Page:Graphic methods for presenting facts (1914).djvu/151

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

Fig. 121 has been drawn to assist in proving the preceding statement regarding curve slope. Starting with one dollar, it was assumed that a uniform increase of 10 per cent of the 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 dollar has increased to nearly thirty-one dollars. Though the accumulated fund is shown by a smooth curve throughout the period of thirty-six years, the curve is constantly changing its slope in spite of the fact that the rate of increase remains constant at 10 per cent per year. The curve in Fig. 121 is very similar in shape to the curve for the United States in Fig. 120. This similarity in shape shows conclusively how much the reader would be misled if he should assume that the increasing slope of the curve in Fig. 120 proved in itself an increase in the rate of growth. The actual percentage rate of the growth for Fig. 120 can best be studied by making an entirely new chart for the purpose of observing percentage rates only.

Fig. 121. Curve Showing the Growth of One Dollar at 10 per cent Compound Interest for Thirty-six Years

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