CHARTOGRAPHY 6 4 8 7 ARYt ACUITY 1 1 TEN^'lJ^S^SOiNS rnANR J.VWARNE CHARTOGRAPHY IN TEN LESSONS BY FRANK J. WARNE AUTHOH OP warne's book of charts warne's elementary course in chartography, etc. ILLUSTRATIONS BY H. F. CHURCH PUBLIHHED BY FRANK J. WARNE, SOUTHERN RUILDING WASHINOTON. r). C. Copyright, 1919, By F. J. WARNE (Authorship also protected in Great Britain and her Colonies, including Canada) HA^ ■; TABLE OF CONTENTS S Page u. Preface VU Introduction 13C Lesson I '-» Building the Chart •^ Value of Table of Contents 1 (s Statistics and Chartography 3 ''^'^ Definition of a Chart 3 The Statistics 4 Horizontal Lines 5 i| Vertical Lines " i - A Choice of Methods 8 The Use of Pencil Dots 10 The Framework 10 i Lesson II ^ The Scales '^ Statistical Variables 13 The Independent Variable 13 The Dependent Variable 14 The IIorizontHl Scale 15 Detcrrainirif,' the Vertical Scale 15 The Scale Lines Ifi Reading the Scales 1 ' Plotting the StiiHstics 19 The Use of (iradicnlcs 20 iii iv Chartography in Ten Lessons Lesson III The Curve Chart Page Making the Curve Heavier 25 The Horizontal Scale Unit 26 Squares Should be Equal 27 Effects of Different Scale Units 28 Dropping the Zero Line 30 Indicating the Absence of the Zero Line 31 Divisors for the Vertical Scale 33 Lesson IV Features of a Complete Chart The Statistical Table 37 Table Should Appear on Chart 39 The Make-Up of the Table 40 Spacing the Columns 41 The Form of the Table 42 Duplicating the Scale Units 44 The Place for the Horizontal Scale 44 Word Designation of the Scale 46 The Title 47 The Foot-Notes 48 The Neat Lines 49 Lesson V The Bar Chart Making Bars from a Curve 53 Making a Curve from Bars 55 Advantages of the Horizontal Bar 56 Reversing the Scales 57 Width of the Bar 59 Table of Contents v Paob Separation of the Bars 60 Location of the Table 61 The Bar and the Curve 62 Lesson VI The Tools of the Chartographer Cross Section Paper 65 The Lead Pencil 69 The Kind of Ink 70 The Ruling Pen 71 Correct Position for Holding Pen 71 Pen Points 73 The Drawing Board 74 The T-Square 75 The Triangle 75 The Engineer's Scale 77 The Dividers 78 The Essential Tools 79 Lesson VII Accuracy in Charlography The Use of the Typewriter 81 Drawing Letters for the Title 83 Exaggerating the Curve 86 Effects of Exaggerating the Curve 88 Advantages of Extra Squares 91 Lesson VIII Curve and Bar Designations Disadvantages of the Unbroken Curve 93 Curve Designations 95 vi Chartography in Ten Lessons Page Word Designations of Curves 98 The Peak-Top Curve 99 Determining the Scale Spacing 101 Utility of the Curve Chart 102 Chartography Based on Comparisons 103 Bar Designations 105 Interpreting the Bar 108 Some Characteristics of a Good Bar Chart .... 109 Word Designation of Scale Units Ill Lesson IX Value of Statistics to Chartography The Statistical Table II4 Aids in Reading the Table 116 The Substitution of Ciphers II9 The Table of Ratios 120 Building up a Table 12l The Percentage Increase and Decrease 123 The Zero Line 126 The Arithmetic Average 129 The Misuse of the Average 13 1 Statistical Class Limits 132 Lesson X Primary Principles of Chartography Planning the Chart 137 Importance of the Right Method 139 Essentials of Good Chart Making 140 Planning the Size of the Chart 141 Planning a Reduction in Size 143 The Reducing Glass 147 The French Curves 149 Checking up the Completed Chart 151 PREFACE No attempt is made in these ten Lessons to cover the entire field of chartography. To do so adequately would require several large volumes. All that these Lessons aim to do is to familiarize the student with the primary or elementary prin- ciples. These underlie chart plotting ajid con- struction as applied to the curve and bar charts. These principles are applicable to all kinds of charts, variations being explained by the differ- ences in the circumstances surrounding the special problems. These Lessons are the by-product of an experi- ence covering a period of ten years during which time the author has been engaged professionally in the application of the principles of chartography to the working out of practical problems of the work-a-day world. In the presentation by means of diagrams or charts of innumerable statistical problems the author has been able to put the art of chartograj)liy to a severe test before such authoritative tribimals as the Literstate Com- merce Commission, various state public utilities and railroad coinmissions, })oards of arbitration appointed by the President of the United States for the peaceable .settlement of labor contro- vii vdii Chartography in Ten Lessons versies and various committees of Congress. In this professional work he has been called upon to till entirely new fields, for there were few authoritative guides to follow, and in conse- quence he has been compelled to pioneer his way amid innumerable uncharted difficulties. Such an experience should contain lessons of value to others engaged and about to engage in the making of charts. In presenting this formu- lation of the principles of chartography the author begs leave to express the hope that these Lessons may serve the beginner in chartography as a safe guide over the innumerable pitfalls that inevitably must be encountered unless he is warned to guard himself against them. An endeavor has been made to bring these Lessons within a reasonable price to the student. The cost of production of "Warne's Elementary Course in Chartography," which was published two years ago and the price of which was fifty dollars for the twenty Lessons (including "Warne's Book of Charts"), was such as to pro- hibit a lower price, and in consequence it could not be made to serve the class of students the author desired most to reach. Parts of that Course have been completely revised in these Lessons. INTRODUCTION The Value of Chartography (Revised from "Wame's Elementary Course in Chartography" and "Warne's Book of Charts") To the average citizen statistics are as incom- prehensible as a Chinese puzzle. To him they are a mental "Mystic Moorish Maze." He looks upon columns of figures with suspicion because he cannot understand them. Perhaps he has so often been misled by the wrong use of statistics or by the use of incorrect statistics that he has become sceptical of them as repre- senting reliable evidence as to facts and, like an automaton, he mechanically repeats "while figures may not lie, all liars, figure," or the equally common libel, "there are three kinds of lies — lies, damn lies and statistics." And yet statistics are an infallible indicator of economic conditions — they measure the heart- throbs of a nation's or of an industry's life- blood. They register the conditions of any given static situation; they point the direction of a trend or tendency with the accuracy of the ther- mometer in measuring the temj)erature. 