Die Jahresringe der Holzgewächse. 369 



averaging, but the majority are due to climatic variations and form the essential 

 object of our investigations. Our purpose is to discover how far a given irre- 

 gularity in one part of the curve represents climatic conditions like those giving 

 rise to a similar irregularity in another part. A glance at the main features of the 

 curve for an individual tree shows that in its general course from youth to old age 

 it corresponds to the ideal smoothed curve. It is also evident that in the portions 

 of the curve where the tree is growing at the average rate of 0,20 inch per year, 

 an increase of 0,10 inch above the average rate of growth means no more than does 

 an increase of 0,05 where the average rate of growth is 0,10. In both cases the 

 increase amounts to 50 per cent, and it is incumbent upon us to apply a corrective 

 factor in such a way as to cause the two to be reckoned as of the same value. 

 Mathematically this means merely that we must reduce the smoothed curve, that 

 is, the solid line of figure 26, to a straight line lying in a horizontal position. This 

 can readily be done by selecting some point as representing the standard of normal 

 growth and then multiplying the value of every other point on the line by a number 

 which will raise or lower the given value to an equality with the value of the 

 point selected as the standard. Manifestly, if all the points on a line have the 

 same value — that is, if they are all at an equal distance from the horizontal base 

 line — the line in question will be straight. Thus the process under discussion 

 reduces the smoothed curve of growth to a straight line. It does not, however, 

 eliminate the irregular idiosyncrasies of the curve of an individual tree, although it 

 changes their relative importance. In the example under consideration the average 

 growth during the first year is 0,10. Let us take this as the standard or normal 

 growth. During the fortieth year the growth is 0,20, or twice as much; to reduce 

 20 to 10 means simply dividing by 2. Similarly during the two-hundredth year 

 the growth amounts to 0,05; to reduce 0,05 to 0,10 means multiplying by two. In 

 other words, the corrective factor for age during the fortieth year is one-half, or 

 0,50, while that during the two-hundredth is 2. Having this corrective factor for 

 each year of the tree's life we must apply it to the curves of individual trees. In 

 this way the dot-and-dash line shown in the diagram is reduced to the form shown 

 by the dash line above it. The sinuosities occur at the same time as before, but 

 are less marked than previously during the early years of the tree's growth and 

 more marked during old age, when the tree was growing so slowly that the original 

 curve became very flat. In this final curve the difference in rate of growth between 

 old trees and young has no effect. The variations that remain are due either to 

 accidents, to climate, or to another factor which we shall now consider. 



„In the original investigation whose results are here being set forth, a puzzling 

 feature appeared when the correction for age was applied to the first three or four 

 species. In the earlier portion of each curve — that is, in the part where only 

 the oldest trees could be used — there was a systematic lowering of position. 

 This appeared to indicate markedly drier conditions in the past than in the 

 present, but the apparent difference was greater than could possibly have existed, 

 and it occurred at different times in different trees, being dependent apparently on 

 the age of that special species. Moreover, it occurred at times when other lines 

 of evidence seem to point to exactly the opposite state of affairs. In attempting to 

 ascertain the cause of this, it was soon discovered that, other things being equal, 

 trees which are destined to live to a ripe old age grow in their youth more slowly 

 than do those of the same species and in the same locality which are destined to 

 die young or to live only until maturity." 



„Evidently a 'correction for longevity' is as necessary as one for age . . . The 

 process is clearly the same as that of obtaining the corrective factor for age — that 

 is, it consists in multiplying the value of each point of a smoothed ideal curve by 

 a corrective factor which reduces the curve to a straight, horizontal line." 



