters if the slides were carefully prepared 
and arranged in a logical sequence. By using simple methods of 
charting, almost any kind of facts could be portrayed so that they 
would surely be correctly understood. Concise statements in con- 
junction with the charts should, of course, be used, somewhat as the 
main titles are placed under the illustrations of this book. Slides 
showing snappy questions could be thrown on the screen rapidly, 
and the succeeding slides could then answer the questions. Recent 
public improvements, bridges, etc., could be illustrated by maps and 
actual photographs. Pictures of fire apparatus and views showing 
the efficiency of the street-cleaning methods, etc., could be used to 
add interest and to bring out certain points in regard to the operation 
of specific departments. There is no doubt that properly prepared 
lantern slides would have great weight with the voters, for lantern 
slides might seem to present a less biased point of view than would 
the average partisan campaign orator. 

In using lantern slides for campaign purposes it is not necessary 
to have a large hall for each showing of the lantern slides. Auto- 
mobiles could readily be equipped so that two cars could work to- 
gether. One auto would carry a screen, which could be very quickly 
put up, somewhat in the manner of a sail, when that part of the town 
had been reached where the lantern talk was to be given to a crowd 
in the street or on some vacant lot. The other automobile could carry 
the lantern on a stand between the front and rear seats. The power 
for the lantern would be obtained in the ordinary manner from tanks 
of oxygen and hydrogen carried in the car. A car containing the lan- 
tern equipment would be entirely self-contained and no electric wires 
or other attachments would be necessary. The lantern car would be 
stopped the proper distance away from the lantern screen on the 
other car, and the slides could be shown on the screen within three 
minutes after arrival in any desired section of the city. In thickly 
populated districts it would probably not be necessary to announce 
a political meeting of this kind, as word would be passed very rapidly 
that a lantern talk was in progress and the desired crowd would collect 
spontaneously. 



340 GRAPHIC METHODS 

One very great advantage of the lantern presentation in political 
work comes from the fact that after one good set of slides has been 
prepared, these slides may be duplicated at very small expense. Twen- 
ty or even fifty sets of slides might be shown in different parts of a 
city simultaneously on the last few nights just before election. The 
main candidates are never able to make speeches at all of the desired 
points during the last few days, and they probably always feel that the 
last days or hours before an election are the most valuable of the whole 
campaign. When many sets of lantern slides are made from the same 
original charts there is very little additional expense, and the number 
of people who may get the benefit of the carefully prepared slides is 
tremendously increased. In every city there are many young lawyers 
or business men who would be willing to make a speech to accompany 
the slides if they could depend upon the slides for their main material. 
The number of people who may be reached during the last few hours of 
a campaign is thus almost unlimited if the lantern-slide method of pres- 
entation is used. 

From the educational point of view, it would probably be very de- 
sirable to have lantern slides used in campaign work, because there 
would be a very great amount of valuable information conveyed by 
the slides shown. With lantern slides showing well prepared charts, 
probably ten times as much information could be absorbed by an au- 
dience as could be obtained by listening to the most expert campaign 
speaker. In addition, there would be the great advantage that the 
facts presented by lantern slides would be understood and remembered 
months after the oratory of a campaign speaker had lost its beguiling 
effect and his statements been forgotten. 

It need not be thought that lantern talks such as are suggested need 
be devoid of all those spectacular climaxes which are so common with a 
campaign orator. Whenever it is desired to raise some enthusiasm, a 
photograph of a candidate could be thrown on the screen and a cheer 
would be sure to follow. There is an almost unlimited field for the 
exercise of ingenuity in the preparing of campaign charts. The sets 
of slides would have tremendous educational value, as well as great 
power in presenting political arguments in such manner as would most 
positively affect the vote. 

Methods used by newspaper offices and political clubs for giving 
out election returns to great crowds in the streets on the night of elec- 
tion day are not all that they might be made if a little thought were 



GENERAL METHODS 341 

given to the subject. Though the projecting lantern is now used almost 
universally in presenting election returns in large cities, thus far the 
lantern slides give only very brief scrawled statements that certain 
cities or certain districts have gone for some particular candidate 
with some estimated plurality. A person coming out into the street 
after an evening at the theater has no way of knowing the import of 
the various telegraphic statements which may have been thrown on 
the screen earlier in the evening. It is only by watching the bulletin- 
board screen for half an hour or more that a newcomer is able to get any 
definite idea of how things are going. 

When arrangements have already been made for using a lantern to 
show the returns on a screen, it would cost comparatively little more 
to give election returns which would be of much interest to the whole 
gathering, as well as of great effectiveness in showing the situation 
clearly to any newcomer who might join the crowd. For a national 
election, slides could be prepared to the number of twenty -five or more, 
giving an outline map of the United States and showing only the State 
lines. As the returns come in, some man well acquainted with the 
political situation could summarize the telegrams received up to the 
last moment and give his opinion as to which candidates are leading 
each State. A person accustomed to coloring lantern slides could then 
immediately color in one of the map slides according to some key, so 
the colors red, green, yellow, etc., on different areas would show that 
certain candidates were ahead in those States or districts. For muni- 
cipal elections, the wards and different divisions of the city could be 
colored in exactly the same manner as suggested for the States. The 
appearance of the suggested map as thrown on a screen may be judged 
somewhat from the map seen in Fig. 177. It would add much to the 
enthusiasm of the crowd if it were announced before election day that 
some well-known person would make the summary estimates from which 
the colored slides would be prepared. It would probably take less than 
fifteen minutes to color a lantern slide after the summary had been made 
up by the person watching the telegrams, and it would be feasible to 
show on the slide itself the hour at which the slide "went to press", 
as 9.30 p.m., 9.45 p.m., etc. As a new slide could be prepared about 
every fifteen minutes, a map summary shown on the screen need be 
only about fifteen minutes behind the latest telegraphic reports. 

In addition to the actual colored map, each slide should contain 
colored bars which would show by their length the estimated summary 



342 GRAPHIC METHODS 

of all the States or districts, so that the totals of different candidates 
might be easily compared. Thus, in a presidential election, the count- 
ing of the number of States for each candidate does not by any means 
give the whole story. The important thing is the number of electoral 
votes, and these would be best represented by the bar summary which 
would take into account the number of electoral votes of each State 
estimated as won by any candidate. With the combination slide show- 
ing, in the form of bars, both a map and estimated totals, any person 
coming out of the theater to join the election-night crowd could see 
instantly how the situation stood up to the moment the last slide was 
colored. 

With the election-return method outlined, the concise telegrams 
in handwriting would still be shown on the screen one by one as the 
news came in over the wire. A popular appeal to a large crowd can 
always be made by snappy statements such as "Jones concedes Chicago 
to Smith", or "California goes for Brown". Instead of holding state- 
ments of this kind on the screen until other news could arrive, however, 
any statement in written words would be taken off as soon as it had been 
grasped by the crowd and one of the colored maps would be thrown on 
the screen. Slides with colored maps and colored bars would be used 
as fillers, to be kept on the screen continuously whenever there were 
no telegraphic reports to be projected on the screen in written words. 
It would probably be found desirable, in many cases, to show telegraphic 
reports in such manner that a map would be thrown on the screen be- 
tween each two telegraphic reports, and also held on the screen whenever 
telegraphic reports should not come in fast enough. 

Election returns are sometimes told to a whole city by search lights 
thrown from the top of some high building. National, State, or munic- 
ipal election returns can be kept distinct by the search-light method if 
certain directions, north, east, south, or west are announced for the 
lantern beams referring to the different kinds of election returns. 
Until complete reports have been received the lantern beams can be 
moved gradually up and down. After complete reports are in the beam 
can be held steady, so that the watchers even miles away may know 
from the angle of the light and its position that a conclusion has been 
reached, and who wins. 

Educational material shown in parades gives an effective way for 
reaching vast numbers of people. Fig. 238 illustrates some of the floats 
used in presenting statistical information in the municipal parade by 



GENERAL METHODS 



343 




l-'holo by the l7U':rnatio?ial News Service 

Fig. 238. Statistical Exhibits in the Municipal Parade by the Employees of the City 

of New York, May 17, 1913 

Many very large charts, curves and other statistical displays were mounted on wagons in such manner that 
interpretation was possible from either side of the street. The Health Department, in particular, made 
excellent use of graphic methods, showing in most convincing manner how the death rate is being reduced 
by modern methods of sanitation and nursing 

the employees of the City of New York, May 17, 1913. The progress 
made in recent years by practically every city department was shown by 
comparative models, charts, or large printed statements which could 
be read with ease from either side of the street. Even though the day 
of the parade was rainy, great crowds lined the sidewalks. There can 
be no doubt that many of the thousands who saw the parade came away 
with the feeling that much is being accomplished to improve the condi- 
tions of municipal management. A great amount of work was neces- 
sary to prepare the exhibits, but the results gave ample reward. 