1*.^'); Every business, whether organized on a large or a small scale needs statistics — in fact, statistics ix X Chartography in Ten Lessons are vital to its successful existence. Without them the executives cannot know the status or tendency of the economic factors which control their affairs. This practical value of statistics in every-day business life is coming to be more and more correctly appraised at its true worth. The Railway Age of February 23, 1917, says: An officer of a western road recently made the statement that each department of a large railroad system should have on its staff a thor- oughly competent man whose duty it should be to analyze statistics. The assertion was not made without deliberation, and it might be perti- nent to ask whether we are getting the most out of the statistical department. The amounts which are spent by American railroads in com- piling statistics bearing on the functions of the various departments are extremely large, and no one who knows the importance of the compara- tive figures to the oflBcers will question the wisdom of the expenditure. Some of the statistical data which the railroads compile is readily analyzed, and the important figures, such as average tons per train, or pounds of coal per thousand gross ton-miles, are always readily available. A closer analysis of data which is regularly compiled would develop important facts which are not brought out in the routine reports. The head of a department may desire more information than that regularly furnished him, but he cannot take the time to get it himself, and a clerk could not understand its meaning or application, and would Introduction xi overlook important points. Great stress is laid on the comparison of results for successive months, and the comparison with figures for the corres- ponding months of the previous year, but statis- tics are no less important as a means of forecasting results by comparing a proposed method with the one in practice. The great expenditure for statistics is relied upon to show the leaks and determine wasteful methods. The field of the statistician should be broadened and he should give more attention to the possibility of con- structive activity. The statistical department has long been depended upon to keep costs from going up. It is time we recognize that it lies within its province to show how costs can be brought down. Statistics have become a vital, every-day need not only in transportation but also in indus- tries of all kinds, in finance, in journalism, in social work, in public life, and in business of every description. They are necessary to men of affairs, publicists, economists, and even to the average citizen if the significance of facts and the trend of events are to be comprehended. Virtu- ally our entire political life, both state and nation- al, is now regulated and its course determined by statistics. Every important branch of govern- ment has its statistical bureaus. Large financial institutions, industries, manufactories, railroads and other transportation companies have their xii Chartography in Ten Lessons statistical departments. Innumerable associa- tions must resort to statistics in order efficiently and effectively to carry on their work. This recent growth in the demand for reliable statistics and their correct interpretation has suddenly raised the standing of the statistician to one of importance, and this has been accom- panied by a corresponding increase in his remuner- ation. Today the openings for one versed in the fundamental laws of statistics — in their collection, compilation, presentation, and interpretation — are innumerable. The demand is greater than the supply. The value of statistics, while great, is inestim- ably enhanced by the aid of chartography. It supplements statistics — it supplies the best known method for their presentation and interpretation. In all those phases of presentation which count for clearness and quickness of comprehension, no other method is equal to it. It makes clear at a glance, even to the uninformed and unin- itiated, the significance and tendency of the fac- tors that are portrayed. As nine-tenths of the problem in interpretation is clear presentation the value of the service rendered to statistics by chartography cannot be over-emphasized. Especially is this realized when it is remembered that statistics, to be useful and valuable, must Introduction xiii not only be accurately compiled but must also be correctly interpreted. Relatively, too much time is spent in the collection and assembling of statis- tical material and too little in its clear and forcible presentation. Here is where chartography be- comes an invaluable handmaid to statistics. The graphic presentation and interpretation of statistics as the basis of a recognition and an understanding of industrial, political, financial, social, economic, and other tendencies has become essential to practical men of affairs as well as to publicists, economists, and others. It can be made of incalculable value in any line or depart- ment of business — in that of finance, corporate relations, internal organization, traffic, supplies, production, prices, wages, costs, and scores of others. It not only will repay its cost but will be found of such great value in so many ways that, once instituted, it will never be abandoned. It will save in the time of the busy executive alone more than its cost, because it will enable him to analyze the facts and tendencies at a glance in- stead of spending hours in studying the relations of the figures in the different columns. It will make more certain the correct interj)retation of the basal information necessary to action and the formulation of a successful