THE CORRECTION AND COMPARISON OF CURVES OF GROWTH. 



125 



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

 of exceptional warmth and moisture and the Uke, will have caused a very slow or very rapid 

 growth in certain trees at certain times. Nevertheless the variations from a mathematicall}' 

 perfect curve are shght, partly because the number 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 cHmatic 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 eUminated. If we had an infinite number of trees of all ages, 

 even the shght irregularities which now exist would be eliminated and we should obtain a 

 smooth curve hke the solid hne 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 and remained constant during the hfe of the tree. 



10 20 30 40 50 60 70 80 90 100 150 



Fig. 26. — Ideal Curves illastrating Correction for Age. 



200 Age 



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 fii'st 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 will be eliminated by 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 irregularity in one part of the curve represents climatic 

 conditions hke 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 fine lying in a 

 horizontal position. This can readily be done by selecting some point as representing 

 the standard or normal growth and then multiplying the value of every other point on the 

 hne 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 hne have the same 

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



