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.

\ -'/ < ,,«.< ^^-- T*or o«5- of_55 '■'- -^ II- -''' '/ en %, ff iJ! E no leo uio I70 izo Uk I i k I \ i t I t I iAi Includes a * loo loan Fig. 137. Loans Each Month Made to Employees of a Large Industrial Corporation and Amounts Paid Back Each Month. Number of Accounts Opened and also Number of Accounts Closed Are Shown on a Cumulative Basis Note how the curve for repayment …

After the two curves have been plotted separately to carefully selected scales, they may be superimposed and read through both sheets of paper held in front of a bright light. xVs the horizontal scales for the two curves are the same, it will be found, if the curves depend upon each other without the element of "lag." that the peaks and valleys will almost coincide. If there …

In Fig. 137 the growth in the importance of the loan department can readily be seen by considering the twelve-months progressive moving average showing the average total monthly loans. Though there is, in January, 1912, a very high peak which overshadows all other peaks, the general tendency of the curve is still rapidly upward, because of the fact that a number of high points …

It also shows that since numerous accounts are being closed, the loans are being made to other employees rather than being repeated continually to the same employees. Fig. 138 is a study made to determine the size of tank necessary to supply sufficient boiler-feed water for a number of locomotives and tugboats. The average amount of water used each day by all the locomotives …

'^ Ln :ru££j 10,000 5.000 r / ^ =°^ ia-- -•- -*-- r £ ■ > * s n. 3 ■* s > « I a z. : > ^ P. a s 10 •> r; Fig. 138. Cumulative Curves Plotted to Determine the Minimum Size of Tank and the Minimum Steady Flow of Water Required for a Group of Locomotives and a Group of Tugboats Taking Boiler-Feed Water from the Same Source of Supply Curves for locomotives and tugs are plotted …

In order to see what would happen if the locomotives and the tugs should take water from the same tanks, the combined curve was made for both locomotives and tugboats by adding the quantities for each one-hour period. The easiest way to make a combined curve when only two curves are to be combined, is to use a pair of dividers, taking the vertical distance above zero for each …

c5 -r ^ be ^ -tj rt rt rf o o t; .. . . §■020 CUMULATIVE CURVES 161 distances stepped off by the dividers locate the new combined curve so that it can be quickly drawn in. The combined curve in Fig. 138 shows at a glance that the locomotives and tugs together take water in such manner that the greatest rate of flow from the tank occurs between six and eight in the morning. One …

Thus, if from the point on the line for 40,000 at which the diagonal line intersects the vertical line for five a. m., we count 10 blocks horizontally to the right, we see that it takes 9.1 blocks before we again reach the diagonal line. Nine and one-tenth vertical blocks correspond on the scale to 45,500 gallons of water flowing in 10 hours, so that the minimum steady rate of …

Between six and eight a. m., when the amount which can flow into the tank through the regular flow-pipe is limited to the cpantity indicated by the dimension mark "B", the draught on the tank is so rapid that all of the water indicated by the dimension mark "A" must be furnished by the storage capacity of the tank itself. The water does not flow into the tank nearly so fast as …

The measurement of the greatest distance which shows between any depression in the consumption curve and the minimum-flow line which joins the peaks on either side of it gives the minimum steady rate of flow. There is great practical value in charts like Fig. 138. In this case the minimum-flow line determines the size of the pipe, pumps, or other machinery which must be …

In Fig. 139 the method is nearly identical with that used in Fig. 138, except that in Fig. 139 we are determining the greatest possible rate of uniform consumption from a fiuctuating supply, instead of determining the smallest possible rate of uniform supply for a fluctuating consumption. In Fig. 139, the lines beginning at the hump in 1870 are drawn at different angles to …

Though engineers have used curves for many years to represent data relating to the laws of physics, the engineer has made practically no use of frequency curves such as are used by the biologist. This is probably due to the fact that the engineer can determine the laws of physics from mathematical computations based on a relatively small number of observations, while the …

The heights of the different piles show the relative frequency of shells having the different numbers of ribs. Seventeen-rib shells were found much more commonly than shells with any other number of ribs. K a line were drawn through the tops of the different shell piles, we should have a frequency curve FREQUENCY CURVES relating to the frequency with which different …

There is a fairly large number of shells in the pile for sixteen ribs, and a somewhat greater number of shells in the pile for eighteen ribs. Though it is unfortunate that no horizontal scale or vertical Fig. C. B. Davenport, in Popular Science Monthly 141. Forty University Students Arranged in Rows, According to Stature by Inches, as follows: 56 to 57.9, 58 to 59.9, 60 to …

A glance at the photograph taken looking down on this group of men shows that there are more men shorter than the most frequent height than there are men taller. If an ink line were drawn as a smooth curve to represent the outline of the whole group of men, when arranged in rows as shown here, the top of the curve at the end of the longest row would be called the "mode", as it …

Frequency charts are sometimes made for popular illustration by drawing vertical lines to represent the number of individuals found in each class designated by the horizontal scale. Thus, a representation could be made for the data of Fig. 141 by having a horizontal scale to represent heights, and drawing vertical lines to a scale by, which the length of each vertical line or …

The Number of Persons Working On and Above the Sixth Floor in the Cloak and Suit Industry and the Dress and Waist Industry in New York City This chart was made first for a wall exhibit and was later used in a widely distributed report. The co-ordinate ruling has the shape of a New York manufacturing building. By observing this illustration from the left edge of the page the …

In order to see the general shape of a frequency curve when plotted with flat tops instead of peaked tops, the book may be turned so that the illustration is seen from the left-hand edge. This chart was drawn primarily as a wall exhibit, to be used later as an illustration in a printed report. The general scheme is excellent and it could scarcely be improved upon, even though …