Chapter XVII 
A FEW CAUTIONS 

THE title for any chart presenting data in the graphic form should 
be so clear and so complete that the chart and its title could 
be removed from the context and yet give all the information 
necessary for a complete interpretation of the data. Charts which 
present new or especially interesting facts are very frequently copied 
by many magazines. A chart with its title should be considered a 
unit, so that anyone wishing to make an abstract of the article in 
which the chart appears could safely transfer the chart and its title for 
use elsewhere. In the preparation of this book it has been found that 
a number of the charts used have been copied from one magazine to 
another, and that the titles under the charts have suffered much in the 
copying. This is due chiefly to the fact that the titles are not considered 
as an integral part of a chart, and that many magazine editors feel at 
liberty to use for a chart whatever title they happen to see fit. If 
each chart as first presented has a complete and clear title it will greatly 
assist in establishing a practice that anyone making a copy of a chart 
should copy the title as well as the chart itself. 

It is unfortunate that so many authors send in illustrations or charts 
for magazine articles without the titles to be used with the illustra- 
tions when printed. This often forces the editor to make the titles, 
and if he does not have complete information before him he cannot be 
blamed if he makes a mistake by using a title which does not correctly 
represent the data of the chart. To avoid the possibility of error, 
the editor may use only the most brief title under the illustration, and 
then trust to the chart being fully described in the context which goes 
with it. In such a case, the reader who may happen to be especially 
interested in the chart is forced to plow through a great quantity of 
context to find the particular paragraph which may happen to explain 
the chart. Though it is true that great care is necessary to give in a 

344 



A FEW CAUTIONS 



345 




!of $500 

wife of 

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In 18S1 

(VBd In 
be late 



ay 

. slig-hi,. ,,i3 sail. 
s he contributed. 
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fided to her that She had thou 
sfeen Mrs. Hayden yesterday 
noon in New To»-i<. 




KANSAS P ROUD OF RECORD. 

Has Reduced Drinking 2,000 Per 

Cent. In 30 Years — Jails Are Empty. 

Speciat it The New York Times. 

TOPEKAv Sept. 18.— That Kansas has 
reduced Its drinking 2,000 per cent. In 
thirty years, and Its per capita consump- 
tion of Mquora Is tiow $1.48 as compared 
with Missouri's $24 a yearj Is the mes- 
Ba^ sent to Tennessee to-day by John 
S. Dawson, Attorney General. Tennessee 
iida a prohibition fitrht on its hands this 
Fall. 

" The test of value of prohibition 

I- tv- 



Re 
Bureau^ 
day dei 
as Btrlc 
p.lm up 
downw- 
dlrectlj 

Admii 
present 
nary 
asalr 



D*' 



few words a title for a complex chart, the result is well worth the effort 
and a chart should not be considered complete until such a title has 
been made. 

When large numbers 
of curves and charts are 
used by a corporation, 
it will be found advan- 
tageous to have certain 
standard abbreviations 
and symbols on the face 
of the chart so that in- 
formation may be given 
in condensed form as a 
signal to anyone reading 
the charts. Fig. 240 is 
shown here as an ex- 
cellent example of what 
may be done in mak- 
ing symbols which would 
be instantly understood 
by anyone seeing them. 
Though these particular 
symbols are not fitted for use in chart drawing, they may give a sugges- 
tion of the possibilities which exist for abbreviating into symbol form 
certain remarks or instructions, which it may be frequently convenient 
to place on the face of a chart as a guide to prevent misinterpretation 
by the reader. If the symbols for chart work are not too numerous, 
they would very soon be understood by each of the persons who 
regularly go over the operating charts of a company. 

It may be well to point out here that very large charts are sometimes 
a disadvantage rather than an advantage. In preparing reports, 
especially those reports which are used in typewritten form for limited 
distribution, there is a tendency to accompany the typewritten report 
with charts on very large sheets of paper, bulky and inconvenient to 
handle. Sometimes the scales of these accompanying charts are so 
large that the reader is puzzled to get clearly in his mind what the whole 
chart is driving at. There is a possibility of making a simple chart on 
such a large scale that the mere size of the chart adds to its complexity 
by causing the reader to glance from one side of the chart to the other 



Fig. 239. A Clear and Accurate Title is of Great 
Importance 

The clipping above, taken from the front page of a very prom- 
inent newspaper, shows an absurd title. If a thing is reduced 
100 per cent, it is all gone. How can drinking be reduced 
2,000 per cent.? 



346 



GRAPHIC METHODS 




SHARP TURN TO TXE RICMT 

t a-. lUi 



SHARP TURN TO THE LEFT 
£ S: ffi 



STEEP DESCEHT 

S; » iS « 



STEEP ASCENT 



vyin 




SHUP TURN AND DESCENT 




SERPENTINE 



MAD UNSUITABLE FOR CARS 



RAILWAY CROSSINt 



OANtEROUS ROAD CROSSINB 

Courtesy of "Motor" 



Fig. 240. International Road Signs that Are Being Erected on the Highways of Japan 

by the Nippon Automobile Club 

Any conventional symbols or signals adopted for use in graphic work should be as clear and suggestive as it 
is possible to make them. The above illustration is shown here as an admirable example of good prac- 
tice in the making of graphic symbols 

in trying to get a condensed visualization of the chart. There are 
relatively few curve charts which cannot be presented for report pur- 
poses on paper 8j^ by 11 inches, the commonest size used for a type- 
writer. Though the placing of a chart on paper of typewriter size 
requires more care than is necessary if a very large sheet of paper is used, 
the resulting chart is frequently more easy to interpret than it would 
be if made to a larger scale. 

A warning seems justifiable that the background of a chart should 
not be made any more prominent than actually necessary. Many 
charts have such heavy co-ordinate ruling and such relatively narrow 
lines for curves or other data that the real facts the chart is intended to 
portray do not stand out clearly from the background. No more co- 
ordinate lines should be used than are absolutely necessary to guide 
the eye of the reader and to permit an easy reading of the curves. Too 



A FEW CAUTIONS 



347 



many magazine articles and transactions of scientific societies contain 
charts which are reproduced direct from finely ruled co-ordinate paper 
and show all of the lines of the co-ordinate paper in the finished illus- 
tration. Co-ordinate ruling does not appear prominently on most 
original charts because the ruling is usually printed in some color of ink 
distinct from the curve itself. When, however, a chart is reproduced 
in a line engraving the co-ordinate lines come out the same color as the 
curve or other important data, and there may be too little contrast to 
assist the reader. 

Curves are sometimes shown plotted vertically when a horizontal 
arrangement could be used without any difficulty. There seems to be no 



1910 
1911 

1912 
1913 

1910 

1911 
1912 

1913 

1910 
1911 
1912 
1913 



. Cy/inder Bore^ </ ^ ^ 


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ValvG Arranaemenf . ^ . ^ 

10% 3o% 30% -fofo so^ 6o% ro7' ao% 90/& 




Ignition Systems -^ ^ ^ 

/o% ao% 3o7/ 4ofo so% eo7o 7o7o sojo soy<, 


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Fig. 241. Comparison of American Automobiles for Four Years, in Cylinder Bore, 
Valve Arrangement, and Ignition System 

There is no necessity for plotting curves in the vertical position shown here for it is only confusing to the 
reader. These curves cannot be read conveniently even by turning the book to read from the left 
because some of the type would then be upside down. See Fig. U'i 



348 



GRAPHIC METHODS 



real reason why Fig. 241 should have the curves arranged in the ver- 
tical direction. The vertical arrangement confuses the reader until 
he ascertains how the curves may be read by turning the book so that 
the curves may be read from the left in their proper position. 

Fig. 242 shows the data of Fig. 241 plotted in standard manner 
Fig. 242 is also of interest because it shows curves plotted from only 
a few points for each curve. Though one may be tempted to use 
some other method than curve presentation when only few points 



Per Cent 
lOO 



90 



SO 



70 



60 



50 



40 



30 



20 



10 



O 




Percent 
100 



SO 



60 



70 



60 



50 



40 



30 



20 



10 























































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70 



60 



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40 



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20 



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19IO 1 1 



12 



13 



1910 II 



■|2 '13 1910 "1! 12 '13 



Cylinder 
Bore 



Valve 
Arrangement 



Ignition 
Systems 



Fig. 242. Comparison of American Automobiles for Four Years, in Cylinder Bore, 
Valve Arrangement, and Ignition System 

The standard arrangement of the curves on this chart permits easy reading. Notice that curves are per- 
fectly feasible as a method of presentation even though the^re are only a few points available for each curve 



A FEW CAUTIONS 



349 



for a curve are available, it can be seen that even if there were only 
three points instead of four in Fig. 242, the curve would still be valu- 
able to convey the desired information. In Fig. 53 and Fig. 54 methods 
are shown by which charts which are essentially curve charts may be 
drawn even though there are available only two points for each curve. 