pr)hcy. It will en- large and extend his individual experience and xiv Chartography in Ten Lessons his accumulation of knowledge of the details and principles of his business. It will replace vague- ness and indefiniteness by assurance and certainty, hazy conceptions will become clear-cut perspec- tives, and these in turn will lead to a compre- hensive grasp of the entire problem. The recent development in and the growing demand for diagrammatic statistics will continue, and he who masters the few simple yet funda- mental laws or rules upon which it is based will be in a position to become an authority in his par- ticular field and to command a comfortable in- come. Frank J. Warne. Washington, D. C. October 1, 1919. LESSON I Building the Chart Value of Table of Contents — Statistics and Chartography — Definition of a Chart — The Statistics — Horizontal Lines — Vertical Lines — A Choice of Methods — The Use of Pencil Dots — The Framework. In the Table of Contents preceding this Lesson has been given a comprehensive outHne of the field the beginner in chartography is to cover in this and succeeding pages. It is a bird's-eye view of the course of study that has been mapped out for him in these I^essons. It should not be passed over lightly but should be studied seri- ously, for the reason that such a study will give to the student at the very outset a broad per- spective of the problems he is to encounter and overcome. Figuratively, he is starting on a mental journey, with its ups and downs, its delights and pleasures, its perplexities and obstacles — with a good deal of play and some hard work ahead. Tlie Table of Contents is tlic itinerary, kej)! by one who has many times covered tlie same ground and who thus is able to point out the significance of 1 2 Chartography in Ten Lessons the things that are to be encountered. The student will benefit greatly in the mastery of these Lessons if he will frequently re-read the Contents. VALUE OF TABLE OF CONTENTS The Table of Contents can also be likened to a railroad map in the hands of one starting on a long journey. It enables him to traverse with his eyes the entire distance of the trip, noting the general characteristics of the country through which he is to pass, its mountains and rivers, and the principal cities along the way. Thus he secures, before he starts on the journey, a much better idea of where he is going and becomes more familiar with the country through which he passes than he would if he studied the railroad map piecemeal after the journey begins. These ten Lessons will take the student on an intellectual trip in the course of which he will be called upon to exercise such mental traits as application, concentration, observation, and im- agination in overcoming the various obstacles on his way to the acquisition of knowledge concern- ing the art of chartography. He cannot reach this desirable end without progressing step by step in mastering its various features. And at every step in this progress the broad view of his Building the Chart 3 final destination which he will hav^e acquired by a close and frequent study of the Contents will be of material assistance to him. It will not only enable him to cover the ground much more quickly and with less exertion, but also with much more satisfaction to himself. STATISTICS AND CHARTOGRAPHY The value and usefulness of statistics and the relation to them of chartography, as well as the objects of chartography, have been pointed out in the Introduction. From a reading of those pages it should be plain that figures in tabular form, or which can easily be arranged in the form of a statistical table, are essential to the drawing of a chart — they are the reason for the chart being made. DEFINITION OF A CHART The drawing of a chart therefore presumes the existence of the statistics. It has nothing to do with their collection or compilation. A chart is merely a sheet of paper on which tabu- lated facts are presented grai)hically. It is also called a diagram or "graph." In a limited sense it can l)e likened to a moving pi<-ture, with this difference: In the case of the chart it is the eye and not the picture that moves. 4 Chartography in Ten Lessons the statistics For the purpose of familiarizing the beginner with the various steps in the process of making the framework of a chart these figures are selected : 1913 1914 1915 1916 1917 1918 1919 26.7 26.7 26.4 28.1 38.2 49.5 57.2 The first line of figures represents calendar years and the second line the average retail price of a pound of bacon in the United States on April 15 of each specified year. This information is from page 77 of the Monthly Labor Review of the Bureau of Labor Statistics of the United States Department of Labor. To make a chart from these figures is a simple proposition — as simple as the alphabet, that is, provided one knows the alphabet. It is as difli- cult to one who does not know how as the alphabet is to the child first beginning to lisp the letters. That which at first appears to be a very com- plicated and difficult thing to do comes to be surprisingly simple after one has acquired the necessary knowledge and facility. In the be- ginning all that is needed is a lead pencil, an ordinary ruler, and a blank sheet of paper. horizontal lines A glance at the statistical table shows there Building the Chart ' 5 are seven prices to be recorded. These can be represented for the present by as many lines drawn with the lead pencil at equal distances apart from left to right across the blank sheet of paper. The result gives the lines A-A, B-B, C-C, D-D, E-E, F-F, and G-G on this page. These are horizontal lines. It is important that the begirmer bear this fact in mind. lie should remember that a horizontal line always 6 Chartography in Ten Lessons extends in the direction of the horizon, that is, parallel to the horizon. Here the horizon is represented by the top edge of the sheet. Hori- zontal lines are drawn from left to right, never from right to left. VERTICAL lines In our statistical table we have another set of seven figures. These represent that number of years. So we mark off on the bottom horizontal line G-G, by means of the inch and its fractional units of the ruler, seven dots each an equal dist- ance apart, the first