Frequencj^ curves are very often used, however, with numbers rather than percentages represented on the vertical scale, and the vertical scale then shows the actual number in each class. To assist the reader, the total number of observations made would usually be recorded, perhaps in the title of the illustration. In biological work observations are usually made in vast …

of sufficient number to permit the formation of any general laws. Thus for Fig. 143 we are not justified in saying that-all college women marry at the particular ages indicated by this chart. The number of women taken into consideration for the preparation of the chart was not sufficient to allow any final conclusion, certainly not to justify any general statement that college …

Compare the upper chart with Fig. 145 In biological work the number of observations taken is ordinarily sufficient to permit drawing a smooth curve to represent the general law, after a chart drawn with numerous straight lines has been made by the method used in Fig. 143. It would not be desirable to draw a smooth curve in the case of Fig. 143, as the smooth curve would be …

In the Atlas, colors were used for the different areas which must be represented here by cross-hatching. Though these illustrations hold some very valuable and interesting information, the information is contained Per CenT lOO ^"^^^ "^^ \ ARRIED i ^y -y^ ^^ -^'^^;- "*"''*'"^^..^^^ \ \/ / ^^t^ ) "^ \ /\J / \ .>^^ \ 5?/ .f.C3 y 1 J / ^N ^i)^^-^ -,p-0_^,x--^ ^, J 1/ ■*^><^ ^"^i^^ …

The information sought is the percentage at different ages for each of the sexes, and this must be read from the horizontal scale, in violation of one of the most important rules for graphic work. Another bad feature of the chart is that data for male and female are shown in the right and left direction from the center line, making it almost impossible for the reader to …

It would appear that many widows must be reporting themselves as single instead of as widows, or the chart would probably not be so different in shape from the chart for the aggregate population of the United States. In Fig. 145 the scale for age has been properly placed horizontally and the scale for percentage placed vertically. The whole population is considered as single …

In this chart, however, we are considering three things, and the chart shows the percentage who recorded themselves as married, rather than the actual age at which marriage occurred. The percentage of those who report themselves married is affected by the number who are single and also by the number who are widowed. If in the later age classes, deaths of husbands occur more …

As the husbands are older than the wives, the expectation of life for the husband is, of course, less than for the wives, and the number of widows at any age is far in excess of the number of widowers, on this account alone. Industrial accidents, war, etc., also tend to make a high death rate among the men and cause more widows than widowers. In Fig. 145 the curve for men has …

This selection of horizontal distances makes the curves into much more nearly their correct shape than is possible on the Census Office chart, where five-year and ten-year class intervals are shown by equal scale distances. Perhaps the greatest gain made in clearness in Fig. 145 is due to the placing of the curves for male and female on the same ruled field, so that they can …

The chart was drawn to bring out the data clearly and, if clearness is not attained, the data might just as well be expressed in columns of figures. Here again the variables have been reversed and the independent variable improperly made the vertical scale. In Fig. 147 the data of Fig. 146 are redrawn into two curves by which the number of deaths occurring at different ages …

-- _ 3-4 ^H^^H ■i 1 - Z ^ ■ = = tf g ■ y ^Sg a g s ^ = ^ ^ lZ -- -- United States Stalislical Atlas, 1900 Census Fig. 146. Comparative Proportion of Deaths at Different Ages from Pneumonia per 1,000 Deaths from Pneumonia in the Registration Area of the United States, 1890 and 1900 The right-and-left arrangement of this chart makes comparison for the two different years almost …

If the chart had been made the full width of the page it would have been possible to get room enough to show the figures for single years at ages under five by using a space only one-fifth of the horizontal distance used for the five-year intervals. The large number of deaths at ages five to nine inclusive is very striking on the curve. Possibly the large death rate from five …

It is not until after a considerable amount of puzzling that one notices that the triangles have absolutely no significance and that they are only a means of showing the distance from the base line to the various points representing decrease or increase. It would have been better if plain black bars had been used for Fig. 148 instead of the triangles. Bars are so familiar to …

/ ^ y^ / ^. \ / y • -- oo \ >!> / / '/ \ '/ ^ \ s "- <00 I I I I I I I I I I I I I I I I I I I I I I I + <0-NO^inOiDOiooinoinoinoinOinOinOin Fig. 147. Comparative Proportion of Deaths at Different Ages from Pneumonia per 1,000 Deaths from Pneumonia in the Registration Area of the United States, 1890 and 1900 Comparison of the two years can be made instantly throughout the …

Though Fig. 149 might not attract deep interest on the part of a newspaper reader, it would not be likely to be misinterpreted. Fig. 148 might serve to attract attention, but what is the use in attracting attention unless a correct impression is given after attention has been attracted.'* Frequency curves thus far considered have permitted reading from the vertical scale only …

In Fig. 143 the percentage who married at each age is given in figures at the top of the chart. By observing the figures at the top of Fig. 143 and the figures at the top of Fig. 150, the method for plotting a cumulative frequency curve will be apparent. Beginning with the percentages for the later ages in Fig. 143, the figures for the various years are added cumulatively to …

Putting the data in the form of a curve like Fig. 151 lets the stockholder see at once just what conditions are on his road, in so far as rail weight is concerned. Thus, in Fig. 151, the stockholder may see at a glance that a very small percentage of the rails on this railroad weigh in excess of 75 pounds per yard, and that only about half of the rails weigh niore than 70 …

The increase in deatti rates for ages over forty is here showTi in great contrast with the decrease in death rates for ages less than forty. The hea^"^' zero line and the arrows pointing upward and downward make misinterpretation almost impossible It would have been better if Fig. 151 had, at the lower left-hand corner, the words "more than", with an arrow pointing …

Thus, in considering the weight, roughly 6 per cent of all the rails on the system are more than 75 pounds per yard, and using the right-hand scale it is seen that, roughly, 94 per cent of all the rails are "less than" 75 pounds per yard. There is not ordinarily any necessity for using a double scale in this manner. It is done here only to show the difference in reading a …