Shoriuge 



1907 



'Surplus 




Shorfage 1908 



Surplus 





Box Can 



All Can. 



100,000 ZOO,000 



Shorfage 1910 




Surplus 



Bon Can 



All Can 



Shorloffe 1911 



Surplus 




loo.ooc zooooo 



American Railway Association 

Fig. 243. Freight-Car Shortage and Surplus in the United States for Four Years, 

1907 to 191 1, Inclusive 

The horizontal bars here are so numerous and are placed so close together that the charts have practically 
the general form of curves drawn vertically instead of horizontally. It would seem just as well to repre- 
sent the data by real curves drawn with the standard horizontal arrangement 

When curves become as widely understood as the bar method of 
presentation, it will be found that curves can be used advantageously 
in almost every case where it is now common to use either vertical 
or horizontal bars. 

In Fig. 243 the horizontal-bar method has been elaborated so that 
the resulting chart has practically the general effect which would 
be obtained by a curve chart. The reader who wishes to read Fig. 
243 in the form of curves is, however, forced to turn the book so that 
he may see the chart from the left with the curves running in a generally 
horizontal direction. The data would likely be just as well understood 
by railroad men if shown by real curves drawn in the standard manner. 



350 



GRAPHIC METHODS 



.^• 


18 
1896 


9718 
1898 


99 19 
1900 


01 IS 
1902 


0319 
1904 


0519 

1906 


0719 
1908 


(f9 19 
1910 


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— 



New York Times Annalist 

Fig. 244. Average per Capita in the 
United States of Total Savings-bank 
Deposits 

At first glance the impression is that Americans are 
growing rich very rapidly. Yet total deposits 
per capita have not doubled in the sixteen years 
shown. If the bottom line of the chart were at 
the zero of the vertical scale, an entirely different 
impression would be given. See Fig. 245 



At numerous places through- 
out this book criticisms have 
been made of curves and charts 
in which no zero hne for the 
vertical scale was shown on the 
chart. Though this subject has 
been mentioned elsewhere it seems 
best to show here a few examples 
on the same general argument. 
In Fig. 244 the first glance im- 
pression that savings-banks de- 
posits have increased with great 
rapidity is not entirely confirmed 
when it is noticed that the left- 
hand scale does not begin anywhere 
near zero. It is nearly always 
possible to make a chart so that 
the zero of the vertical scale will show. Usually, of course, the zero 
line is at the bottom of the chart unless there are negative quantities 
so that the curve crosses over the zero line and extends below it. 
In all cases the zero line can be made a heavy line. If the curve should 
extend below the zero line the width of the zero line should be ' so 
great that the reader will be cer- 
tain to interpret the chart from 
the zero line rather than from 
the bottom line of the chart it- 
self. 

It sometimes happens that the 
data for a chart involve high numeri- 
cal figures so that a large amount 
of space must be used if the zero 
line of the vertical scale is to be 
shown in the final illustration. In 
such a case, the bottom of the chart 
may have a wavy line as seen in 
Fig. 245 which portrays the same 
data as Fig. 244. Fig. 244 could 
have been extended so that the bot- 
tom line would be the zero line if a 



$ 


1896 


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1S98 


9.9 19 
1900 


01 19 
1902 


0319 
1904 


05 Id 
1906 


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1908 


09 19 

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Fig. 245. Average per Capita of Total 
Savings-bank Deposits in the United 
States 

Whenever possible a chart containing curves should 
be so drawn that the zero of the vertical scale 
appears in the chart. If the zero line is not 
shown on the chart, that fact should be indicated 
by a wavy line at the bottom warning the reader 
that interpretation must be made from the ver- 
tical scale and not by visual measurement from 
the bottom line of the chart 



A FEW CAUTIONS 



351 



teathmt 


Indicatinq ll^CREASE In Deaths trom Degenerative Diseases and DECREASE from Tuberculosis 




18 30 1890 1900 IfllO 


38 
36 


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38 


54 


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16 
14 



Elmer Rittenhouse, in the New York Times 

Pig. 246. Comparison of Death Rates in the United States, Showing Reduction in 
Death Rate for Tuberculosis and Increase in Death Rate for Degenerative Dis- 
eases 

The chart gives the impression of very rapid decreases and increases, chiefly because the bottom line is 
not at the zero of the vertical scale. The figures used for the vertical scale are rather small in size and 
the rapid reader is not likely to notice that the scale does not begin at zero. Compare Fig. 2-17 and Fig. 
248 



somewhat greater amount of photographic reduction had been used 
in making the hne engraving or if the proportions between the hori- 
zontal- and vertical-scale distances had been changed somewhat. 
There is really no necessity for using the wavy line for the bottom 
of Fig. 245 since the chart would have been better made with the 
zero line showing the bottom. Fig. 245 will serve, however, as an 
example to illustrate how the wavy line can be drawn to any chart 
where it is really inconvenient to extend the chart itself so that the 
zero line may show. 



Death Rate 
Per lO.OOO 




leso 



1S90 

oTuberculosis 



300 



I910 



mmmimm Degenerat^ive Diseases 
(Heart-, Kidney, etc.^ 

Data of Elmer Rittenhouse 

Fig. 247. Comparison of Death Rates in the United States, Showing Reduction in 
Death Rate for Tuberculosis and Increase in Death Rate for Degenerative Dis- 
eases 

This chart is made from the same data as Fig. 246. Here the zero line is shown and the changes in death 
rate appear much less rapid than they do in Fig. 246. See also Fig. 248 



352 



GRAPHIC METHODS 



Fig. 246 gives another example where neglecting to show the zero 
line may cause an entirely erroneous impression regarding the facts 
which the chart is intended to bring out. The failure to show the 
zero line at the bottom of a chart is so common a fault, found in nearly 
all publications, that some typical examples are shown here in the 
hope that a bad practice may be somewhat reduced. 

Fig. 247 gives the data of Fig. 246 redrawn so that the zero line 
is shown at the bottom of the chart. It is believed that this illustra- 
tion will prove conclusively how great an error may be made if charts 
are read hastily on the assumption that the bottom line of the chart 
is the zero line. Since some persons are almost sure to read a chart 
from the bottom line, it seems desirable that all charts should be so 
made that the reader may interpret from the bottom line as a zero 
line, or else receive positive warning that he should not do so. 



temimi Indicating INCREASE In Deaths from Degenerative Diseases end DECREASE fivm Tubenulosjs 



ferinm 



1666 



1890 




Data of Elmer Rittenftouse 



Fig. 248. Comparison of Death Rates in the United States, Showing Reduction in 
Death Rate for Tuberculosis and Increase in Death Rate for Degenerative Dis- 
eases 

This illustration is' identical with Fig. 246 except that here a wavy line is used at the base showing that the 
bottom of the chart is not at the zero of the vertical scale. It is always desu-able to have the bottom line 
at zero. If that is not possible the wavy line should be used as a warning to the reader 

Though there is no necessity for showing Fig. 246 without having 
a zero line at the bottom of the chart. Fig. 248 is presented here to 
prove how easj^ it is to make a wavy line at the bottom of a chart if 
there should be any real reason why the chart cannot be made so 
as to include the zero hue of the vertical scale. Fig. 248 is exactly 
the same as Fig. 246 except that the wavy hue is used instead of the 
straight line at the bottom. 

The beginner in curve plotting and in curve reading is apt to be 
somewhat puzzled by the different effects which may be obtained by 
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 plot- 



A FEW CAUTIONS 353 

ting 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 exaggerations unless the person 
preparing the charts uses as much care as he would ordinarily use to 
avoid exaggeration if presenting his material by written or spoken 
words. Most authors would greatly resent it if they were told that 
their writings contained great exaggerations, yet many of these same 
authors permit their work to be illustrated with charts which are 
so arranged as to cause an erroneous interpretation. If authors and 
editors will inspect their charts as carefully as they revise their written 
matter, we shall have, in a very short time, a standard of reliability 
in charts and illustrations just as high as now found in the average 
printed page. 

Fig. 249 shows an interesting application of the use of charts to 
corporation reports. The back page of the annual report of the Ameri- 
can Telephone and Telegraph Company has the proportions seen in 
Fig. 249. As a report to stockholders is intended to be as optimistic 
as possible within the limits of truthfulness, there can scarcely be any 
criticism that the chart was so made that the growth in business was 
shown on the long direction of the page instead of on the short dimen- 
sion of the page. The chart in Fig. 249 is simple to understand, and 
probably very few stockholders would have any difficulty in making a 
fairly accurate interpretation. For the annual report of a corporation, 
it is likely that the vertical-bar method of Fig. 249 is preferable, from 
an advertising standpoint, to a smooth curve like that shown in Fig. 250. 