dot starting at the beginning of the line on the left. These dots we repeat on the top horizontal line A-A. Next we draw seven vertical lines connecting these dots, be- ginning with the first dot on horizontal line G-G. Upon completion of the last vertical line erase the dots on the top and bottom horizontal lines. Do not draw these vertical lines backward, that is, downward from line A-A to line G-G. A vertical line is an upright line, that is, it is directed perpendicularly to the plane of the hori- zon, as distinct from the horizontal line which, as has been said, is parallel to the horizon. These seven vertical lines we designate as H-H, I-I, J-J, K-K, L-L, M-M, and N-N. Superim- posed on the seven horizontal lines these vertical Building the Chart 7 lines give the framework shown in the following drawing. K M N H M The distinction between iiorizontal and vertical lines should he clear to the student. The junc- tion of a horizontal and a vertical line forms a right angle. 8 Chartography in Ten Lessons Another way to begin the erection of the frame- work of a chart, and one which will likely appeal more favorably to the student after he has ac- quired greater knowledge of the subject, is to draw first the horizontal lines G-G and A-A and then the vertical lines H-H and N-N. This gives the outline on the opposite page. These four lines are the really important lines of a curve chart. In relative importance they are in this order: H-H, A-A, G-G, and N-N. The uses to which each is put the student will become more familiar with in subsequent Lessons. All that is necessary for him to know now is that: Line H-H is the vertical scale line and with its units of measurement virtually determines the distance the curve is to move. In other words, all movements of the curve are measured by this line. Line A-A is the horizontal scale line, and in all curve charts involving elements of time it takes the time units. In our present problem as to the price of bacon it provides positions for the years. Line G-G is the base line of the chart. Figur- atively, it is the foundation line upon which all the vertical lines rest and from which they start. This base line is the zero of the vertical scale and, whenever possible, should always be indicated Building the Chart 9 by a cipher. All movements of the curve are measured /ro 771 this line. Line N-N is the least important of these four lines, but this is not saying that it is not necessary and useful. Its functions will be pointed out to the student later. 10 Chartography in Ten Lessons the use of pencil dots With the four lines I have described already drawn on the sheet, the beginner next divides by dot markings the base line G-G into six equal spaces, starting the first of the five dots the dis- tance of one space from the left end of the base line G-G and ending the dots the same distance from the right end of the base line. Duplicate these five dots at their respective distance apart on the top line A-A. Now connect these dots with vertical lines extending from the bottom to the top line. This gives the five lines I-I, J-J, K-K, I^L, and M-M. Repeat the pencil dots with the same space between them on vertical lines H-H and N-N, beginning the first of the five dots the distance of one space from the bottom of lines H-H and N-N, Connecting these dots with horizontal lines gives the lines B-B, C-C, D-D, E-E, and F-F. Now erase all the dot markings. The result is the same as that shown on page 7. THE FRAMEWORK OF THE CHART This is the framework of the chart. It is the scaffolding by means of which the curve is to be erected or constructed. It is the skeleton structure for supporting the curve. Without it Building the Chart 11 the curve could not be constructed properly or correctly; neither could the curve adequately perform the service for which a chart is drawn. The lines will be found to occupy positions behind the curve, or rather to form a setting or back- ground for it. The framework is essential for determining the movement of the curve and must be built up before the curve can be placed. QUESTIONS FOR SELF-EXAMINATION 1. Describe the broad view of the field of chartography gained from a study of the Table of Contents. What ser- vice does this table perform for the student? 2. Describe the relation between chartography and statistics. 3. Of what value are statistics to business? To other activities? What is the service chartography performs? 4. Do these Lessons cover the entire field of chartogra- phy? Why? 5. Define a chart. What is a horizontal line? A vertical line? How is each drawn with a pencil? 6. What is the framework of a chart? How is it con- structed? 7. What are the most important lines of the framework? Describe their uses. 8. Of what use are pencil dots in drawing the lines? How are these dots employed in laying out the vertical and horizontal lines? 12 LESSON II The Scales Statistical Variables — The Independent Vari- able — The Dependent Variable — The Horizon- tal Scale — Determining the Vertical Scale — The Scale Lines — Reading the Scales — Plotting the Statistics — The Use of Gradicules. The essence of a chart is in the relation which it shows exists between two or more statistical elements. Chartography involves a comparison. Probably the most frequent comparison is that of figures representing the trend or tendency of the same or similar element or factor over a period of time, as in the present instance of our statistics showing the average price of bacon on April 1.5th of different years. STATISTICAL VARIABLES This price is not the same for all the years — it has the capacity of changing or varying with the different i)eriods of time. Thus in relation to each other these two groups of figures are called variables. THE INDEPENDENT VARIAHLK A comparison being involved, one or the other group must be made use of as the standard by which the other group is measured or interpreted. 