Percentage of 439 Married Graduates of Mount Holyoke College (Women) Graduating 1890 to 1909, who Married at Ages Greater than Any Specific Age Selected from the Horizontal Scale of the Chart This is a cumulative frequency curve plotted from exactly the same data as Fig. 143. The word "over" with the arrow at the lower left-hand corner of the chart shows that the chart does …

In Curve "C" it can be seen that only 30 per cent of the calls of that class were answered in less than four seconds, as against 60 per cent for curve "A". Though curve "A" is higher up on the chart than curve "C", it really represents a smaller length of time required to answer telephone calls than shown by curve "C". Since twice as large a percentage of the calls were …

Weight of Rails per Yard in the Main Line Track of the Seaboard Air Line Railway as Published in the Annual Report to Stockholders for the Fiscal Year Ending June 30, When using the left-hand scale the chart is read on a "more than" basis as if the words "more than" had been used with the horizontal scale as seen in Fig. 158. If the right- , , . 1 1 1 ■ ■ 1 hand scale is …

In Fig. 152 the curves show the time required to answer calls in different cities, while Fig. 153 shows a comparison of answering times in different classes of service. Notice that in each of these two charts it seems that two seconds is about the minimum which can be expected in answering telephone calls with the existing types of equipment. Fig. 153 certainly gives in …

The chart, however, is likely to be very misleading, as it has been plotted by methods which are not in accordance with usual practice. The variables have been reversed, and the independent variable has incorrectly been made the vertical scale. Besides that, the vertical scale reads downward instead of upward. In all kinds of curve plotting it is common to have the two scales …

These curves start at the lower left-hand portion of the field and trend upward, showing that they are plotted on a "less than" basis. Curve A shows a smaller time required to answer calls than Curves B or C, yet the actual position of Curve A on the chart is higher than either curves B or C. If cumulative frequency curves are plotted on a "more than" basis the position of …

The position of the curves one above the other would lead the reader at once to think of the upper curves as showing higher wages. Here the upper curves do indicate the higher wages, but they would not do so if they were plotted on a "less than" basis instead of on a "more than" basis. Though it may cause some confusion at first, it seems desirable as a general rule that …

I ^ ** 3 / - i a\a^ t Z* T ,*' / ^^ I t J -I 4L .t X-t / - -If--,' 1 . ^ ± JL 3 „ „ ^ Vnswering Time of 1 1 \ A OPERA! ORS &TouL Recording Opers. Ui -L ,„„ 1 / / t -To// fie tording Operators under Supervision ill 2- * withcut If A- - No overload i t B- t -T C- r 1 t 1 L I c ^ t~ -- f - Li T. _._:: Courtesy of W. S. Gifford, American Telephone & Telegraph Co. Fig- 153 …

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: ALA5 Courtesy of Factory Fig. 154. Comparison of Earnings of Men Wage Earners in Different Portions of the United States in 1905 This chart is almost hopelessly confused because the scales have been so arranged that the two scale zeros appear at the upper left-hand comer of the chart instead of at the lower left-hand comer. The vertical scale reads downward when it should …

Only 62 per cent of these laborers make more than $9.00 per week and but 80 per cent of them get more than $5.00 per Pen Cent lOO 7 8 9 10 12 15 WEEKLY EARNINGS - DOLLARS .. .^. r- United States N.Atlantic ■■ o . S.Atlantic N. Central .-- .-- . s. Central Western Alaska Fig. 155. Chart Showing What Percentage of the Wage Earners in Different Portions of the United States …

This chart could have been improved if the words "more than" and an arrow had been placed at the lower lefthand corner on the general scheme of Fig. 158 GRAPHIC METHODS o WAGE COMPAHTSON IN VAEIOUS DEPAETMEHIS. Feroent. O 56 O 4 c 96 « o •J "»l \ _L <^ _ ^ *«s - -- 7^" -- -- -- -- -- -- _ _ -- _ _ : ^ -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \ \ ^^\ \ r> \ ^ \ \ '■r^ v \ …

Comparison of Actual Weekly Earnings in Different Departments of a Large Industrial Plant Showing Percentage of Men in Each Department Receiving More than Any Specified Amount of Earnings per Week This illustration was made by photographing directly from the universallj' ruled paper shown also in Figures 57, 103, 130 and 134. The scales and the different titles were put on the …

Since all the laborers were paid the same rate per hour, the only possible explanation of the fact that a large number of men earn as little as $5.00 per week must be that the laborers were not employed continuously. More continuity of employment for a smaller number of laborers would, in this particular case, have resulted in more money being paid on an average to each man …

That some of the foremen receive as low as $6.00 per week and that only 93 per cent of the foremen receive over $11.00 per week is due to the fact that some of the men were off because of sickness or on leave of absence. If the attendance of these men were more regular the curves would not have such a decided peak at $11.00 per week. Though Fig. 156 has been plotted on a "more …

No of Percent & Pieces No orOrders 2000 100 \ \ \ \ \l \ \ \ \ "'^ \ ^^ \ ■ ^ y V^ ^ \ '-"'^ ^\^ •^ c ^ -^ ^^ -.^ \ V'^ ""-^ X \ ^^^ / \ \ '' ' -- ^ / ^^ \ \ ^ ■ ^^^ / "^ ■ ^^ ^-^ D ^^^ .. ' -- ~ . =^»-..,,_ ** 5 10 15 20 25 75 100 Size of Order in Number of Pieces Fig. 157. Cumulative Frequency Curve Study of the Number and the Size of All Orders Handled During a Ten-days …

from the right-hand scale Curve "C" shows by small circles the total number of pieces (or packages) carried by the various orders which are found in each group. Curve "C" is read from the left-hand scale Curve "A" shows the percentage of the total orders handled which contain more than any given number of pieces considered on the horizontal scale of the chart Curve " B " shows …

