368 



Ernst Antevs. 



illustrated iu the accompanying- diagram, figure 26. Let the horizontal line represent 

 the course of time as indicated in years by the figures 10, 20, 30, 40, etc. Let the 

 vertical distance indicate the average thickness of the ring of wood added each 

 year. Suppose that we have averaged up the rate of growth of all these trees 

 during the first year of their lives and find that it amounts to one-tenth of an inch. 

 In the same way we find that the growth during the tenth year amounts to 0,15 of 

 an inch; during the twentieth year 0,175; during the thirtieth, 0,19; and the fortieth 

 0,20. After the fortieth year the rate of growth begins to diminish until at the 

 one-hundredth year it has fallen to a figure no larger than that of the first, while 

 at the two-hundredth it has fallen still lower, to 0,05 of an inch. Manifestly it is an 

 easy matter to plot a curve from these figures. The curve will rise rapidly at first, 

 as appears in figure 26, and then will fall more and more slowly. Such a curve, 

 when plotted, will not be perfectly regular, but will be somewhat wavy, as shown 

 in the dotted line, because accidental circumstances, such as shading in youth, or 

 periods of exceptional warmth and moisture and the like, will have caused a very 

 slow or very rapid growth in certain trees at certain times. Nevertheless the varia- 

 tions from a mathematically perfect curve are slight, partly because the number 



Growth 

 0.10 



0.20 

 0.15 

 O.ltJ 



0.05 

 0.00 



10 20 



30 40 .50 (50 70 80 90 100 150 



Fig. 26. Ideal Curves illustrating Correction for Age. 



20Û Age 



of trees is large enough so that the averages are little affected by accidents to 

 individuals, and partly because of the fact that the first year of one tree may fall 

 150 years before the first of another, and the rest may be distributed anywhere 

 between these two. Thus the average of any year, whether it be the first, the 

 tenth, or the hundredth, does not represent the climatic conditions of a single year, 

 but of 100 years selected at random. Thus not only the effect of accidents, but 

 also that of climate, is largely eliminated. If we had an infinite number of trees 

 of all ages, even the slight irregularities which now exist would be eliminated and 

 we should obtain a smooth curve like the solid line of figure 26. This would 

 represent the relative rate at which trees of a given species would grow during 

 different parts of their life in the particular locality under consideration, provided 

 that the conditions of sunlight, rainfall, temperature, and soil, as well as the relation 

 of the plant to other vegetation and to accidents, were of the average type an<l 

 remained constant during the life of the tree. 



„If the curve of growth of an individual tree — ■ the dot-and-dash line, for 

 example, in figure 26 — be compared with the ideal smoothed curve, the first feature 

 which strikes the attention is the marked idiosyncrasies, the repeated and (irregular 

 ups and downs. So far as these are due to accidents they wiU be eliminated by 