13 14 Chartography in Ten Lessons The group so used becomes the independent variable. Where the element of time enters into the situation it is nearly always the standard and thus becomes the independent variable. THE DEPENDENT VARIABLE The statistical group that is to be measured or interpreted is called the dependent variable. In our present problem the price of bacon being dependent upon the specified periods of time is the dependent variable. The relation between or the tendency of the units or elements of the dependent variable is measured by scales. One of these is the horizontal scale and the other the vertical scale. Generally the independent variable takes the horizontal scale. This fact is important, as a great deal of confusion results from a violation of this simple principle of chartography. "It should be a strict rule for all kinds of curve plotting," says Brinton in his Graphic Methods for Presenting Facts, "that the horizontal scale must be used for the independent variable and the vertical scale for the dependent variable. When the curves are plotted by this rule the reader can instantly select a set of conditions from the horizontal scale and read the informa- tion from the vertical scale. If there were no The Scales 15 rule relating to the arrangement of scales for the independent and dependent variables, the reader would never be able to tell whether he should approach a chart from the vertical scale and read the information for the horizontal scale, or the reverse. If charts are always plotted with the independent variable as the horizontal scale, there need be no question in the reader's mind as to how he should interpret the chart." THE HORIZONTAL SCALE Following out this principle of chartography we substitute on the horizontal line A-A of the framework on page 7 (Lesson I), in place of the letters H, I, J, K, L, M, and N, the figures repre- senting the years in our statistical table. This gives the following horizontal scale line: A 1913 1914 1915 1916 1917 1913 I9l=i 1 A (H) (1) (J) CK) (L) (M) CM) detp:rmixing the vertical scale With the years representing the horizontal scale, the average price of bacon figures — the dci)endent variable — must necessarily be meas- ured by the vertical scale. The units of this 16 Chartography in Ten Lessons scale are determined arbitrarily by figures that must have a spread sufficient to include the lowest as well as the highest price of bacon that is to be recorded according to the statistical table. The lowest price is 26.4 cents in the year 1915 and the highest is 57.2 cents for the year 1919. It has already been stated that the lower or base horizontal line is zero and should be indi- cated by a cipher. This also means, inasmuch as the vertical lines rest upon the base line, that the beginning or start of the vertical lines must be at zero. The framework above the base or zero line G-G on page 7 (Lesson I) provides six squares within which the highest number — 57.2 — of our statistical table has to be recorded. With these facts to consider it is a simple mathe- matical computation which shov/s that the small- est unit that can be made for the vertical scale is that of 10 for each square. Placing this unit from to 60 on the vertical scale line H-H of the framework shown on page 7 (Lesson I) instead of the letters G, F, E, D, C, B, and A, gives the vertical scale on opposite page. THE SCALE LINES We have completed both the horizontal and vertical scales as determined by the figures of our statistical table. Substituting these scales on The Scales 17 the fratne-work of our chart in place of the letters designating the lines gives the results shown on the next page. ~H These scale lines — the horizontal and ^^' ^' vertical — are very important features of a chart ; in fact, without them a chart is unintelligible. They must be adapted to the arbitrary limitations of space, and this adaptation is readily brought _ (Q) about by increasing or decreasing the space allotted to each unit of each scale to correspond to the requirements of - (D) the particular statistical problem. The vertical scale unit itself can also be in- creased or decreased as the particular ~ problem requires. This scale measures, by equal distance along all the vertical _ ,^ lines, the units of the variables that are being charted — it represents Vjy space on the lines of the chart the equivalent — (6) of an agreed uj)on element of the statis- tics as determined by the units selected. READING THE SCALES The horizontal scale should read from left to right with the earliest year to be recorded appear- ing first and the remaining years following con- secutively in i>oint of tijne. 40 30 20 10 18 Chartography in Ten Lessons The vertical scale beginning at zero should read upward from the bottom or base line to the top or horizontal scale line. 1913 1914 1915 1916 1917 1918 1919 60i 50 AO 30 20 10 '■' ■ 572 49.5 36.2 26 7 26 7 264 28 1 This arrangement "faces" the chart to the left. A chart that faces to the right, faces in the wrong direction, or, putting it another way, a The Scales 19 chart that does not face to the left does not face in the "right" direction. PLOTTING THE STATISTICS We are now prepared to begin the plotting of the statistics. With the vertical and horizontal lines drawn the proper distance apart and with the figures of the years and vertical scale units cor- rectl}'^ indicated by lead pencil marks, the student next begins to plot on the respective vertical lines, by means of pencil dots, the exact positions of the figures of the statistical table as determined by the vertical scale. This scale applies similarly to measiu-ements on all the other vertical lines as much as it does on the vertical scale line itself. That is, any unit of the vertical scale line, say 30 of our present scale, has exactly the same relative position on all the vertical lines as it has on the vertical scale line. The first figure of om- statistical table that is to be located on the chart is 2(5.7, representing in cents the average jirice of a |)ouiid of bacon on April 15, 1913. The first vertical line, wliicli is our vertical scale line, also rei)resents that year, as indicated by the figures 1913 at the top of the line. Starting at the ba.se of this line at we proceed upward to 10, to 20, and .somewhere be- 20 Chartography in Ten Lessons tween this unit designation and the next one, 30, must be the proper location for the figures 26.7, THE USE OF GRADICULES It is easy to locate where 25 should be — midway between 20 and 30 — even without the aid of the slight projections or gradicules which have been inserted