In handling large quantities of freight the different orders cover many diverse kinds of material, and the jobs vary from one package up to many thousands of packages on one order. The pieces or packages referred to here may be anything from a single casting weighing 20 tons to a shipment of canned goods with 5,000 boxes or cases on a single shipping order. In the long run …

After the orders have been separated into piles, it is a simple matter to count the number of orders in each pile to obtain the data from which curve "D" is plotted. It will be noticed from the shape of the curve that the upper and lower limits for each class are well selected so that there is a fairly uniform decrease in the number of orders in each group as the size of the …

Though there are not so many orders of large size as of small size, the small numbers of large orders nevertheless carry many more packages than the large numbers of small orders. The executive is, of course, interested in revenue and, for revenue purposes, as mentioned above, all packages may be considered of the same size. Revenue obviously depends upon the number of …

We can see instantly that, because of the large number of small orders, only 22 per cent of all the orders handled were larger than twenty-five pieces per order. Only 13 per cent of all the orders handled exceeded fifty pieces per order. Also, by reading from the vertical scale opposite the figure for 50 per cent, we can see at once that only half of all the orders handled …

Curve "B" thus shows that, though there are not many large orders, about 69 per cent of all the revenue comes from those orders which contain more than twenty -five packages. Fifty-six per cent of the business (and the revenue) is due to orders containing more than fifty packages. Twenty -nine per cent of all of the revenue comes from orders containing more than one hundred …

Since clerical work depends chiefly on the number of separate orders, the manager would be able to reduce his clerical work on this particular class of orders somewhere near 45 per cent if he would refuse to handle orders of less than ten packages, and, by such a decision, he would lose only 9 per cent of his revenue. For most businesses, it would pay handsomely to neglect …

When it is seen what a large amount of clerical work is involved in handling orders which produce only a small portion of the revenue, thought could be given to the methods of handling small orders so that the small orders may not cause any more expense than absolutelj^ necessary. Usually it is possible to handle small orders in a different manner from the large orders, and …

Though these orders of over twenty -five packages do not involve a large amount of clerical work, they nevertheless bring in such a large percentage of the revenue that any dividends from this particular department must probably be paid from the revenue brought in by orders in excess of twenty-five packages each. The general methods used in plotting Fig. 157 have been …

Cumulative Frequency Curve Study of the Number and the Size of All Orders Handled During One Week in a Certain Kind of Freight-handling Work Carried on in Two Closely-related Departments Curve "H" shows by small circles the actual number of orders found in each size-ot-order-elass. Note that at the left of the chart there are numerous orders shown in each class even though …

One sub-department of the business handled the orders portrayed by Curve "A" and Curve "E". The other sub-department handled orders portrayed by Curve "C" and curve "G". The combined work of the two departments is shown by Curve " B " and Curve " F" The percentage of the total number of orders handled in each of tlie two different departments, up to any size of order read on …

Department stores might also have use for charts on the general plan of Fig. 157. Different departments could be considered by the number of orders of various sizes. As the margin of profit in different classes of goods in different quantity sold would be fairly well known, the manager could get a good idea as to how much of the time of his sales force was occupied in handling …

In Fig. 153 it was shown that, because the curves were plotted on a "less than" basis, the curve showing the smaller length of time appears at the top of the chart, when one would naturally expect to find the smaller quantities of time recorded relatively toward the bottom of the chart. In Fig. 158 the data are plotted on a "more than" basis, and the curves are seen in their …

chart shows that the department to which curve "G" relates handles a larger percentage of the total number of packages and produces a larger percentage of the revenue than the department to which curve "E" relates. If this chart had been plotted on a "less than" basis instead of on a "more than" basis, the position of these two curves giving detailed information for the main …

These lines would not appear this way if a piece of paper had been torn out of a large-size chart. The curve lines should have continued up to the break in the drawing more nearly on the slope seen in the left-hand portion of the chart. The lines for curves "G", "F" and "E" would, if correctly made, show much less slope also at the right of the break where they lead down to …

Though this method of averaging all orders together without respect to the size of the order is sufficiently accurate for many purposes, there are times when such a method may gravely mislead an executive. It is almost invariably true that small orders cost more per unit of output than orders of large size. A man who makes a selling price for his work on the average cost of …

On some days all the orders for one commodity might be small orders, and on the next day a very large quantity of that same commodity might be handled all in one large order, so that a gang of men could work steadily all day on that one order. Naturally if a large gang of men work all day on one order, the cost per package handled would be very much less than if several …

The co-ordinate paper for the chart itself was mounted on three layers of corrugated straw-board, having the ribs of the middle layer at right angles to the ribs of the two outside layers, as described in Chapter XII. A binding of gummed cloth -tape around the edge of the board gave a neat appearance and assisted to preserve the boards during rough service and long use. These …

B -= Distribution of packages C -- Average cost per package for orders of various size <i \ / \ ' \ J, y / / • • / ' • > \ • / 9> ; % • / / * * / / •f / • y / > / ® / / ^ /'* / • ^_ ^ _ r •«• <0 •t to N -- < ^«. 4* .oOOOOOOOOOOO tf^oa)a)t»<o<o^co(M -- • • • r • • 1 . ■ <» - • ; .' • • • • / .1 • ® <£ li f • •* •• f.J .< L* 1 ' rat >• • • • • « • • Prrf •• f* C»" • • ^e « • • …

The cost per package would be figured up for each order ticket and, in the board reserved for that particular commodity, a tall pin would be placed for each order completed the preceding day, showing by the position of the pin the number of packages on the order and the cost per package of handling that particular order. In considering the pin marked 8 at the right of Fig. 159 …

