It was at once manifest that the rate of growth so determined shewed a tendency to fluctuate in a long period of between 100 and 200 years. I then smoothed in groups of 100 (according to Gauss’s method) the yearly values, so that each number thus found represented the mean annual increase during a century: that is to say, the value ascribed to the year 1500 represented the _average annual growth_ during the whole period between 1450 and 1550, and so on. These values give us a curve of beautiful and surprising smoothness, from which we seem compelled to draw the direct conclusion that the climate of Arizona, during the last 500 years, has fluctuated with a regular periodicity of almost precisely 150 years. Here again we should be left in doubt (so far as these {123} observations go) whether the essential factor be a fluctuation of temperature or an alternation of moisture and aridity; but the character of the Arizona climate, and the known facts of recent years, encourage the belief that the latter is the more direct and more important factor. [Illustration: Fig. 32. Long-period fluctuation in rate of growth of Arizona trees (smoothed in 100-year periods), from A.D. 1390–1490 to A.D. 1810–1910.] It has been often remarked that our common European trees, such for instance as the elm or the cherry, tend to have larger leaves the further north we go; but in this case the phenomenon is to be ascribed rather to the longer hours of daylight than to any difference of temperature[152]. The point is a physiological one, and consequently of little importance to us here[153]; the main point for the morphologist is the very simple one that physical or climatic conditions have greatly influenced the rate of growth. The case is analogous to the direct influence of temperature in modifying the colouration of organisms, such as certain butterflies. Now if temperature affects the rate of growth in strict uniformity, alike in all directions and in all parts or organs, its direct effect must be limited to the production of local races or varieties differing from one another in actual magnitude, as the Siberian goldfinch or bullfinch, for instance, differ from our own. But if there be even ever so little of a discriminating action in the enhancement of growth by temperature, such that it accelerates the growth of one tissue or one organ more than another, then it is evident that it must at once lead to an actual difference of racial, or even “specific” form. It is not to be doubted that the various factors of climate have some such discriminating influence. The leaves of our northern trees may themselves be an instance of it; and we have, {124} probably, a still better instance of it in the case of Alpine plants[154], whose general habit is dwarfed, though their floral organs suffer little or no reduction. The subject, however, has been little investigated, and great as its theoretic importance would be to us, we must meanwhile leave it alone.