on the left of the vertical scale line in the chart on page 18 for the purpose of aiding the beginner. Each of these gradicules represents one-tenth of the vertical scale unit, or 1, and there are ten gradicules betAveen each unit of 10. They perform a function similar to the sub- divisions of the inch unit on the ordinary ruler — thty enable the student to locate with facility on the framework any figure of the statistical table that falls within the round numbers of the vertical scale units. With the assistance of these gradicules it is a simple matter to determine the correct location on the vertical scale line of the figures 26.7. This is indicated by means of a pencil dot. The same procedure is followed in locating on their respective vertical lines, as indicated by the vertical scale, the remaining figiu"es for each of the other six years of the horizontal scale. The locating of each number on each vertical line should be done by starting at the base or The Scales 21 zero line and counting upward, and not by start- ing from the position of the preceding pencil dot. One reason for this is to prevent the possibility of error in the location of the num- bers in case a mistake happens to be made in placing the first one on the vertical scale line. Besides, it is important that the beginner should have impressed upon his mind at the outset that all positions of numbers charted by means of a curve are determined in relation to the base or zero line. This is clearly indicated on page 18. On this drawing the numbers represented by the pencil dots, and which are those of our statistical table, are i)laced opposite their respective dots to emphasize their location. This presentation has prepared the student for the actual drawing of the curve. This he does by starting his pencil at the dot on the vertical scale line representing the number 26.7 for the year 1913, and by means of a straight line marks the space between this dot and the dot rei)rescnting 26.7 on the second vertical line, which latter, according to the horizontal .scale, represents the year 1914. It .so liai)i)ens that the average price of bacon on April 15, 1914, is identical with the i>rice on April lH, 1013, ac- cording to onr statistical tabic. This gives a straight line connecting vertical lines 191.'5 and 22 Chartography in Ten Lessons 1914 at the point 26.7. The dot on the vertical line representing the year 1915 is at 26.4, this figure being the average price of bacon on April 15 of that year. The student connects the dot . 1913 60 50 1914 1915 1916 1917 1918 1919 40 30 20 10 / / / / / YEAR CENTS 1913 26.7 1914 26.7 1915 26.4 1916 28. 1 1917 38 2 1916 495 1919 572 --^ / representing 26.7 for the year 1914 with the dot at 26.4 for 1915. Continuing this process for the remaining dots gives the curve shown above. The Scales 23 In this drawing the lead pencil dots have been erased, as have also the gradicules along the vertical scale line shown in the chart on page 18, these dots and gradicules being of no further use. The figures representing the price of bacon for the different years have also been removed from their positions opposite the dots and have been placed in statistical table form, with the years in the first and the prices of bacon in the second columns. QUESTIONS FOR SELF-EXAMINATION 1. What is the essence of a chart? 2. What are variables? What is an independent varia- ble? A dependent variable? 3. What are scales? Describe the horizontal scale. The vertical scale. 4. What is the relation between the variables and the scales? 5. What scale does the independent variable take? The dependent variable? 6. How is the vertical scale determined? 7. What is the base line? What service does it per- form? What is the zero line? What is the relation between the lower horizontal line and the zero line? Between the lower horizontal line and the base line? 8. What is a square? How is it formed? What is its function in chartography? 9. What is the vertical scale unit? How is it deter- mined? 10. What is a vertical scale line? A horizontal scale line? What relation to these are the vertical and hori- zontal scale units? 11. How should the horizontal scale be read? The ver- tical scale? In what direction should a curve chart face? 12. What is meant by plotting the statistics? How is it done? 13. What is the relation of the vertical scale units to vertical lines other than the vertical scale line? 14. What are gradicules? Of what use are they in plot- ting the statistics? Where are they located? Of what use are pencil dots in plotting the statistics? 15. How are the positions of the figures of the statistical table on the framework determined? What service does the zero line perform in this determination? 24 LESSON III The Curve Chart Making the Curve Heavier — The Horizontal Scale Unit — Squares Should be Equal — Effects of Different Scale Units — Dropping the Zero Line — Indicating the Absence of the Zero Line — Divisors for the Vertical Scale. In drawing the curve remember to make it heavier than any other Hne. The purpose of this is to have it stand out prominently and so catch and hold the eye of the reader. The curve should he the most conspicuous of any line on the chart for the reason that it embodies or symVjolizes the most important facts that are presented — it is the why and the wherefore of the chart being called into existence. Con- versely, the framework lines making up the back- ground of the chart, that is, the horizontal and vertical lines, should be drawn with a lighter touch of the pencil to paj)cr. The curve is a continuous, unbroken line, and has its origin at the i)oint along the vertical scale line that is determined for the time or other designation of that line by the statistics and the vertical scale. It moves across the page from point to point on the vertical lines and in the 25 26 Chartography in Ten Lessons direction from left to right as the respective numbers of the statistical table determine. The curve terminates on the last vertical line at the point the statistics require. It takes the shortest distance between two points and generally should approach each slantingly. THE horizontal SCALE UNIT In a curve chart the unit of the horizontal scale element — in our present case this is a