Thus, a superintendent seeing a board of the kind described would know that on the preceding day those orders had been completed which in Figure 159 are shown by numbered dots. His attention would be drawn at once to the orders represented by dots numbered 4, 5, 6 and 8. These dots show costs much above the average cost recorded for orders of those sizes. The cost clerk could …

The chart brings out this information very clearly. Since the superintendent can take the matter up with the various foremen before noon of the day after the work was completed, the foremen soon get the feeling that the superintendent knows what the cost should be, and, if anything happens to prevent work being done cheaply and quickly, the foremen are likely to report the …

The ordinary type of tall pins or tacks used with wooden boards would not be at all satisfactory for this class of work, as it would be impossible to work with such boards containing thousands of tacks without knocking the tacks loose, so that they would be in a continuous process of becoming lost -- much to the detriment of accuracy and to the disgust of a cost clerk. The …

Thus, if any particular campaign were made to reduce the cost for small orders by handling small orders on some different method from that previously used, the pins near the left-hand side of the board might appear considerably lower down on the chart than the pins of the color which had been used in the six months preceding the change in method. When the board gets so full of …

In the upper portion of Fig. 159 is shown a summary chart of the data contained on the pin board itself. Curve "C" is a smooth curve drawn through the center of gravity of all pins on any vertical line which shows the size of order. It will be noticed that the cost decreases very little when orders become larger than three hundred packages, but for this particular commodity …

Assuming that a loss occurs on all orders shown on Fig. 159 up to the size of one hundred and fifty packages per order, the number of dots to the left of the line for 150 on the horizontal scale indicates just how great the total monetary loss would be. Curve "A" in Fig. 159 shows the percentage of orders which contain more than any specified number of packages selected on the …

In Fig. 160 is shown a chart which may help to make clearer the general principles used in drawing the charts seen in Fig. 157, Fig. 158 and Fig. 159. Fig. 160 shows the appearance of the curves if there are the same number of orders in each class or group and if all classes or groups are of uniform size. It makes no difference in the shape of the curves how many orders there …

In Fig. 159 the reader may easily see for himself that there are many more small orders than there are large orders, because the pins are largely concentrated toward the left-hand side of the chart. It is this concentration at the left-hand side which has so greatly affected Fig. i6o. Chart to Show the Theoretical Shape of Cumulative Curves for the Percentage of Total Orders …

If there is not the same number of orders in all groups or zones the curves will take some other shape and the shape will depend on the peculiar distribution of orders as may be seen in Fig. 157, Fig. 158 and Fig. 159 FREQUENCY CURVES the shape of curve "A" and curve "B" in Fig. 159. By comparing Fig. 160, we can see that if the distribution of orders in Fig. 159 had been …

^/ ,. ' ^ ^ , Fig. i6i. Curves to Show the Percentages of the Total Population of Prussia in 1892 and in 190 1 that Received Various Percentages of the Total Income as Considered on the Horizontal Scale L. <u E60 <to 50 0) O40 / / / / • •7' f / / / / :/ .•/ / / ^ 30 40 50 60 70 Percents of Total I ncome 80 90 100 EQUALITY PRUSSIA 1892. PRUSSIA 1901 M. O. Lorenz, in the …

It would then be simple to compute the income of each group as a percentage of the combined income for all groups. The resulting group percentages would be plotted cumulatively as the dependent variable on a chart for which percentages of population would be the independent variable. Fig. 161 unfortunately shows the independent variable used for the vertical scale. A better …

In Fig. 161 we have the curves for two widely separated years plotted side by side, so that we may tell from the general shape of the curves whether the distribution of wealth is approaching uniformity of tending in the direction of great concentration in the hands of a few people. The more nearly the curve approaches a straight line the more nearly wealth is distributed …

The dotted line is drawn through points on the chart for data furnished by the manufacturer as his estimate of good practice A curve of this general type, proving a close relationship between two variables, may be called a correlation curve CORRELATION 199 members of the population. In Fig. 161 the hne was more bowed in the later year than in the earlier year, and the …

Thus, considering the two dots which are given for trucks of 2,000-pounds capacity, it will be noticed that both of these dots are far below the position on the chart which one would expect the average to occupy if one should judge by the general tendency of the curve as a whole. It may have happened that the particular trucks which these two dots represent were run with very …

A manufacturer of machinery has recently revised many of his manufacturing and selling policies from the information obtained from a chart showing the relations of cost and selling price of his equipment to the actual size of the equipment. On the horizontal scale of charts used for this study the size of the apparatus was shown according to its actual working capacity. In a …

Some sizes of apparatus were particularly suitable to the public, and on these sizes the quantities were much larger than on other sizes. The sizes more commonly sold were naturally better equipped with jigs and tools than other sizes, and for that reason the cost was lower than would otherwise be expected. After the cost curves had been thoroughly studied for different kinds …

After sufficient observations had been made throughout the whole range of the horizontal scale, smooth curves were drawn which would most nearly represent the various dots plotted. In drawing curves of this kind, care should be taken to have each portion of the curve as nearly as possible at the center of gravity of the dots in any vertical section of the chart. Accuracy is …

Velocity of circulating- "water -=ft. per sec. '~^1\ Geo. A. Orrok, in Journal American Society of Mechanical Engineers Fig. 163. Relation of the Rate of Heat Transmission to the Velocity of the Circulating Water in Surface Condensers Correlation charts of this type have sometimes been called "shot-gun diagrams " The investigator makes a dot for each observation recorded, and …

Care in shifting the irregular curve will permit drawing a clean, smooth curve line, even though the irregular curve used is quite different in shape from the curve line which is drawn. • o^ -^ -^ ^ ^0 ■ 9 ^ ^ ea ^ -- o Z^ ^(b ^o ^^ -' 52 63 54 55 56 57 59 59 60 61 62 63 64 6S 66 67 60 69 70 71 7e Noiher't Span (=1/) in Inches. Karl Pearson in "Blometrika" Fig. 164 …