One special point relating to Fig. 249 is worthy of mention. At the 
bottom of the chart will be noticed the statement that the figures re- 
corded are those of "January 1st of each year". This statement may 
lead to an erroneous conclusion on the part of the reader, for he may 
feel that the difference in height between the bar marked 1911 and that 
for 1912 shows the number of telephones installed during 1912, when, 
in reality, it shows the number of telephones installed during 1911, 
since the bars represent the number of 'phones installed to the first of 
January of each year. If the statement at the bottom of the chart had 
been made "December 31st of each year" there would be no danger 
of misinterpretation. If the statement were made for December 31 
it would, of course, be necessary to change the numbers at the bottom 



DIAGRAM 

SHOWING THE GROWTH IN 

SUBSCRIBERS' STATIONS 

CONNECTED TO THE SYSTEM 
OF THE 

BELL TELEPHONE 
COMPANIES 

FROM 

JAN. 1,1876— JAN. 1,1912. 



On January I, 1912, there was on. Bell Telaphond 

Station to each 14 of the Total Population Of the 

United Statu. 



1876 1878 1880 1882 1864 1886 1688 1890 )892 I 94 1896 1898 1900 1902 1904 1906 1908 1910 1912 
JANUARY 1st OF EACHYEAR. 



6,700.000 

6,600,000 

6,600,000 

6,400.000 

6,300,000 

6,200,000 

6,100,000 

6,000,000 

5.900.000 

6,800,000 

5,700,000 

6,600,000 

6,600,000 

6,400,000 

6,300,000 

6,200,000 

5,100,000 

6,000,000 

4,900,000 

4,800,000 

4,700.000 

4,600,000 

4,600.000 

4.400.000 

4,300,000 

4,200.000 

4,100,000(0 

4,000.000§ 

3,goo,ooop 

3,800,000 < 
3,700,000(0 
3,600.000. 
3,600.000^ 
3,400. OOOU 
3.3OO.OOO5 
3,200,000u 
3,100.000g 
3.000.000 3 
2,900,000"' 
2,800.000 g 
2.700.000 

2.600.000g 

2.500.000 m 

2,400.000 § 

2,300.000z 

2,200.000 

2,100.000 

2,000.000 

1,900,000 

1,800.000 

1,700,000 

1,600.000 

1,600.000 

1,400,000 

1,300,000 

1,200,000 

ItlOO.OOO 

1,000,000 

900.000 

800,000 

700,000 

600,000 

600,000 

400,000 

300,000 

200,000 

100,000 





Americo.n Telephone dc Telegraph Co. 

Fig. 249. The Number of Subscribers' Stations Connected to the System of the Bell 

Telephone Companies 

This illustration was shown on the back cover of the 1911 annual report to stockholders of the American 
Telephone & Telegraph Company. For the average stockholder the vertical bars would probably be 
understood more readily than the curve shown in Fig. 250. Compare with Fig. 250 and Fig. 251 

354 



6,700,000 
6,600,000 
6,600,000 
6,400,000 
6,300,000 
6,200,000 
6,100,000 
6,000,000 
6,900,000 
6,800,000 
6,700,000 
6,600,000 
6,600,000 
6,400,000 
6,300,000 
6,200,000 
6,100,000 
6,000,000 
4,900,000 
4,800,000 
4,700,000 
4,600,000 
4,500,000 
4,400,000 
4,300,000 
4,200,000 
4,100,000 
4,000,000 
3,900,000 
3,800,000 
3,700,000 
3,600,000 
3,600,000 
3,400,000 
3,300,000 
3,200,000 
3,100,000 
3,000,000 
2,900,000 
J!, 800,000 
2,700,000 
2,600,000 
2,600,000 
2,400,000 
2,300,000 
2,200,000 
2,100,000 
2,000,000 
1,900,000 
1,800,000 
1,700,000 
1,600,000 
1,600,000 
1,400,000 
1,300,000 
1,200,000 
1,100,000 
1,000,000 
900,000 
800,000 
700,000 
600,000 
600,000 
400,000 
300,000 
200,000 
100,000 


















f 




1 1 




1 




niAr^DAlU L 








SHOWING THE GROWTH ll\| / 








SUBSCRIBERS' STATIONS J 








CONNECTED TO THE SYSTEM f 




OF THE r 








BELL TELEPHONE T 








nnniPAiVTirc! x 




ljUJXirAllII!i3 j 




FROM T 




JAIV 1 1R7R IAN 1 1Q19 I 




0/Ul> ±f J.O/U — d/Ulal, Xyjuii 1 




1 




On Jinuary 1, 1912, there wa> one B«ll Tolaphons ~f' 












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6,700,000 
6,600,000 
6,500,000 
6,400,000 
6,300,000 
6,200,000 
6,100,000 
6,000,000 
5,900,000 
6,800,000 
5,700,000 
6,600,000 
5,600,000 
5,400,000 
5,300,000 
5,200,000 
5,100,000 
6,000,000 
4,300,000 
4,800,000 
4,700,000 
4,600,000 
4,500,000 
4,400,000 
4,300,000 
4,200,000 
4,100,000 
4,000,000 
3,900,000 
3,800,000 
3,700,000 
3,600,000 
3,600,000 
3,400,000 
3,300,000 
3,200,000 
3,100,000 
3,000,000 
2,900,000 
2,800,000 
2,700,000 
2,600,000 
2,600,000 
2,400,000 
2,300,000 
2,200,000 
2,100,000 
2,000,000 
1,900,000 
1,800,000 
1,700,000 
1,600,000 
1,500,000 
1,400,000 
1,300,000 
1,200,000 
1,100,000 
1,000,000 
900,000 
800,000 
700,000 
600,000 
600,000 
400,000 
300,000 
200,000 
100,000 




Fig. 250. The Number of Subscribers' Stations Connected to the System of the Bell 
Telephone Companies, December 31st of Each Year 

The curve permits quicker and more accurate interpretation than the vertical bars but unfortunately curves 
are not readily understood by as many people. Note that the date on which the telephones are recorded 
is here specified as December 31st instead of as January 1st. Compare Fig. 251 

355 



356 



GRAPHIC METHODS 




A FEW CAUTIONS 357 

of each vertical bar so that they would appear in each case one less than 
the figures given. With Fig. 249 as it is, the 1908 bar shows a great 
increase over 1907 and the reader is quite justified in wondering how 
it happened that a greatly increased number of telephones were installed 
during a panic year. From the chart as shown the reader is not likely 
to realize that 1908 is getting credit for the telephones installed during 
1907, which happened to be a very prosperous business year. Having 
the data recorded as of December 31 each year overcomes the difficulty 
and makes certain that no false impression can be obtained. 

Fig. 250 shows the data of Fig. 249 plotted as a smooth curve. For 
a trained class of readers the curve presentation is preferable to the bar 
presentation, for it permits seeing the fluctuations which have occurred 
from year to year more easily than they can be seen by glancing from 
bar to bar in Fig. 249. Within a few years it is probable that curves 
will be so well understood that a report to stockholders could best be 
made using the method of Fig. 250 instead of the method of Fig. 249. 

In order to show the different impressions which may be had if 
various proportions between the horizontal and vertical scales are used, 
Fig. 251 has been plotted from the same data as Fig. 249 and Fig. 250. 
For Fig. 251 an assumption was made that the chart would be printed 
on exactly the same size page as was used for Fig. 249. The scales for 
Fig. 250 were, however, arranged in the other direction on the page and 
the co-ordinate ruling was made so that some space would be allowed 
for extension of the curve in future years. As seen from Fig. 251 the 
growth in the telephone business does not appear nearly so rapid as 
would be thought from observing Fig. 250. Each of these charts is, 
however, plotted to exact scale and the difference in the impression 
obtained is caused only by the proportions of the vertical and the hori- 
zontal scales. The appearance of less rapid growth in Fig. 250 is 
assisted somewhat by the fact that the large-type title of the chart is 
arranged horizontally instead of in the form of a square as seen in Fig. 
250. The heavy black type with much greater spread horizontally 
than vertically tends to overshadow the curve itself and causes for the 
curve a more distinctly horizontal impression than would otherwise 
be obtained. A person reading charts must take great care 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 percentage increase 
or decrease as judged from the figures of the vertical scale. The proper 
choice of scales for curve plotting is largely a matter of judgment, and 



358 



GRAPHIC METHODS 



Courtesy of the Grolier Society 

Fig. 252. An Optical Illu- 
sion 

The black line at the left appears 
longer than the one at the right. 
The two lines are, however, of 
the same length 



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 
vertical and horizontal scales have been so selected that the chart gives 
\ ..•• a fair representation of the facts. 

