Page:The Scientific Monthly vol. 3.djvu/375

 OUR NATIONAL PROSPERITY 369

picions of some general law of incomes displayed therein. In every one of the eighteen groups the mean rate of increase of the incomes is greater than the mean rate in the preceding group. It is not remark- able that the incomes continually increase from left to right, for they were so arranged as a condition of the drawing — ^but it is remarkable that their rate of increase should continually increase. True, this was also the case in the other two diagrams, but the continuity of curvature was not so marked and in the case of Fig. 1 we were free to make the curve fairly smooth, since we were bound to only two points. But here we are bound to eighteen points, all of which lie on a strikingly graceful curve.* Only ten of these eighteen points are shown on the diagram, the others all lying on the vertical limb beyond the limits of the draw- ing. But by plotting to other scales the same continuity is exhibited in all parts of this vertical Umb. No manner of plotting will show sat- isfactorily the full extent of both horizontal and vertical limb at the same time.

What does this continuity of curvature mean? It means that in- comes increase throughout their whole range at an expanding rate. In the fourth group the rate of increase is nineteen cents per person, while in the fifth group the rate is forty-two cents per person. In the first group the rate is one cent per person, while in the seventeenth group the rate is $2,280 per person. Or to put it in another way — a man in the seventeenth group, in order to raise his income by $2,280, must get ahead of but one other man in the race, whereas a man in the first group must pass some 228,000 others in order to raise his income by a like amount. It all means that the greater a man's income the easier it is for him to augment it — a state of affairs curiously incongruous, since the greater his income the less need for him to augment it. But this is the principle in distribution that accounts for the enormous inequalities of property shown by Pig. 1. It is what Herbert Spencer would call an example of the law of the '^ multiplication of effects.'' Or in current platitudes, " nothing succeeds like success." It would seem to show that a condition even approaching equality was one of unstable equilibrium and that society contains within itself the seeds of economic destruction. We do not assert that such is the case for there may be other seeds in society with an opposing tendency, but such opposing forces are not now, at least, in evidence.

4 The curve in Fig. 3 has the general shape of the mathematical curve xy^ = a. A curve of this form was forced to pass through the three points A, B and C by conditioning three of its parameters. These were the position of its two axes, and the constant a. If for coordinate axes we take the axis of X, .34 units below the horizontal base; and for the axis of Y, a line .039 units to the left of our right-hand vertical, then the curve a;t/2 = 3.85 so referred, will pass verj close to all ten points. At the $10,000 point it will be about .05 units too high, but at the other points the variation is too slight to show upon a drawing.

�� �