calendar year — marks a point as distinct from space between points. Each vertical line pro- jects or extends its horizontal scale unit down- ward all along the entire distance of that line even to the base or zero line. The curve cannot and does not affect it — the curve does not move any horizontal scale unit a hair's breadth from its place on a particular vertical line. Or, rather, the horizontal scale unit does not follow the curve from its point of contact with it on one vertical line to the point of contact with another horizontal scale unit on another vertical line. For instance, the year 1913 ends with the vertical line so designated and does not cover the space between vertical lines 1913 and 1914. Quite commonly in curve charts this distinction is overlooked, particularly by beginners, and the horizontal scale element is sometimes made to The Curve Chart 27 represent space on the horizontal scale line and between the vertical lines. This is a mistake. SQUARES SHOULD BE EQUAL In a curve chart it is desirable to have the curve move from point to point in squares or areas of equal spacing in all directions, whether these be large or small. This means that both the horizontal and vertical scales should be deter- mined upon a basis that will permit equal spacing between the units of each scale, that is, between the horizontal lines of one scale and the vertical lines of the other. This allows the curve to move up or down and from left to right an equal distance for each unit of measurement of both .scales. Many curve charts are being made in which this rule is violated. It must be added, however, that the observance of this principle is not always possible owing to the arbitrary limitations of .space and to the necessities of the scales. The problem for the chartographer is to secure as accu- rate an observance of this rule as his difficulties will permit. He should constantly koej) in mind the important fac-t that tlie horizontal and vertical lines are made use of to measure the quantity or volume or other specified quality of the .statistical element that is charted, and that these rules of measurement should be as fair as possible. 28 Chartogkaphy in Ten Lessons It is recommended that the beginner at first draw liis frame work or scaffolding lines, both hori- zontal and vertical, exactly one inch apart, thus giving square inches within which the curve moves. Each scale will then have its units of measurement one inch distant from each other. Later on the student can practice with lessening or lengthening this distance, keeping in mind not to move the scale units to points less than one- half inch or further apart than one and one-half inches. He should not permit the units of either scale to be separated by any greater distance than the units of the other scale. EFFECTS OF DIFFERENT SCALE UNITS The student should also practice changing the unit of the vertical scale within the inch square, increasing or decreasing it to other selected units, in order to observe carefully the effects these dif- erent units have upon the movement of the curve. In the drawing on page 22 the unit is 10. Let us substitute for it the unit 5, as in the drawing on the opposite page. A study of these two drawings will disclose a number of important differences. Probably the most important of these is the fact that a vertical scale unit one-half as large, other factors remaining the same, doubles the space within which the curve moves. Conversely, The Curve Chart 29 doubling the scale unit decreases by one-half the distance the curve moves. This space in the drawing on page 22 requires 1913 1914 1915 1916 I9l7 1918 19 60 55 50 45 40 35 30 / / / 1 / ( / ' 9«; vertically a fraction more than tiircc of the squares — the Hj)rea(i in the difrcronce between the lowest and highest numbers of the statistical 30 Chartography in Ten Lessons table is 30.5 and with 10 as the unit this leaves .5 more than three times 10. In the drawing on the preceding page the vertical scale unit 5 requires a fraction of .5 more than six times 5 to accommodate the curve, or seven vertical squares at the very least. As the drawing on page 22 provides only six squares, another one has to be added to the framework, as is done on the page preceding. This is accomplished by inserting an additional horizontal line, either above the top or below the bottom horizontal line, and then extend- . ing to it all the vertical lines. With the new vertical scale unit being 5 and with the highest number to be charted being 57.2 for the year 1919, a square must be provided for each of the units of 5 if the scale is to begin at zero. This demands at least twelve squares for the vertical scale from to 60. But it is physically impossible to accommodate this many squares of the present size within the space limitations. DROPPING THE ZERO LINE The next step is to ascertain from the statis- tical table the lowest number to be recorded. This is 26.4 for 1915. It is clear from this that the space occupied by all the squares below the vertical scale unit 25 will not be needed for record- ing the movement of any part of the curve, for The Curve Chart 31 in not a single year of all the seven given in the statistical table does the price of bacon fall below that unit. Consequently, beginning the vertical scale at 25 instead of at permits the elimination from the framework of iSve squares. The number that remains, which is seven, is sufficient for the requirements. It has been made clear in preceding lessons that the bottom horizontal or base line of a curve chart represents zero of the vertical scale and is indicated by a cipher as follows: INDICATING THE ABSENCE OF THE ZERO LINE Such a line, of course, cannot possibly be used as the base line with the unit of our vertical scale starting at 25, so the zero designation is omitted. Attention should always be called to this omis- sion on the chart itself and this can be done by inserting directly below the base lirje, witii its proper unit designation, a faijit lino of dashes or one of dots, or a wavy or slightly undulating line, as indicated on the next page. Rulers pro- vided with these undulations can be purchiised. 