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judgments and yet be saved from disaster, or even thrust into success, by the sheer momentum of the national growth. If he failed to sense the coming of a depression, or to time it accurately, why worry? Even the depression bottom was higher than the peak of a few years before. This situation is no longer true. It has not been true since 1918. A greater premium than ever before is imposed on the ability to time the turns in the business cycle correctly.

      Many of our businessmen have looked on the depths that were reached in 1932-1933 as a development completely accidental, and one unlikely to recur. But one glance at the second part of Fig. 3 shows why the recurrence of a fall of magnitude seems probable if and when our economy slides into a depression again. This chart shows how the trend line in our economy has leveled out, so that no rising trend is present to compensate for a fall in the business cycle.

      The phenomenon of increasing intensity of depression — as an economy approaches the upper level, or asymptote, of its trend — is shown suggestively in the history of the Spanish Empire, one of the earliest social organisms for which we have any useful statistical record. E. J. Hamilton, in his study American Treasure and the Price Revolution in Spain, has provided us with elaborately detailed estimates of Spain’s total imports, valued in standard pesos, from 1503 to 1660. On the basis of this data, Harold T. Davis has constructed an index of Spanish trade for this period which is charted in Fig. 4, together with a trend line which has been added by the authors. The period includes most of the great growth and expansion of the Spanish Empire. Of particular interest is the series of deep depressions that begin to appear after the trend line begins to reach maturity.

      Fig. 4. Index of Spanish Trade

      Data—1530-1650 (after Davis and Hamilton) together with Trend. (For the same data plotted on ratio scale, see Appendix I, Fig. 8.)

      In very recent years we have discovered a great deal of new information on this subject, and a new application of scientific methods in its use. But before we reach the problem of the cycle we must know more about trends, and how they are determined and estimated.

      II

       Patterns in Growth of Organisms

      A growth trend amounts to a pattern; and the pattern is similar for almost all organisms, whether a group of cells in a pumpkin or a group of human beings in a nation. The one has a range of life measured in months, the other in centuries. But the general pattern of growth is much the same. Even more surprising, a similar pattern may be discovered in the growth of human institutions like corporations and industries, as we shall see.

      Much of our current knowledge of the laws of growth has developed from the pioneering work of Lowell J. Reed and Raymond Pearl, of Johns Hopkins University. Pearl has briefly described the outcome of their initial research, begun in 1920, as follows:

      As a result of applying certain biological reasoning to the problem, we hit upon an equation to describe the growth of populations, which subsequent work has clearly demonstrated to be a first approximation to the required law. As we were in process of publishing the first discussion of the matter, we found that a Belgian mathematician, P. F. Verhulst, had as early as 1838 used this same curve, which he called the “logistic curve,” as the expression of the law of population growth.*

      [* The Biology of Population Growth (p. 3-4), copyright, 1925, Alfred A. Knopf, Inc.

      While there are scientists who have shown a disposition to question some of the Pearl methods — on the ground, for instance, that he did not determine the probable errors of constants — and while almost limitless work in this field is still to be done, it remains that Pearl’s contribution is of extraordinary usefulness.]

      The study which Pearl published in 1925 under the title The Biology of Population Growth is still, some twenty years later, a readable, elegantly simple statement of a profound truth which has since been put to work in many fields. The curves Pearl and Reed explored permit city planners to forecast future city populations within a small margin of error; enable great utility companies to know with fair accuracy where facilities will be in greatest demand at a given future time. The Biology of Population Growth is still required reading for any executive concerned with a scientific approach to the future; a few of its many charts are reproduced here with the publisher’s permission.

      Fig. i. Growth in Body Weight of a Male White Rat (After Pearl)

      As Pearl points out, every living being starts as a single cell; the cell divides and is multiplied; the process goes on at different rates but without cessation until complete adult development is reached. Counting the cells is impossible after the very earliest growth stages; but periodically repeated weighings give a rough yet sufficiently accurate index of the increase in their number.

      “The results of such periodic weighings give rise, when plotted upon co-ordinate paper, to a curve of peculiarly characteristic shape,” Pearl showed. It is something like the shape of an elongated italic S. The curve is similar, for instance, for the growth in body weight of a white rat (Fig. 1) ; for the growth in weight of a pumpkin (Fig. 2); and for the growth of a population of yeast cells in a test tube (Fig. 3) and of fruit flies, or Drosophila, living in a bottle (Fig. 4).

      Fig. 2. Growth in Weight of a Pumpkin (After Pearl)

      This much seems extremely logical. A population of yeast cells or fruit flies, living in a closed environment, could be expected to reach some upper limit of balance between the number of cells and the living space available. To find a consistent curve in approaching such a balance does not seem surprising. But when Pearl turned to the study of human populations, he found the same law of growth operating.

      Fig. 3. Growth of a Population of Yeast Cells (After Pearl)

      Fig. 4. Growth of a Population of Fruit Flies in a Bottle (After Pearl)

      Fig. 5. Growth of the Population of Sweden (After Pearl)

      This demonstration does not conform so readily with the processes of our human logic. For human populations are subject to plagues and wars, to emigration and immigration, to birth-control movements and counter birth-control movements. They grow under conditions that seem far removed from the controlled environment of Drosophila in a test tube. And yet, as Pearl showed:

      Sweden has grown in a manner which, in its quantitative relations at least, is essentially like the manner in which a population of yeast cells grows. . . . Except for the amount of time covered by the observations, this curve for the United States is strikingly like that of Sweden. . . . For France . . . the growth has evidently followed, during the epoch or cycle in which it now is, the same basic law as that of Sweden and the United States. The same thing is true of the known population growth of Austria, Belgium, Denmark, England and Wales, Hungary, Italy, Scotland, Serbia, Japan, Java, Philippine Islands, the world as a whole, and Baltimore city.*

      [* Ibid., pp. 13-17.]

      The similarities Pearl mentions show up graphically in his charts for Sweden, the United States, and France, reproduced in Figs. 5, 6, and 7.

      Now comes a vital and significantly useful fact. When a consistent pattern of growth exists, we have sound grounds for making predictions. However qualified those predictions may be, they have the probabilities on their side. Thus, when we have enough census records — as for the United States — to establish a number of points on the

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