Curves like those seen in Fig. 163 are properly drawn as smooth curves because they are based upon some definite laws of nature. It is only because of the crudity of the observations of mankind that the dots are so widely scattered. If human knowledge were sufficient to obtain measurements with exactness, curves for data relating to the laws of nature would fall exactly on …

By using the straight lines instead of the smooth curves to connect points, the reader is warned that the chart represents facts as found, rather than facts which are assumed to be in accordance with any definite laws. Where smooth curves are proper, as in Fig. 163, it is feasible to have a mathematical formula to represent the shape of the smooth curve. As the determination …

There were naturally fewer observations at either end of the chart, for the very small spans and for the very large spans, than for the intermediate spans. It was probably because of the small number of observations at either end of the curve that the dots there are so far away from the curve line. If more numerous observations were taken it is probable that all the averages …

whicli the dots fell. The upper edge of the cross-hatching shows the maximum of the incomes, and the lower limit of the cross-hatching shows the minimum of the incomes reported for different years after graduation. The reader can thus get the whole story at a glance without being confused by the complexity which would result if all the dots were shown. Attention should be …

This general method is a worthy one closer to the bottom of the shaded area than to the top of the area. This fact shows that, though there are several graduates getting high salaries much above the average income, nevertheless, if all of the dots were shown, most of the dots would fall below the average line rather than above the average line. A few extremely large incomes …

With few observations it might be desirable to show dots on the chart to actual scale rather than in classes by tens. Ordinarily a line drawn like the heavy wavy line in Fig. 166 would be so placed that the points on the line would be at the center of gravity for the dots vertically on either side of the line. Here, however, the line is so drawn that there are an equal number …

In the case of those girls who do well in both English and arithmetic, there seems to be improved facility in the field of arithmetic. ao f V) < I- bJ £ ■I ~~^ \, ■ • • •. ■ ^ ■ 7A ^/ ^^ -<\ \ / • ^ .•.. \ • • • ! ^ \ '.'.'. "■ :■:::; / / \ ^ii: ^ . . . ........ /] 1/ : ^ \ ■ y. / J. :-:^ \ \ :::;::• j^ '^ -* ■*: •vx. \ ii --^=i • i lO O 10 20 30 40 50 60 70 80 90 100 English …

Though Fig. 167 appears to represent a soHd model, there was in reahty no sohd model made in order to obtain this illustration. By using isometric paper a chart like Fig. 167 can be made with comparatively little work. Isometric paper has lines ruled on the paper right and left at an angle of 30 degrees to the horizontal. By selecting a vertical scale to portray by separate …

of the arrows CORRELATION 207 The reader should note carefully that the scale arrangement of Fig. 167 is entirely different from that used in Fig. 166. In Fig. 166, the two zeros fall together as they ordinarily should do in chart work of this sort. In Fig. 167, however, the two scale zeros are not together and the reader is accordingly prevented from interpreting Fig. 167 …

The number of beads on each wire can represent to scale the data for the particular square at the center of which the bead wire is placed. The heights of the columns of beads on the different wires would then show clearly the facts for any one section of the field in a manner similar to that of Fig. 167. The beads would probably be more generally understood by an untrained …

It is always difficult to get non-technical persons to take an interest in proposals which are shown only by blue prints and ordinary maps. Architects realize this so well that it is common practice among them to submit carefully prepared wash-drawings to show the appearance of the building for which they are submitting plans. Most engineering work cannot be easily represented …

If maps must be printed in a report, a book, or a magazine, it is usually necessary, on account of the high cost of color printing, to use some arrangement of black ink for shading those areas which on a single map would ordinarily be colored by hand. Fig. 169 is a sample of what can be done without the use of color. If the drawing is made considerably larger than the finished …

a. o TO ^ 0/ o IJ ~ 3 a 6 ti o (D o o n 1-1 ft> i-i a. p crp ^ n W !-*> tt! o So ' fp o 1-hO en o p* o tr cr o GRAPHIC METHODS Plains Engineering Record Fig. 169. Drainage Area of the Canadian River, New Mexico Areas of different kinds may be distinguished on maps by various classes of shading when color printing is not available expense. Sometimes only one map is available …

The main difficulty with the celluloid method is that the inks will rub off if the celluloid is handled too much with moist hands. Ease of erasure has some advantages, however, for tentative schemes can be rubbed out or changed at will, simply by using a damp cloth. After the final adoption of the plan, tracing cloth can be laid over the combined map and celluloid sheet, and …

The relative proportion can be indicated best when care is taken to have the several areas drawn to the same scale and placed in a good position for comparison. Fig. 171 is shown here only as an example of the almost unlimited range which the application of graphic methods may have. The average person would never think of charting a football game, yet the graphic method …

The vertical scale of Fig. 173 should have been shown on the chart. The heights stated for different cities give a fair indication of what the vertical scale is and a reader can, if he must, measure on the drawing the height for any city and from that determine to what scale the drawing has been made. As a broad rule, the scale should be indicated in an easily seen position on …

chart like Fig. 174 so that the facts which it is desired to prove may be brought out clearly . Numerous methods are available for presenting such data. There is no general rule for determining which method is the best, and judgment must be used to choose the method w^hich is best fitted to each individual case. Note that in Fig. 174 we have a scale reading to quarters of a …

Country Gentleman Fig. 172. Dates for Planting Com, Showing How the Season Advances in Different Parts of the United States This illustration is similar to the well-knowB weather maps on which lines are drawn through all points where conditions are the same Railroad Operating Costs, Suffern & Son, New York Fig. 173. Profile of the Pennsylvania Railroad from Jersey City to …