The English language has so many 
words with double meaning and so many 
words for which the shades of meaning 
are rather indistinct that there are really 
many more chances of false impression 
from the written or spoken language than 
there are from the data expressed in graphic 
form. Nevertheless, a few examples of op- 
tical illusions are shown here so that the 
reader may have some idea of those peculiar 
things which may enter in to cause strange impressions if charts do not 
receive some degree of preliminary care and final inspection. Though 
many of the effects seen in Fig. 252, Fig. 253, Fig. 254, Fig. 255, and 
Fig. 256 are not likely to appear in 
ordinary chart work, they may not- 
withstanding cause difficulty in some 
kinds of very large wall exhibits. Fig. 
254, in particular, shows an effect which 
is to be avoided where large quan- 
tities of black ink are used. In a 
recent series of charts comparisons were 
made between different white squares, 
surrounded in each case by a black 
border practically as wide as the square at the center. It is not likely 
that a reader seeing a series of black squares with white centers of dif- 
ferent size would be able to judge correctly the relative size of the 

white squares at the center. 

Fig. 256 shows some of the difficulties 
which may be encountered if an attempt 
is made to present data by comparing the 
relative heights of pictures of the human form. 
courtesy or the Grolier society Therc arc fcw pcoplc who will beheve until 
Fig. 254. An Optical lUu- ^^ ^^^^ measurements that the figure 

The white square appears larger of the girl lU Fig. 256 IS really of greater 
than the black one, yet the two -i ,-• ,i ,i ■ j? . i t mi -n 

are of the same size length than that ot the policeman. The illusion 



Courtesy of the Grolier Society 

Fig. 253. An Optical Illusion 

The left-hand arrangement looks wider than 
it is high while the right-hand arrange- 
ment looks higher than it is wide. On 
each side the height is the same as the 
width 




A FEW CAUTIONS 



359 



is caused chiefly by the perspective hnes of the drawing which force 

one to estimate relative height to a certain extent by the number of 

perspective hnes intersected instead of by the actual size of the black 

pictures. 

Before charts are sent to an engraver to 

have plates made for printing it is wise to 

have each chart run the gauntlet of a series of 

questions, so that the time of the person doing 

the checking may be saved and also that the 

points more frequently overlooked may be 

thoroughly considered in each case. Below are 

given a series of questions which may be found 

convenient to anyone having charts to prepare. 

This list is not by any means complete, and 

the questions are given here as general sugges- 
tions only. The person checking a chart simply 

reads the ques- 
tions one by one 
from the book, 
and then care- 
fully observes 
the chart to see 
whether it comes 
up to the stand- 
ard. Whenever 
possible it is well 
to have the chart 



mm^ 





% .w^ 'mm. 

Courtesy of the Grolier Society 

Fig- 255. An Optical 
Illusion 

checked by some The columns appear bent The 

•^ left-hand pair seem closest 

person other than ?t the ends, while the right 



hand pair seem closest at 
the center. The sides of the 
columns are really straight 
and parallel 



the one who drew 
it. In every edi- 
torial office the 

fact is recognized that one proof-reader 
will find important errors that were 
overlooked by another reader equally 
expert. Further, a mind much occupied 
with an idea may often fail to see important gaps in its statement, 
verbal or graphic, until perhaps they are noted by someone less familiar 
with the subject. Two points of view are always better than one. 



Courtesy of the Orolier Society and of Popular Mechanics 

Fig. 256. An Optical Illusion 

The policeman appears much taller than the 
girl. In reality the figure of the girl is ^\ 
inch taller than the figure of the policeman 



360 GRAPHIC METHODS 

CHECKING LIST FOR GRAPHIC PRESENTATIONS 

1. Are the data of the chart correct? 

2. Has the best method been used for showing the data? 

3. Are the proportions of the chart the best possible to show the 
data? ,, 

4. When the chart is reduced in size will the proportions be those 
best suited to the space in which it must be printed? 

5. Are the proportions such that there will be sufficient space for 
the title of the chart when the chart has been reduced to final printing 
size? ,, . 

6. Are all scales in place? 

7. Have the scales been selected and placed in the best possible 
manner? 

8. Are the points accurately plotted? ; 

9. Are the numerical figures for the data shown as a portion of the 
chart? 

10. Have the figures for the data been copied correctly? 

11. Can the figures for the data be added and the total shown? 

12. Are all dates accurately shown? 

13. Is the zero of the vertical scale shown on the chart? 

14. Are all zero lines and the 100 per cent lines made broad enough? 

15. Are all lines on the chart broad enough to stand the reduction 
to the size used in printing? 

16. Does lettering appear large enough and black enough when 
seen under a reducing glass in the size which will be used for printing? 

17. Is all the lettering placed on the chart in the proper directions 
for reading? 

18. Is cross-hatching well made with lines evenly spaced? 

19. Can Ben Day work be used advantageously instead of cross- 
hatching? 

20. Do the Ben Day shadings selected have sufficient contrast? 

21. Are all instructions for Ben Day work given so that it will be 
impossible for the engraver to make a mistake? 

22. Are dimension lines used wherever advantageous? 

23. Is a key or legend necessary? 

24. Does the key or legend correspond with the drawing? 

25. Is there a complete title, clear and concise? 

26. Is the drafting work of good quality? 



A FEW CAUTIONS 361 

27. Have all pencil lines which might show in the engraving been 
erased? 

28. Is there any portion of the illustration which should be cropped 
off to save space.'' 

29. Are the instructions for the final size of the plate so given 
that the engraver cannot make a mistake.'' 

30. Is the chart in every way ready to mark "O.K"? 

The English language has a grammar with hundreds of detailed 
rules concerning almost every possible construction. Though graphic 
presentations are used to a very large extent to-day there are at present 
no standard rules by which the person preparing a chart may know 
that he is following good practice. This is unfortunate because it 
permits every one making a chart to follow his own sweet will. Many 
charts are being put out to-day from which it would seem that the person 
making them had tried deliberately to get up some method as different 
as possible from any which had ever been used previously. Anyone 
of us would be thought of as a freak instead of as a genius, if he tried 
to invent his own constructions for the English language and to place 
words in some order never before seen, yet many persons are doing 
something akin to this when they attempt to present data by some 
new and outlandish method of charting. Below are given a few rules 
which may be of assistance toward getting graphic presentations more 
on a standard basis so that they may be instantly read. These rules 
are included here simply as suggestions, and they should be considered 
as only tentative until such time as definite rules have been agreed 
upon and sanctioned by authoritative bodies. 

RULES FOR GRAPHIC PRESENTATION 

1. Avoid using areas or volumes when representing quantities. 
Presentations read from only one dimension are the least likely to 
be misinterpreted. 

2. The general arrangement of a chart should proceed from left to 
right. 

3. Figures for the horizontal scale should always be placed at the 
bottom of a chart. If needed, a scale may be placed at the top also. 

4. Figures for the vertical scale should always be placed at the left 
of a chart. If needed, a scale may be placed at the right also. 

5. Whenever possible, include in the chart the numerical data from 
which the chart was made. 



362 GRAPHIC METHODS 

6. If numerical data cannot be included in the chart, it is well to 
show the numerical data in tabular form accompanying the chart. 

7. All lettering and all figures on a chart should be placed so as to 
be read from the base or from the right-hand edge of the chart. 

8. A column of figures relating to dates should be arranged with the 
earliest date at the top. 

9. Separate columns of figures, with each column relating to a 
different date, should be arranged to show the column for the earliest 
date at the left. 

10. When charts are colored, the color green should be used to 
indicate features which are desirable or which are commended, and red 
for features which are undesirable or criticized adversely. 

11. For most charts, and for all curves, the independent variable 
should be shown in the horizontal direction. 

12. As a general rule, the horizontal scale for curves should read 
from left to right and the vertical scale from bottom to top. 

13. For curves drawn on arithmetically ruled paper, the vertical 
scale, whenever possible, should be so selected that the zero line will 
show on the chart. , 

14. The zero line of the vertical scale for a curve should be a much 
broader line than the average co-ordinate lines. 

15. If the zero line of the vertical scale cannot be shown at the 
bottom of a curve chart, the bottom line should be a slightly wavy 
line indicating that the field has been broken off and does not reach to 
zero. 

16. When curves are drawn on logarithmically ruled paper, the 
bottom line and the top line of the chart should each be at some power 
of ten on the vertical scale. 

17. When the scale of a curve chart refers to percentages, the line 
at 100 per cent should be a broad line of the same width as a zero line. 

18. If the horizontal scale for a curve begins at zero, the vertical 
line at zero (usually the left-hand edge of the field) should be a broad 
line. 

19. When the horizontal scale expresses time, the lines at the left- 
and right-hand edges of a curve chart should not be made heavy, since 
a chart cannot be made to include the beginning or the end of time. 

20. When curves are to be printed, do not show any more co- 
ordinate lines than necessary for the data and to guide the eye. Lines 
l^:;i^-inch apart are sufficient to guide the eye. 



