682 THE AMERICAN JOURNAL OF SOCIOLOGY
the process of self-improvement goes on in the most active man- ner, but when the organism begins to mature, the speed de- creases; this is represented by the portion QR S of the "prog- ress curve," rising first rapidly, then more slowly. Finally the organism becomes tired, and decadence is the result ; this is illustrated by the last part, 57", of the figure, showing diminishing ordinates. It seems to me and this is precisely my contention that an individual or a society feels most contented, most satis- fied, not at the point 5 of the curve, but at the point R (i. e., at the point of the greatest inclination of the curve), notwithstand- ing the fact that the quantity of goods enjoyed at S is perhaps twice as large as that at R. I make this assertion because at R the quantity of goods increases most rapidly in a given time. The individual at this period is sanguine and full of hope; every day brings something new into his life; he is conscious of the fruits of his labor.
At 5 the contrary is the case. The absolute quantity of goods possessed is here comparatively large ; but this quantity is immovable ; every day brings the same thing ; the entire work of the organism is expended uselessly at some point, just as in a bad machine friction and internal resistances impede the movement in spite of its labors, it does not go forward. Thus it is clear that life-contentment must be smaller here than at R. Moreover, I assert that even at PQ, where the absolute quantity of goods is very small, there is more satisfaction than at S, because there is still some progress at PQ, while there is none at 5.
In short, my thought may be expressed mathematically as follows : The degree of life -satis faction of an individual or a society is independent of the ordinate of the "progress curve," but is a func- tion of the angle which the tangent to this curve forms with the axle of the absciss CB; or
where 5 is the degree of life-satisfaction, the quantity of goods possessed, and t the time. 1 The truth of this statement is
1 For those unfamiliar with mathematical analysis it may be observed that the
