THE CORRECTION AND COMPARISON OF CURVES OF GROWTH. 



129 



available analyses of trees over 200 years of age have been used, and to them have been 



added an approximately equal number of younger trees in order to afford fair comparisons. 



The results obtained from the data furnished by IMr. Recknagel are shown in figures 28 



and 29. In figure 28 it will be seen that during the first 10 years of their lives the trees 



an average grew fairly 



on 



Date 



0.30 



0.1i> 



Fig. 29. 



-Cmve of Growth of 50 Yellow Pines over 280 Years of Ago, from 

 1590 to 1910 A. D. 



rapidly, or 0.46 inch for the 

 10 years. During the next 

 two decades the rate of growth 

 increased rapidly and reached 

 a maximum of 0.63 inch during 

 the third decade. Then it de- 

 creased rapidly at first, and 

 then more and more slowly 

 until at old age it had sunk to 

 half of its value when the trees 

 first started. Naturally the 

 original curve, the dotted line 

 of figure 28, shows a certain 

 amount of sinuousity due to 

 the various accidents, cUmatic 

 and otherwise, to which the 

 272 trees which it represents 

 have been sub j ected. In order 

 to obtain the true corrective 

 factor the curve has been 

 smoothed as indicated in the solid line. Table 3a shows the measurement. 



The use of the corrective factor is illustrated in figure 29. In this case 50 of the oldest 

 of the yellow pines of New Mexico have been taken, trees that began growing previous to 

 1630. The upper dotted line shows their rate of growth as actually measured; that is, 

 before any correction has been applied. In its early portions for 50 years the curve rises 

 with extreme rapidity; then for another 60 years it drops off almost equally fast; then 

 we have another rise for 30 years, followed by a fall for 40, a rise for 20, and so on to the 

 end. The irregularities are in part an indication of fluctuations of growth because of 

 climatic variations or other accidents, but the main fall is due to the fact that after 1655 a. d. 

 all the trees were of such age that their rate of growth was decreasing in accordance with 

 the curve of figure 28. When the corrective factor for age is applied, the form of the 

 curve is changed greatly and brought down to the position of the lower dash line. Here we 

 find that the sinuosities continue to appear at the same periods as formerly, but their 

 relative size is changed and those in the first century become more manifest because 

 not masked by the extremely rapid growth of youth. 



The curve as thus corrected for age drops extremely low in its early portions. If no 

 further correction were necessary, we should infer that climatic conditions were very 

 unfavorable during the seventeenth century. The low position, however, is tlue to the 

 fact that no corrective factor for longevity has yet been applied. 



The necessity for a correction for longevity is illustrated in figure 30, which represents 

 an actual case of the same kind as that which appears in figure 27 in its simplest ideal form. 

 The horizontal distances indicate various groups of trees, varying from those which were 

 only 100 years of age at the time of cutting to a small group of three whose average age 

 when cut was 390 years. The age of the trees of the respective groups is given in the 

 upper row of figures just under the letters A, B, etc. The number of trees in each group 

 is indicated in the second row of figures, and is also shown graphically in the rectangular 



10 