A FEW CAUTIONS 363 

21. Make curves with much broader lines than the co-ordinate 
ruhng so that the curves may be clearly distinguished from the back- 
ground. 

22. Whenever possible have a vertical line of the co-ordinate ruling 
for each point plotted on a curve so that the vertical lines may show the 
frequency of the data observations. 

23. If there are not too many curves drawn in one field it is desirable 
to show at the top of the chart the figures representing the value of 
each point plotted in a curve. 

24. When figures are given at the top of a chart for each point in a 
curve, have the figures added if possible to show yearly totals or other 
totals which may be useful in reading. 

25. Make the title of a chart so complete and so clear that misinter- 
pretation will be impossible. 

The American Society of Mechanical Engineers has invited about 
fifteen of the societies of national scope in America to co-operate in a 
Joint Committee on Standards for Graphic Presentation. The societies 
included are largely societies whose members have extensive use for 
graphic presentation in their daily work. One member from each 
society will be on this committee. It is hoped that the committee will be 
able to recommend a small number of brief and simple rules which may 
be used as a sort of grammar by persons who have graphic presentations 
to prepare and to interpret. Reports from this joint committee should 
be watched for so that any rules which may be agreed upon may be 
put into effect as soon as possible. 

Improvements in the means of transportation by water, rail, auto- 
mobile, wire, and wireless in recent years have caused a tremendous 
increase in the amount of printed matter and the amount of statistical 
material read by the average person. Newspapers and magazines are 
daily presenting more and more statistical information. If we study 
the subject even a little, it will be seen that each of us deals daily with a 
vast number of facts of a quantitative nature which could preferably 
be presented in graphic form. When graphic methods are more widely 
used for portraying quantitative facts, there will be a tremendous gain 
to accuracy of thought as well as a great saving of that most valuable 
thing in the world — time. 

THE END 



INDEX 



Abbreviations for chart work, 345, 346 
Accidents, as affected by daylight, 140 

in industrial plants, 144, 145 

on railroads of United States, 134, 135 
Accountants, viewpoint of, 300 
Accuracy and significant figures, 326 
Acker, Merrall & Condit Co., 116 
Adding machines, pocket, 325 
Advertising, bead maps for, 253 

maps for, 238, 239 

use of curves for, 77, 78 
Allen, William H., 250 
American Jersey Cattle Club, 278 
American Machinist, 335 
American Railway Association, 349 
American Review of Reviews, 46, 47, 229, 231 
American Society of Mechanical Engineers, 

ii, 31, 52, 54, 122, 363 
American Statistical Association, 167, 176, 

197 
American Telephone & Telegraph Co., 5, 

179, 240, 309, 353, 354, 355, 356 
Analysis of sales, 188 
Angle of a cumulative curve, 150 

of a curve, 131 
Annalist, the, see Neiv York Times Annalist 
Annual reports, corporation, 307 
Apples, price curves of, 127, 128, 129 
Arithmetically ruled co-ordinate paper, 132 
Atlas of the U. S. Census, see Statistical 

Atlas 
Atomizer for spraying ink, 57 
Authorization for curve records, 284 
Automobile exports of United States, 41, 43 

factory records, 263 

factory schedule curves, 150 

sales records, 255, 264 
Automobiles, comparison of, 347, 348 
Averages, moving, 97, 283 

progressive, 153 

weighted, 103 

Babson, Roger W., 120, 121 
Bacteria in river water, 20 

in river water at varying depths, 85 



Bald Eagle Valley Railroad, 67 
Bar diagrams versus curves, 310 
Bars combined with a curve, 54 

certain made prominent, 29, 30 

for use in comparison, 22 

horizontal, 4 

horizontal, representing time, 53 

vertical, 46, 47 

vertical, for components, 138 
Bead maps, 251 
Beads for map use, 247, 248 

for statistical charts, 207 
Bell Telephone system, 353, 354, 355, 356 
Ben Day shading, 216, 220, 331, 332 

shading on maps, 209 

work, 331, 332 
Bertillon, 220 

Biologists, use of curves by, 203 
Biometrika, 202 
Blue-printing, 328 

cards, 259, 261 

curve cards, 291, 296 

machines, 261, 296 
Boards for pin records of costs, 191, 192 
Bonus earned chart, 52, 54 
Boston Elevated Railroad, 4 
Boston Globe, 212 

Boston Health Department Report, 30, 109 
Bowley, Arthur L., ii, 98 
Breaks in drawings, 190 
Bridges, drawing, upon photographs, 209 
Brotherhood of Railroad Trainmen, 103 
Building construction in United States, 120, 

121 
Buildings, maps for showing height of, 220 
Bureau of Railway Economics, 257 
Butter-fat curves, 279 

Camera lenses, 330 

Cameras, motion picture, for time study, 50 
Campaigns, political, 338 
Car-floats, dispatching, 61, 62 
Cars, shortage and surplus, 349 
Cardboard for blue-printing, 259, 261 
models, 336 



365 



366 



GRAPHIC METHODS 



Card-sorting machines, 322 
Cards for blue-printing, 259, 261 

for curve-plotting, 256 

for curves, 275 

for tabulating machines, 320 
Cards, information, 287 
Carson, John M., 326 
Cartoon drawings, 20, 21 
Cattle distribution in United States, 215 
Cautions, a few, 344 

Celluloid-covered tacks for maps, 247, 248 
Celluloid, erasing drawings from, 210 

flags for maps, 247 

for drawings with maps, 210 

for mounting maps, 210 

tacks for writing, 247, 248 
Cement plants in United States, 243 

price of for thirty years, 77 
Census Abstract, 218 

Census Atlas of United States. See Statis- 
tical Atlas 
Census-Office methods, 320, 321 
Census tabulating card, 320 
Charts, best size for, 345 

in political campaigns, 338 

on walls, 306 
Checking list for graphic work, 359, 360 
Chicago Burlington & Quincy Railroad, 

40 
Chicago pin map for population, 246 
Chicago telephone rates, 126 
Choice of scales, 352 

Cincinnati, homes of factory workers, 214 
Circle and sectors, 5 
Circles compared, 36, 37 
Clamps for hanging maps, 232 
Cleveland Plain Dealer, 92 
Cloak and suit industry in New York, 166 
Coals, comparative value of, 88 
Coloring maps, 209 
Color-printing, 5, 331 
Colors for chart work, 57 
Columns of figures, order for, 45 
Combined curves, 125 
Commerce of the United States, 70, 71 

of the world, 76 
Commercial geography, 21 
Commercial Museum of Philadelphia, 70, 

74, 76, 112 
Commission on Economy and Efficiency, 

33, 34 
Comparisons, 20 

involving time, 36 
Comparison of curves, 107 
Compo-board, 232 



Component parts, 1 

parts grouped, 33 

parts shown by curves, 138 
Compound-interest curve, 131 
Conjugal condition of population, 9 

of population of United States, 168, 169 
Construction of graphical charts, 335 
Co-ordinate lines, spacing of, 362 

paper, 55 

paper for weekly records, 150 

paper, universal, 60 

ruling, 284 
Copper production, 26 
Copying drawings, 329 
Copyrights on maps, 237 
Cork composition for map mounting, 232 
Corn crop in United States, 44 

planting dates in United States, 213 

yield and rainfall, 124 

yield per acre in United States, 217 
Corporation directors, 289, 298 

executives, 28D 

financial reports, 307 

record department, 292 
Correlation, 129, 199 

definition of, 199 
Corrugated straw-board for map pins, 191 
Cost analysis by pin boards, 191, 192 

of handling freight, 184, 188, 192 
Cotton goods, production and export, 74, 

75 
Cotton production, 22 

production and export of United States, 
41 
Country Gentlevian, 213, 215, 232 
Cows, individual record curves for, 278, 279 
Crayons for coloring maps, 57, 221 
Crayons, paraffin, 57 
Crests and valleys of curves, 79 

of curves, 79 
Croj) Re-porter, 100 
Cross-hatching, 9 
Cross-index of curves, 291 
Croton water-supply curves, 160 
Cumulative curves, 149 

frequency curves, 174, 176, 177, 182, 184 
Cunningham, Wm. J., 132, 134, 135, 136 
Curtis Publishing Co., 238 
Curve comparison, 107 
Curve plotting, 47, 69, 84 
Curves and vertical bars, 47 

for the executive, 254, 288 

interpretation of, 357 

inversely related, 126 , 

plotted on cards, 259, 275 



INDEX 



367 



Curves and vertical bars, reading of, 30£ 

serial numbers for, 287 

shown by reflectoscope, 803 

versus bar diagrams, 310 
Cycles of curves, 97, 283 - 

in curves, 97, 283 
Cylindrical lenses, 330 

Data, 7, 42, 88, 126, 178, 204, 243, 333 
Data for curves, on face of chart, 80, 258 

for curves, shown on chart, 80, 258 

included in a chart, 24, 25, 26 
Dates, position of, in curve charts, 72 
Davenport, C. B., ii, 164, 165 
Davis, Pierpont V., ii 
Day & Zimmermann, 296, 305, 306 
Death rates in United States, 174, 351 
Decreases shown graphically, 30 
Degenerative diseases, 351 
Department of Agriculture Field Service, 

