THE CORRECTION AND COMPARISON OF CURVES OF GROWTH. 127 



Evidently a "correction for longevity" is as necessary as one for age. It is applied in 

 the same way. Figure 27 illustrates the method. 

 The horizontal line in this case indicates groups of 

 trees of a given species. Group (A) on the right con- 

 sists of trees 500 years old, group (B) of those 400 

 years old, (C) 300, and so forth. The vertical coordi- 

 nates represent the amount of growth made by the ^ „, t i i ,-. ■„ . ,■ r^ 



1 . ,, r- , 1 1 T, -11 1 ,1 , ,1 Fig. 27.— Ideal Curve illustrating Correction 



trees durmg the nrst decade. It will be seen that the ^^j. Longevity. 



trees 100 years old made an average growth of 2 inches ; 



those 200 years old, 1.70 inches; 300 years old, 1.50 inches; 400 years old, 1.35 inches; and 



500 years old, 1.30 inches. 



From this it appears that if the minor fluctuations of climate which took place from 

 year to year during the first decade of the average tree 500 years old are to be compared with 

 those during the corresponding decade of the average tree 200 years old, the growth of 

 theolder trees must be multiplied by 1.70 -i- 1.30 = 1.31, the corrective factor for longevity. 

 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. The determination of the 

 corrective factor for longevity, however, is more difficult than the determination of that 

 for age, not because the factor for longevity is any less real or is any less strictly a mathe- 

 matical function, but because more trees are required in order to secure accuracy. Wliere 

 the number of trees amounts to 200 and the age does not exceed more than 300 or 400 years 

 the factor can be determined with a considerable degree of accuracy. For older trees a 

 larger number of specimens is necessary before high accuracy can be obtained. 



In considering both of the corrective factors it must be borne in mind that they are 

 attempts to get rid of all variations except those due to temporary pulsations of climate. 

 The corrections do not and can not take cognizance of any possible changes of climate 

 which may progress uniformly or continuously from beginning to end of the life of the 

 trees in question; they are calculated on the assumption that the average climate of the 

 past was hke that of the present. The attempt is to smooth the curves as far as possible 

 and to reduce them as closely as may be to straight lines ; the earliest parts are thus brought 

 to the level of the latest in as great a degree as possible. Hence the final curves, while 

 showing all the variations whose periodicity is less than that of the fives of the trees, do not 

 necessarily show long, secular changes which may have taken place. In many cases, to 

 be sure, they appear to show them, the later end of a curve being in general higher or lower 

 than the earlier, but no refiance can be placed on this. It is generally due to errors in 

 applying the corrective factors, and these errors generafiy arise from insufficiency of data. 

 In connection with the corrections which have just been discussed, another matter 

 should be considered : The last two centuries of all the curves of growth are based upon a 

 constant number of trees. For earlier dates, the number gradually diminishes, tree after 

 tree being dropped until only a few of the oldest are available. Theoretically the dropping 

 out of tree after tree is an important matter, and may lead to serious errors unless it is 

 guarded against. If at one special period a number of rapidly growing trees happen to 

 drop out, the curve prior to that time will be relatively too low; and, in the same way, 

 if all the trees which began to grow at a given time happen to have grown slowly, the part 

 of the curve before that time will be too high relative to the succeeding part. In order to 

 avoid errors of this sort it would be possible to apply a correction every time that a tree or 

 group of trees is dropped out. In actual practise, however, I have found it inadvisable 

 to attempt this. Where the total number of trees is ten or twenty times as great as the 

 number that is dropped, and where the other corrections have been properly applied, this 

 particular correction makes only slight differences in the general form of the curve. 