The scale given with the map permits the number of cattle for any State to be read fairly accurately. The degree of accuracy depends upon the map size selected, and upon the number of dots used to represent any given quantity. The more dots used the greater the accuracy. There is. GTaham Romeyn Taylor on "'Satellite Cities" in the Survey Fig. 174. Map Showing that Factory …

In Fig. 176 it would not be feasible to use a much smaller circle if the quarter-circles are used. MAP PBESENTATIONS Country Gentleman Fig- 175- Relative Distribution in the United States of Cattle Other than Dairy Cows For popular presentation, if great accuracy is unimportant, this method of illustration would be difficult to improve upon. It is not possible to get a correct …

If an outline map of suitable size is available, the only hand work necessary for a cut of this kind is in drawing the small circles and placing inside them the figures serving as key numbers for the shading used. The actual shading is done by the engraver making use of the Ben Day process. For information regarding the preparation of engraver's copy for plates on which Ben …

The key scale at the lower left-hand corner of the illustration shows that the different shades do not become darker by any uniform increase in horse power. The range included in shade number eight is 50,000 -- from 50,000 to 100,000. For shading number two, however, the range is 3,000,000 -- from 4,000,000 to 7,000,000. This numerical scale was badly selected, for the steps …

If the steps in the shading scale had been so made that there were nine increasing classes of shading, each representing 1,000,000 horse power, it can be seen that all the States here numbered five to nine inclusively would have the same shading. Such a map made with a scale of uniform steps would appear so entirely different from the map shown here that no one would ever …

On a map of the kind seen in Fig. 177 there may be any number of different shadings, from one to a dozen or more. In order to simplify matters for the reader it seems best to assign the smaller numbers to represent those conditions which are considered most desirable or commendable. The reader may then see instantly which areas are first, second, third, etc., in rank simply by …

The cut was made by photographing a page of the Census Abstract which was printed on rather rough paper. With an original cut made directly by the Ben Day process the distinction GRAPHIC METHODS between the different shades would be considerably clearer than it is in Fig. 179. A cut of this size and complexity is rather expensive when the Ben Day shading is used. Anyone …

The vertical dimension of the group of bars for each district shows the relative total number of houses. The horizontal dimension shows the relative number of houses of each height by stories up about half of the whole United States. A uniform scale varying by $25 per acre would give an erroneous impression regarding those important areas which contain land valued at less than …

Methods of Marking Maps When an Increased Density of Population May be Expected in Following Years Each shading can be made by adding with a pen to the shading used for the next lower density. Pins of different colors placed in a map have an advantage over this scheme in that pins can be removed if population density should happen to decrease limited by the fact that there is …

If it is not necessary to photograph the map, pins with different colors of heads may be used to show density of population. There is one very great advantage in using pins instead of crayons or the pen-and-ink system , of Fig. 181. It sometimes happens that an error is made which may spoil a very valuable map because of the impossibility of erasure. When short pins are used …

The object of the illustration is to show the necessity of a road system that will feed from the farms to the densely settled portion, permit the quick and easy transportation of farm products to the cities, lessen the cost of living, and thus justify the taxing of the State as a whole for the construction of this system corrected by pulling out pins. Also, if there should be …

It is rather surprising that maps for such purposes have not been more generally employed. Though the map record sheet shown in Fig. 183 may appeal to some business men, there would seem to be little advantage in that type of sheet over tabulated figures in a column. The column arrangement would have a desirable feature in that different entries could more easily be compared …

A blank like this can be filled out daily, weekly, or monthly as desired 224> GRAPHIC METHODS Maps on the scheme of Fig. 184 are made entirely in the plane of the paper itself. In Fig. 185 we have a map presentation in which quantities are represented by building verticallj" above the various routes laid out on the map. For the map of Fig. 185, the vertical representation was …

A map of this kind is easilj' made and is often of very great utility. The method can also be used to show the number of passengers carried on railroad, subway, or street-car lines, etc. Compare Fig. 185 The method used in the construction of the model shown in Fig. 185 gives magnificent results, but wooden strips are not practicable except on a very spacious map. The …

In many cases solder is unnecessary, for the strips may be held vertically by notching each strip halfway through so that the strips can be interlocked in the manner shown in Fig. 236. By using sheet metal a much cheaper construction can be obtained than by wood strips. The sheet-metal method also permits the use of a map of much smaller size and finer scale than would be …

The cloth tops, however, fade in the sunlight and collect dust so that in a short time the different colors of tacks on any map, exposed as a wall map must be, cannot be easily distinguished. The crudeness of the cloth-covered tack makes it unsatisfactory for many kinds of map work. Cloth-covered tacks are long, and long tacks which can be pushed only a short distance into the …

This is a point not realized by most men who install map and tack systems, but it usually sooner or later sounds the death-knell of the tack system. 228 GRAPHIC METHODS Generally the tacks are placed in the maps one by one as agencies are established or as data are obtained from correspondence. After the correspondence by which each tack was located has gone to the …

In the ordinary course of human events it is not likely that a tack falling out of a map would be found to give warning that the map record is no longer accurate. The tack system using long projecting tacks may therefore contain unsuspected inaccuracies just because tacks may have come loose. The unpleasant suspicion that a map record may be inaccurate, because of the long …

Since the pin is pushed in to its full length, a blow cannot dislodge it. The spherical head in contact with the map gives a very neat appearance, yet the spherical shape permits the fingers to remove the pin by straight pulling without any difficulty whatever. The smooth needle-point of good quality steel does not rust easily and it does not cut the surface of the map. When a …

A wall exhibit like this is easily made by using a red legal seal and red stars such as can be purchased at many good stationery stores way. A wall map on which pins with spherical glass heads are used can be very cheaply mounted, it needs no glass cover, and the pins can be put in or taken out instantly, thus giving a location record which is at all times in plain view, yet …