232 
Dependent variable, definition, 84 
Depressions, financial, 104 
Dimension lines, 5, 148 
Directors of corporations, 289, 298 
Dispatching charts for trains, 61, 62, 67 
Display fixtures for curves and maps, 305 

fixtures for maps, 233 
Distribution charts, 165 

curves, 165 

of wealth, 197 _ 
Dividends and earnings of Steel Corpora- 
tion, 313, 314 
Dixon, Frank Haigh, 115 
Dodd, Mead & Co., 250 
Dodge's Advanced Geography, 22 
Double co-ordinates for curves, 95 

scales for curves, 95 ' 

Draft curves for water consumption, 160 
Drawing ink, 46, 47, 276 
Dreyfus, Edwin D., 117, 118 
Drinking, reduction in, 345 
Droege, John A., Freight Terminals and 
Trains, 48 

Earnings and dividends of Steel Corpora- 
tion, 313, 314 
of college graduates. 111 
of wage earners in U. S., 180, 181 

Earthwork curves, 163 

Edison Company, New York, 108, 138, 
140, 146 

Eggs, price of, 100 

Elderton, W. P. & E. M., ii 

Election returns, methods of giving, 341 



Engineering Magazine, 12, 14, 17, 18, 116, 

125, 246 
Engineering News, 87 
Engineering Record, 79, 119, 209, 210 
Equitable Life Assurance Co., 174, 175 
Errors in comparison, 20 
Ewerbeck, Dr., 225 
Exaggeration due to scales used, 353 
Examination marks, charting, 205, 206 
Executive control curves, 254, 288 
Executives of corporations, 289 
Exhibition board, 232 
Exports and imports of United States, 37 
Exports from the United Kingdom, 98 
Eye-catchers, 25, 26, 27, 123 

Factory, 147, 155, 180, 256 

Fan tests, 335 

Farm-land values in United States, 218 

Farwell, E. S., 335 

Figures included in a chart, 27 

misleading, 326 

significant, 326 
Files for curve cards, 289, 291 
Financial charts, 104 

prosperity curves, 293 

reports, corporation, 307 
Fire losses in United States, 120, 121 
Fisher, Irving, 10 
Fixtures for displaying curves and maps, 

305 
Flags, celluloid, for maps, 247 
Flat-top curve-plotting, 256 
Flood curves, 77, 79, 119 
Food prices in United States, 103 
Football games, charting, 212 
Foreign trade of United States, 139 
Forms, routing printed, 18 
Formulas for curves, 202 
Frankfurt a.M., Map of, 225 
Freeman, John R., 160 
Freight-car shortage and surplus, 349 

handling, curves for analysis of, 184, 
188, 192 

service on Illinois Central, 310 

service on Union Pacific, 311 

traffic density map, 224 

train operation, 123 
French curves, 201 
Frequency curves, 164 

Gang punch for cards, 324 

Gantt, H. L., 52, 54 

Garnett, W., 205, 206 

Gasoline costs for motor trucks, 198 



368 



GRAPHIC METHODS 



Gasoline-electric generator advertisement, 

78 
Gear teeth, strength of, 334 
General Electric Revietv, 78, 239 
General methods, 321 
Geography books, 22 
Gifford, Walter S., 179, 240 
Gilbreth, Frank B., 50 
Good Housekeeping, 21 
Grammar for graphic work, 361 
Graphic presentation, rules for, 362 
Graphical charts, construction of, 335 
Green ink, making line cuts from, 330, 331 
Grolier Society, 358, 359 
Grouping of component parts, 33 
Grooves in cards for filing, 296 
Gummed letters, 46 

tape for map mounting, 231 

Half-tones from pin maps, 235 

Handling freight, cost of, 184, 188, 192 

Harriman, Mrs. E. H., 250 

Harvard Engineering Journal, 337 

Harvard University, 212 

Harvard University graduates, 251 

Hazen and Whipple, 95 

Health-department reports, 108 

Heating and Ventilating Magazine, 93 

Height of university students, 165 

Hewes, Amy, 167, 176 

Himman, J. J., 114 

Hollerith tabulating machines, 229, 230, 231 

Holmes, H. W., 208 

Horizontal bars, 4 

for comparison, 24 ' 

representing time, 53 " 

Hull, G. H., 104 

Human figure in comparisons, 39 

Illinois Central Railroad, 310 
Illusions, optical, 358, 359 
Imports and exports of United States, 37 
Incandescent-lamp tests, 337 
Income curves, 197 
Income of technical graduates, 204 
Increases shown graphically, 30 
Independent, the, 21, 38 
Independent variable, definition, 84 
Index numbers, 100 
Indianapolis Department of Health, 114 
Indianapolis smoke deposits, 245 
Industrial depressions, 104 
Industrial Engineering, 117, 118 
Infectious diseases shown in contrast, 30 
Information cards, 286, 290 



Ink, drawing, 46, 47, 276 
Internationale Baufach-Ausstellung, 225 
Inversely related curves, 126 
Inverted curves, 96 
Iron Age, the, 110, 119 
Irregular curves, use of, 201 
Isometric drawings, 333 
ruling, 167, 334, 335 

Japanese road signs, 346 
Jersey Cattle Club, American, 278 
Jevons, Stanley, 319 

Joint Board of Sanitary Control, 166, 253 
Joint Committee on Standards for Graphic 
Presentation, ii, 363 

Keufi'el and Esser Company, 326 
Key for charts, 360 
King, Willford I., ii, 328 

Labeling packages, 90, 91 
Lamps, types in use, 138 

tests of incandescent, 337 
Land value in United States, 218 
Lantern slides for election returns, 341 

slides in political campaigns, 339 

talks in political campaigns, 340 
Legend for charts, 360 , 

Lenses, camera, 330 

cylindrical, 330 
"Less than" basis for frequency curves, 179 
Lettering on charts, 26, 82 
Letters of appeal for money, 250 

gummed, 46 , • 

Lighter operation, chart for, 56 
Line cuts from pin maps, 234 

made from green ink, 330, 331 
Line thickness in reduced drawings, 242 
Lines connecting different bars, 31 
Loans to industrial employees, 156 
Locomotive feed-water curves, 159 
Logarithmic co-ordinates, 132 

paper, 334, 362 

ruling, 334 

scale for curves, 132 
Lorenz curve, 197 
Lorenz, M. O., 197 
Lubrication cost at a factory, 256 

Manufactured products of cities, 23 
Map and pin systems, 226 
Map copyrights, 237 

models, 225 

pins, 225 

pins used for cost analysis, 192 



INDEX 



369 



Map pins with numbers, 243, 247 

presentations, 208 

tacks, 225 
Maps, coloring, 209 

for corporation records, 293 

for election returns, 341 

for wall use, 225, 229 

mounting of, 231 

shading, 209 
Marx, Guido H., 334 
Mass curves, 149 
Massachusetts Institute of Technology, 

11, 198 
Mazda lamps, 337 
McAbee, WiUiam D., 245 
McGraw-Hill Book Co., 335 
Mechanical shading, 331, 332 
Merchant tonnage of United States, 112, 

113 
Methods, general, 321 

Metropolitan Sewage Commission, 20, 85 
Milk-analysis curves, 114 
Milk-production curves, 278, 279 
Misleading figures, 326 
Mode, 165, 170 
Models, card-board, 336 

solid, 336 
"More than", basis for frequency curves, 

179 
Morgan, J. P. & Co., 15 
Motion picture cameras for time study, 50 
Motor, 346, 347 
Motor trucks, cost for gasoline, 198 

cost of operating, 11 
Mount Holyoke College, 167, 176 
Mounting maps, 231 
Moving-average curves, 97, 283 
Municipal parades, 343 

record departments, 298 
Muslin facing for pin boards, 231 

Naphtaly, Sam. L., 122 
Natural scale for curves, 132 ■ 
Need for graphic methods, 1 ' 
Newark, N. J., public schools, 2 
Newburgh, N. Y., report on schools, 24 
New York Edison Company, 108, 138, 140, 

146 
New York municipal parade, 343 
New York Public Library, 299, 329 
Neiv York Times Annalist, 13, 45, 313, 350 
New York Times, 120, 121, 222, 351 
Newspaper circulation curves, 92 
Nippon Automobile Club, 346 
Numbered map pins, 243, 247 



