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 the quantities represented by the different areas have changed in actual size or only in relative size. Where great fluctuations occur from time to time and many factors enter into the total, it is best to draw charts in the form of Fig. 129 with a common zero line, or in the form of Fig. 131, where each factor has its own separate base line, or in the form of Fig. 132 and Fig. 133, in which the lines on the chart represent actual quantities rather than percentages of an aggregate or total sum.

Fig. 129. Percentage Distribution of the Expenses of Operating the Railroads 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. This method, though not so popular as the method of Fig. 128, permits more accurate reading

Note in Fig. 130 and Fig. 131 the 8-1/2-inch by 11-inch co-ordinate paper on which the ruling is so arranged that the paper may be used for almost any subdivisions of time, such as days, weeks, months, etc., as seen in Figs. 57, 103, 131, 134, and 156.

In Fig. 130 the paper was used for a time-scale of three years by months, the total height of the chart being put at 100 per cent, using fifty out of the fifty-two spaces on the paper. Fifty-two spaces, corresponding to the number of weeks in a year, of course are necessary when the paper is used to represent weeks on the long dimension of the sheet.

Fig. 131 and Fig. 130 depict exactly the same data. In Fig. 131 the facts, which in Fig. 130 were represented by areas, are shown as separate curves, each curve with its own base line. Having this series of separate curves on one sheet of paper permits an executive to compare the number of accidents in one department with the number of accidents in any other department at any one time, or to study