Brinton, Willard C. Graphic Methods for Presenting Facts. New York: The Engineering Magazine Company, 1914. Internet Archive identifier: cu31924032626792 (Cornell University Library copy). The first American textbook on what we now call data visualization.

It is really a calamity that curves are not more widely understood. Ad vertising men are now frequently unable 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 …

•> / \ s f \ / ^ a m ^ s ; \ ! i i i 5 i i i § 1 i 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 portray 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 …

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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 …

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 / \ / \ o / V. "^ o 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 …

If the co-ordinate 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 impression. The omission of the zero line in charts of this kind is particerror made by persons ZDOOO 24 25 26 27 28 29 JO jr I 2 March. 1913 April Engineering Retard Fig. 77. Flood in the …

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 coordinates, the data would be just as easy to read and to understand as when shown by the …

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 …

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 …

f f > - y / <►' ^ » .--' ) •"^ / •s. ^ - ^ ** . " ** / f # * l» ■ < t "• - ■ ■ m ■ ^ Mil* . •- B m « • • L_ r«a>(0(OQ)(DO<Ofloa)<9<i)0)Ano) intDr"00a>o -- <Meq^in<piscoO)o oinoioioioooooooooo -- 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 …

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 …

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 arrangement gives a neater effect than can be obtained otherwise. 10. Though figures for the dotted curve could be shown at the top …

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 …

This example is an exceptional case and it is named here only to show that, although time is 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 …

scale and read the information from 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 rule for scale arrangement is not always followed, and a so' or/- piEfj-/!- few examples are shown here to indicate the (JImple" …

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 independent 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 …

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 centimeter 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 …

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 consideration 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 …

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 …

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- 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 …

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. 5 10 o 9 o o 7 (J I- 6 <u ? 3 > +3 a ^^ ^ ^ ^^ J\ …

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 anthracite coal." The "price of anthracite coal" is the independent variable and should be plotted …

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 …

The curve for operator No. 1 then appears below the curve for operator No. 2 and the chart shows correctly the relative merits of the two operators. Fig. 86 is a redrawing of the data shown in Fig. 85. Here the curves for the two operators appear in their correct relative position, and it is seen at once that operator No. 1 is the more rapid worker, since he uses less time …

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 …

The actual differences between the two operators would show more clearly, operation by operation, if lines were used joining 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 …

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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 …

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 …

There is a chance that the man who has advertising to place may feel CURVE PLOTTING 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 circulation growth had been plotted in curves having the zero line shown at the bottom of the …

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 …

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 …

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 …

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 carelessness on the part of consumers. The actual percentages of the …

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 …

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 …

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 consumption, even though the population kept on increasing. In 1912, the average total consumption per day went up somewhat above …

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 …

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 average as compared with the number of points in one complete wave or cycle in the data curve, and the moving-average curve …

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 …

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 …

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 …

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 …

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-ordinate field and showing the zero of the vertical scale. Fig. 92 is taken from the United States …

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 …

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 bottom of the chart is not a zero line, and …

< T O 19tO zero line, a chart is obtained which needs little space and which nevertheless 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 various points on the curve. There is very small chance for any …

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 …

Improvement in Economy of Operation of ment in business conditions and in spite of reduced efficiency in the operation of this individual railroad, considered '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 …

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 …

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 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 1 1 i Simple Year Average …

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 …

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 conditions by two-hours' study of this series of charts than he could pos- GRAPHIC METHODS SNO± JO SNOmiW -tO «oot>-Q3ia^ertM" - « IndtistHal Depressions, iv 0. H. HvU Fig. 96. A …

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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 …

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 unfortunate 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 …

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 …

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 …

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 …

I 23-4 56789 lO II IE I 23456789 lO AJvl. P.M. 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 …

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 …

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 nevertheless misleading in that the first glance would indicate a much greater fluctuation in the price of pig iron than actually occurred. nJ^-^C -- .:S ~° ^^ -c:/^.i i 1 H"t Y rSWAtf MsU [4=\=H M T T\4vf rM-UJ in - T TT …

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 …

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. GRAPHIC METHODS s;:: = ss:s:ss = : = 2;sti?,-: | …

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 …

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 combination of bars either vertical or …

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 shipping 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 …

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 fluctuations 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 …

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 …

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 simplified SO that the reader can see at once what has been the tendency of the curve from December to January …

Comparison since 1850 of the Merchant Tonnage 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 …

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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 …

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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 …

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 December to January in each year. This question of repeating one point for curves of different years superinlposed is referred to also in …

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 separated. 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 …

In selecting a scale for Fig. 110 the draftsman is torn between a desire to show the San Francisco 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 Francisco peak so as to show the monthly data on …