32 Chartography in Ten Lessons The student should keep in mind as a general principle the fact that the vertical scale begins on the base line at 0, although he will frequently find that this is physically impossible because of the nature of his statistical problem. This pre- vails more often among large numbers than with percentages. Usually the lowest nu nber to be charted starts at a point so high above that the space required to show the latter on the chart is out of all proportion to that necessary to in- dicate the movement of the curve. Again, frequently in such cases the vertical scale unit determined by including zero becomes so large that fluctuations in the movement of the curve reflecting the trend of the statistics (which fluc- tuations would be made clear by the use of a smaller unit) are smoothed out or flattened so that that which should be a curve approaches nearer to a straight line. Thus it is not always possible to plot a curve chart so that the zero of The Curve Chart 33 the vertical scale will be shown and at the same time clearly present the trend of the statistics, which latter is the primary object of the curve. In beginning to read a curve chart, among the first things to be observed is whether the vertical scale starts at zero and if it does not to make proper allowance for this fact in the inter- pretation of the movement of the curve. Unless this is kept in mind an erroneous idea or impres- sion of the extent of the movement will result. A chart that does not present the zero line and fails to call attention to the omission in the ways indicated, or neglects similar precautions, is constructed in error. Such a chart is very likely to be misleading no matter how excellent or perfect its other features may be. DIVI.SORS FOR THE VERTICAL SCALE The selection of the vertical scale unit is thus not without its difliculties. These the student will learn to overcome as his experience with varying stiitistical problems increases. lie will learn, among other things, that particular numeri- cal divisors are more advantageous as units than some of the others. The divisf)r 3, for instance, is an awkward and inconvenient scale unit, not only for computing on the vertical lines the measurements of the 34 Chartography in Ten Lessons statistical element but also for calculating by the interpreter of the chart. The divisor 2 is much better, and 5 and 10 are nearly always ideal. Such units as 3, 4, 6, 7, 8, and 9 are not as good as 2, 5, 10, 20 and so on, the latter group being more easily divisible into the spaces along the vertical lines as well as into the numbers of the statistical table. Whatever scale unit is selected it must permit the inclusion within the arbitrary limitations of the framework of the smallest as well as the largest number that is to be charted. The unit must be such as to permit of a spread between the lowest and highest numbers charted sufficient to bring out clearly in the curve the points or tend- ency to show which the particular chart has been designed; at the same time it must not be too small as to result in exaggeration. It is as serious an offense to exaggerate with curves as it is with words. Accuracy in chart expression is as im- portant as is the use of words in expressing thought, and the various uses or functions of the vertical scale unit have much to do with accuracy in curve charts. On a finished chart the student will not find any dots and similar marks used as guides in erecting the scaffolding of the framework, which means that all such marks must be erased from The Curve Chart 35 the completed chart. He will find, however, that all the vertical and horizontal lines make complete right angles at all points of junction; that all such lines are straight lines; that they form accurate squares; that the curve is slightly heavier than the other lines; that the scale unit figures are in their correct positions in relation to their respective lines; and that the horizontal and vertical scale unit figures do not crowd the lines but are separated from them by the correct spacing. QUESTIONS FOR SELF-EXAMINATION 1. Why is the curve made heavier than other lines? 2. Define a curve. How is it emphasized in comparison with the horizontal and vertical lines? 3. Define the horizontal scale unit. What function does the vertical scale lines perform for this unit? What is the relation of the curve to it? 4. What effect have unequal squares on the movement of the curve? What relation is there between the squares and the scale units? 5. What are some of the effects of changing the vertical scale unit? 6. When is the zero line omitted? How is this omission indicated? 7. Explain the reasons for omitting the zero line. 8. What effect has the omission of the zero line on the reading of the curve? 9. What are numerical divisors? When and how are they used? What ones are better than others? 10 What must the divisors provide for? 36 LESSON IV Features of a Complete Chart The Statistical Table — Table Should Appear on Chart — The Make-up of the Table — Spac- ing the Columns — The Form of the Table — Duplicating the Scale Units — The Place for the Horizontal Scale — Ward Designation of the Scale— The Title— The Foot-Notes—The Neat Lines. The drawing on page 38 is a complete curve chart constructed according to the instructions of the preceding Lessons. The student should examine carefully every one of its features. Particular study should be given by the student to the statistical table. It occupies the position in the lower right hand corner of the drawing on page 22 (Lesson II) but in the accompanying chart it is located in the upper left hand corner. In each ca.se the location of the table is adapted to the requirements of the fjarticular chart and each is correctly i)laced. It will be found that one or the other of tlie.se two positions is usually the place for the table, the lower left hand corner and the upper right hand corner nearly always being required for the free and unobstructed movement of the curve. S7 (J 38 Chartography in Ten Lessons THE AVERAGE PRICE* OP BACON UNITED STATES. I9I3-I9I9 1913 60 55 50 45 40 35 30 25 1913 1914 1915 CENTS 1916 1917 1916 / YEAR CENTS 1913 26 7 1914 26 7 1915 264 1916 28.1 1917 382 1918 495 1919 57.2 / 1 / / / ^ 1914 1915 1916 1917 1918 1919 60 55 50 45 40 35 30 25 1919 d^arkstics art rr&m Menrtily U&bo*- R«vl«