Optical illusions, 80, 81, 358, 359 

Order of Railroad Conductors, 103 

Orders, routing, 19 

Organization charts, 14, 15 

Orrok, George A., 201 , 

Panics, financial, 104 

Parades, charts shown in, 342, 343 

municipal, 343 
Paraffin crayons, 57 
Paris, height of buildings in, 220 
Paris, plaster of, 336 
Passengers carried on railways, 39 
Passenger service on Union Pacific, 312 
Payroll curves, 260 

record curves, 276 
Peaked-top curves plotting, 256 
Peaks of curves, 99 
Pearson, Karl, 202 
Peddle, John B., 335 
Pencil lines, erasing, 361 ■ : 

Pennsylvania Farmer, 124, 127, 128 
Pennsylvania Railroad, 308 

profile of, 213 
Percentage scales for curves, 132 
Perspective routing charts, 19 
Philadelphia Commercial Museum, 70, 74, 

76, 112 
Philadelphia Transit Commissioner, 245 
Philip's Chamber of Commerce Atlas, 26, 

27 
Philippines, comparative size of, 211 
Photographing bead maps, 252 

pin maps, 230, 234 
Photographs, drawing upon, 209 

progress, 49, 50 

used with maps, 209 
Photostat, the, 296, 330 

use of, 329 
Pin boards for cost analysis, 191, 192 
Pin maps to scale, 246 
Pins for map use, 225 

for population density on maps, 221 
Pipe, cast-iron, 110 

Pittsburgh & Lake Erie Railroad, 81, 82 
Plant, Thomas G. & Co., advertisement, 233 
Plaster of Paris, 336 
Plates, weight of steel, 333 
Pneumonia, deaths from, at different ages, 

172, 173 
Polar co-ordinates for curves, 80 
Political campaigns, charts in, 338 
Popular Science Monthly, 164, 165 
Population curves, 130 

density maps, 221 



370 



GRAPHIC METHODS 



Portland, Oregon, 208 

Power development in United States, 239 

Presidential election analysis, 10 

Princeton graduates, class of 1901, 73 

Princeton University, 111 

Production schedule curves, 150 

Profile drawings, 211 

Progress photographs, 50, 51 

Progressive averages, 153 

Prominent bar for contrast, 30 

Prout, Curtis, ii 

Proportions of charts, 355, 356 

Prosperity charts, 104 

Prussia, distribution of wealth in, 197 

Pujo Money Report, 13 

Punched-card tabulating machines, 320, 

321, 322, 323, 324 
Purchasing-department curves, 293 

Queen Quality shoes, advertisement, 233 

Races in population of the world, 4 
Railway Age-Gazette, 115, 142, 224 
Railroad annual reports, 309 

earnings in United States, 115 

operating costs, 142, 143 
Rank charts, 32, 63, 65, 66 
Rea, Samuel, 308 
Record departments for cities, 299 

room for corporations, 292 
Records for the executive, 288 

needless, 285 
Rectangular co-ordinates, 132 
Reduction of earnings, 329, 330 
Reducing glass, use of, 241, 329 
Reduction in size of drawings, 241 
Reflecting lantern for curves, 303 
Reflectoscope for curves, 304 
Reports of corporations, 307 
Returns, election, 341 

Revenues of railroads of United States, 257 
Review of Reviews, 46, 47, 229, 231 
Rittenhouse, Elmer, 175, 351, 352 
Road signs, Japanese, 346 
Roads in New York State, map, 222 
Routing charts, 17 
Routing of papers in an office, 34 

salesmen, 236 
Royal Statistical Society, 205, 206 
Rule, slide, 326, 328 
Rules for graphic presentation, 361 
Russell Sage Foundation, 24, 32, 33 

St. Louis & San Francisco Railroad, 224 
Sales analysis curves, 188, 269 



Sales records by tabulating machines, 324 

record map, 223 
Salesmen, chart for ranking, 63 

routing of, by pins, 226 
San Francisco fire, 120, 121 
"Satellite Cities", 214 
Saturday Evening Post, 238 
Savings-banks deposits in United States, 

350 
Scale arrangement for charts, 362 
Scales, choice for horizontal and vertical, 
352 

double, for curves, 79 

for charts, 8 

on charts, rule for, 211 
Scallop shells, 164 

Schedule curves for factory output, 150 
Schools of the United States, 32 
Scientific American, the, 29 
Scott, Roscoe, E., 337 
Seaboard Air Line Railway, 177 
Sections omitted from drawings, 190 
Serial numbers for curves, 286 
Shading, Ben Day, 331, 332 

mechanical, 331, 332 
Sheffield Scientific School, 111 
Shipping of various countries, 24 
Ships, length of, 49, 51 
Shot-gun diagrams, 201 
Significant figures, 326 
Simple comparisons, 20 

involving time, 36 
Slide rule, use of, 326, 328 
Slope of curves, 130, 131 
Smoke deposits, measuring, 245 
Smooth curves, 118, 119, 201, 357 
Smoothing curves, 98 
Solid models, 336 
Soot deposits, measuring, 245 
Sophie 19th, milk record, 278 
Spot maps, 246 
Standard corporation, 334 
Standards for graphic presentations, 363 
Statistical Atlas, 8, 28, 36, 65, 80, 130, 168, 

172, 215 
Statisticians for corporations, 293 
Steam, cost of producing, 12 
Steam turbine, tests of, 122 
Steel, curves for strength of, 119 
Steel plates, weight of, 333 
Stockholders of corporations, number of, 308 
Storage capacity curves, 159 
Straw-board for mounting maps for pins, 
230 

for use with map pins, 191 



INDEX 



371 



Street-car service map, 225 

String for routing salesmen, 237 

Stream velocity, 87 

Swazey, Edward Scott, ii 

Subdivision of components, 8 

SuflFern & Son, 30, 213 

Survey, the, 6, 245 

Swinging display fixtures for maps, 233 

Symbols for charts, 345, 346 

System, 15, 90, 123, 223. 

Tabulating Machine Company, 322, 323, 

324, 325 
Tabulating machines, 320, 321, 322, 323, 
324 

machines for cards, 323 
Tacks, celluloid-covered, for maps, 247, 
248 

map, 225, 247, 248 
Tarr and McMurray's new geographies, 

22 
Taylor, Graham Romeyn, 214, 221 
Telephone load curves, 108 

rates, 126 

service curves, 179 

service in Wisconsin, 178 
Telephones in United States, pin map, 
240 

number used in United States, 354 
Temperature curves, 117, 118 
Thompson, A. T. & Co., reflectoscope, 303 
Thomson, H. F., 198 
Three-dimensional charts, 205, 206 
Time charts, 53 
Time-distance charts, 64, 67 

curves, 64, 67 
Titles for charts, 344, 345 
Topographical maps, 235 
Totalizing curves, 125 
Tracing cloth used with maps, 210 
Trading centers in United States, 238 
Train-dispatching charts, 61, 62, 67 
Train-operation curves, 123 
Transparentizing solution, 328 
Trenton, N. J., public schools, 2 
Trucks, costs for gasoline, 198 

cost of operating, 29 
Tuberculosis death rates, 351 
Tug-boat operation, 58 
Turbine, steam, tests of, 122 
Two independent variables, charts for, 205, 
206 



Union Bag & Paper Co., 45 

Union Pacific Railroad, 311, 312 

United States Census Office methods, 320, 

321 
United States Steel Corporation, 313, 314 
University of Cincinnati, 46, 47, 229, 231 

Vacation chart, 53 
Variables for curves, 84 
Variables, two independent, 333 
Velocity of water in streams, 87 
Vertical arrangement of curves, 347, 349 

bar charts, 354 

bars, 46, 47 

for components, 138 

Wage charts, 180, 181, 182 

comparison on railroads, 49 
Wall board, 232 

charts, 306 

exhibits, 358 

maps, 225, 229 
Wall Street Journal, 308 
Warne, Frank J., 103 
Water power in United States, 216 
Water storage-capacity curves, 159 
Wave lengths on curves, 283 
Waves in curves, 97 
Wavy line for bottom of chart, 350, 352, 

362 
Weather cnarts, 93 

Wealth, curves showing distribution, 197 
Weight of steel plates chart, 333 
Weighted averages, 103 
Westinghouse Electric & Manufacturing 

Co., 295 
Westinghouse, George, 31 
Wheat, production of, 1910, 27 
Wheeling & Lake Erie Railroad ^ 02 
Whipple, George C, 95 
White, William Pierrepont, 222 
Worcester Polytechnic Institute, 204 
World's Work, the, 39, 40, 43, 49, 51, 211 
Worsted mill operation, 52, 54 

Yale University, 111, 212 

Years, methods for naming on curves, 82 

Yule, G. Udny, ii 

Zero lines for curves, 82, 140, 350, 351, 352 
Zero lines on curve cards, 271 
Zizek, Franz, ii 



Jiiiiii 11! 



il! i