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 Pittsburgh line was made heavy ttiat it might be most clearly seen. This …

In the preceding illustrations of this chapter there has been such similarity in the shape of the curves considered 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 …

/ , ^^^ \ /, ' \ /. ^" -- _J_ / \ _l \ __ ~-- -^ ] C -J ' W 3l Iron Age 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 Percentage of Contraction or Elongation The heavy line shows ultimate …

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 backward from right to left, giving something of a spiral effect. Though this bent peak may seem rather artificial, it is quite certain that the > ■* (M 0) r) o to 1901 1302 1903 …

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 GRAPHIC METHODS 28.60 28.40 28.20 30.40 30.30 ~~ f7 Tir n ~ _ …

While Fig. 110 gives some general idea of the proportion which American fire losses bear to the value of new building construction, the two fluctuating 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 …

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 …

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" …

Anything used for an eyecatcher should apply definitely to the subject matter of the curves. Here the subject is freight-train operation, but the picture shows the interior of a passenger train 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 …

the graphic method of stepping off the height for the total curve is practically the only one available. 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 …

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 …

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 continuously 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 …

A chart of this kind would be especially striking if used in advertising, or in a report where concentration upon only one general idea was needed, without a great amount of specific detail. Though Fig. 116 shows that telephone rates have had a constantly downward GRAPHIC METHODS je99 1900 1901 I90a (905 1906 1907 (908 (909 Courtesy of Daia, Cfiicago Fig. ii6. Chicago …

The plotted points for different years on a chart of the kind suggested would show by the arrangement of the points whether the prices had changed exactly in accordance 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 …

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 plotted 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 …

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 …

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 hopeless to draw any general conclusion from the arrangement of the dots. Though the dots indicate by their position a general tendency GRAPHIC METHODS for exports to decrease as prices increase …

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 …

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 plotting 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 …

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 …

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 …

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 …

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 accumulated 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 …

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 studied by making an entirely new chart for the purpose of observing percentage rates only. j n^ 1 , ' i f , f …

The true function of such a chart is to portray comparative fluctuations. 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 …

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 …

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 …

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 percentage fluctuation. This wide difference in the amount of vertical movement on a page is one unfortunate …

For persons who understand even slightly the principles involved in reading charts plotted on logarithmic paper. Fig. 123 shows up the facts in much more convenient form than Fig. 122. To make comparison most convenient, the two figures are placed on facing pages, 134 and 135. GRAPHIC METHODS I90Z /904 I90S l9Qb I90S teoo y ■ y y \ \ ^ ' \ ^ ji -\l\ zzoo ^ Ti \\ ^- -- " • ^ -' …

/ s "- / \ ■* / ■^ \ , -- ■-- -- -- s ~ / ■-- -- -- -- --> -^ ' s y \ ^ 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 …

It is unfortunate that there is so much difficulty in obtaining paper liaving the logarithmic ruling in one direction and the arithmetical 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 …

\ \ / eo eo / so / , N*^ / / «o \ / / \ ^ \ / / k ^ \ ^ \ ' \ ^ j \ / \ \ \ ' to \ ) ! __j u 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 …

It is, however, 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 …

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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 difference 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 …

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 proportionately. "To summarize -- with the ordinary arithmetical scale, fluctuations in large factors are very noticeable, while relatively greater fluctuations in smaller factors …

proportionate number, voltage, and candle-power of various types of standard incandescent lamps delivered in different years by the New York Edison 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 …

To show that the chart is absolutely limited to the height representing 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 …

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 …

Industrial Accidents in Different Months of the Year Compared with the Hours of Stmlight 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 …

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 …

Though it is fairly easy to see in Fig. 128 what the changes are which have occurred in, say, the item for "General" 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 …

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 …

As in this case a large part of the construction 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 …

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 …

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 percentage 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 …

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 …

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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 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 …

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 …

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 …

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 …

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 recorded, and the new total point is plotted. Because the figures relating to the last unit of time are always added to the total figures …

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 thereafter, giving a total production of three thousand two hundred automobiles for the whole season. It w^as thought …

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 practically no cars during the month of January, though the schedule shows that one hundred and fifty cars should have been made that month. During …

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 …

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 …

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 November and it made the …

Thus the modified cumulative curve may be used to show the quantities 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 making a curve like this it is ordinarily the practice to strike a balance of the additions and reductions for the …

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 relative widths of …

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 …

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 information 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 …

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 between two curves, the eye is likely to take as the distance between the curves the shortest distance …

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 …

Fig. 137 shows in detail for the same loan department the operations 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" …

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 …

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 economics 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 …