The only safe plan is to use the spherical pin head which is in contact with the map surface itself. Photographic views of a sphere are the same from all directions, thus causing all pins to appear exactly the same size and shape on the photograph. Photographs taken of a large map with flat-headed tacks show the heads in the center of the picture as circles, while the heads …

The middle layer should have the ribs running crosswise of the map so that the map mounting will be safeguarded from bending in either of the two different directions. Where very large wall maps are desired, six or more layers of straw-board may be used to give sufficient strength. If single sheets of straw-board cannot be found as large as the map itself, the map mounting can …

A layer of the cheapest kind of mushn placed over the face of the straw-board will prevent the pins from tearing the surface of the map if they happen not to be pushed in exactly straight. The use of cloth over the straw-board also permits of changing the pins many more times than would be feasible with straw-board without the cloth reinforcing. .'• /.■ Reoiew 0/ Reiyttws Fig …

At the same time the map is pasted on the front of the straw-board, paste a sheet of wet wrapping paper on the back of the straw-board mount. The shrinkage of the wrapping paper on the back will eciualize the shrinkage of the map on the front of the mount. Place the mounted map on a flat table surface or on a smooth floor, and stack books or other heavy articles upon the mount …

Exhibitionboard, compo-board, wall-board, or any of the various boards generally used for wall surfaces may be used as a backing to give strength to the cork. Care should be taken to get a good quality of board which will not warp seriously. The cork composition can be glued to the wall-board and then the map pasted on the cork. A piece of wrapping paper should be pasted on …

with a cloth tape as suggested for straw-board mounts, or the whole built up combination may be framed with picture framing but without using any glass covering. The cork composition used should be Vs-inch thick. Maps backed with cork composition and used with glass-head pins having needle points will permit almost unlimited puncturing from frequently moved pins. If the map is …

When employed with glass-head pins having needle points, the drawer cabinets for maps used to route salesman, etc., can have a layer of cork composition fastened in the bottom of each drawer. The maps are then glued to the surface of the cork composition. The drawer cabinets regularly found on the market have sufficient drawer depth to permit placing a ^^g-inch layer of cork …

If numerous glass-head pins are to be put into a map at one time, the eraser in the end of a lead-pencil should be used to push the pins down until the heads touch the map. Pins can be very quickly located if only their points are pushed into the map by hand, leaving the main pressure to be applied by the lead-pencil eraser after a number of pins have been located. The …

MAPS AND PINS Photographs for hne cuts must have a good contrast of white and black, or colors which photograph as black. Photographs or original drawings containing shades of gray will not produce good line cuts and frequently cannot be used at all for the zinc engraving process. When line cuts are to be made from pin maps it is best to be certain that the glass-head pins are …

Another advantage of half-tones is that different colors of pin heads are represented in the half-tone by different shades of gray, as can be seen in Fig. 191. On the left half of Fig. 191, fourteen different colors of glass-head map pins were used. The photograph Avas not retouched in any way. Fig. 191 thus represents about what can be expected of different colored pin heads …

The maps are very low in cost and yet are remarkably accurate. Fig. 191 was GRAPHIC METHODS MAPS AND PINS 237 purposely photographed at an angle of about 45 degrees. As the upper part of the illustration is out of focus because of the angle, the illustration does not do justice to the Government maps. Another reason why the map does not come out clearly is that brown ink is …

Maps on which large areas as States, or counties, are differentiated by the use of colors red, orange, green, etc., do not produce either good line cuts or good half-tones since the colored areas on the original maps are likely to show as solid black areas and blot out all detail on the photograph. If an illustration must be made from a map it is well to be sure that the map …

As maps are very carefully copyrighted by most map publishers, maps which are copyrighted should not be reproduced without consideration of the copyright. For maps which are photographed down with comparatively little change, permission should be requested from the map publisher, to make certain that unpleasant complications such as damage suits or the holding up of a …

In Fig. 193 a map was used in which there was more detail than really necessary or desirable for a clear illustration. In justice to the General Electric Review it must, however, be said that the map shown in Fig. 193 has been reduced in size and made smaller than it was in the original print. This map could not be reduced further without danger of completely losing the pin …

Location of Water-Power Developments of 1,000 Horse Power, and Over, and Power Sections of Streams in the United States The original of this map would have pins in two different colors. The photograph taken from the map would be retouched by the use of a pen so that squares would replace dots for one of the two colors of pins. The illustration shows a contrast of dots of two …

After a photograph has been made of the pin map it is best to compare the photograph with the original, and then to make squares out of those circles which represent a certain color of pin on the original map. Squares are easily made by using a fine pen on a photograph considerably larger than the cut itself will be. When the final dots are not too small in size it is possible …

It is not easy to find maps with lines sufficiently heavy to permit of the great photographic reduction usually necessary in making illustrations from pin maps or other map representations. Quite often it is necessary for the person making a map chart to go over by hand all outlines such as borders and the divisions between States, counties, etc., to make those particular …

In order to tell how much reduction in size is made by the glass at any given distance, it is possible to look at the original object with one eye and through the reducing glass with the other eye so that by superimposing the two images their length may be compared. When a chart has ruled lines, as co-ordinate lines, it is a simple matter to superimpose the images from the two …

It must be remembered, that most of these pins were in the characteristic blue colors commonly associated with the Bell Telephone System, and, because blue is almost impossible to photograph, the pins do not show out as strikingly as they would if other colors were used. The black splotches on the map were caused by the predominance in those areas of pins with dark blue heads …

This map, costing several hundred dollars to produce, could be injured severely by a few strokes of a janitor's feather duster. If short pins were used with spherical heads in contact with the map there would be no danger of the pins being misplaced. Another disadvantage of the long steel pins is that the steel portion exposed to the atmosphere is likely to rust, especially in …