CHAPTER XII. 

 THE CORRECTION AND COMPARISON OF CURVES OF GROWTH. 



Ill making use of the method of tree measurements elaborated in the previous chapter 

 by Professor Douglass, I have employed two sets of data, those of the United States Forest 

 Service and those obtained by my assistants and myself among the giant sequoias or 

 "Big Trees" of the Sierras during two seasons in California. The Forest Service, through 

 the courtesy of the Forester, Mr. Henry S. Graves, kindly put at the disposal of the Carnegie 

 Institution the large body of "stem analyses" which his Bureau has collected from forests 

 in all parts of the country. A stem analysis is simply the record of the measurement of 

 the thickness of the rings of annual growth. The Forest Service makes such analyses at 

 various points along the trunks of trees that have been cut for lumber, but the only ones 

 that have here been used are the "stump analyses," or measurements made directly upon 

 the top of the cut stump. The method employed by the Forest Service is to pick out an 

 average radius, and begin measuring from the outside inward toward the center. A finely 

 graduated ruler is laid upon the stump and from this the distances are read off and recorded 

 in books especially prepared for the purpose. The unit of measurement is 10 years, since 

 it is difficult to measure the individual years without an undue expenditure of time. More- 

 over, for the purposes of forestry— that is, for determination of the rate of growth of various 

 species under different conditions— a 10-year unit is as good as a smaller one. Only in the 

 case of young trees does the Forest Service employ the year as the unit in stem analyses. 



The measurements which I obtained in Cahfornia were made in the same way as the 

 ordinary stump analyses of the Forest Service, except that in many cases the best radii 

 were chosen instead of the average; these will be discussed fully in the next chapter. At 

 present we shall confine our attention to the measurements made by the Forest Service. 

 We shall consider the two chief ways in which the curves obtained by the simple process of 

 averaging need correction before they give a true idea of the comparative climates of the 

 past and the present, and shall elaborate the method of correcting them, a method which 

 is purely mathematical and does not involve the introduction of the personal equation to 

 any appreciable extent. Then we shall be prepared to inspect the curves and to find out 

 what they indicate as to our main problem. The total number of analyses which were 

 chosen from among the many thousand in the archives of the Forest Service is 2,664. 

 Only those of trees having an age of over 200 years were selected. In the case of many 

 species only a few specimens reach that age, and the number is not large enough to furnish 

 curves sufl^ciently reliable to be worth publishing. In fifteen cases, however, it has been 

 possible to find enough old trees to justify the construction and publication of their curves. 

 The same method of correction was employed with all of them, except that in some cases 

 one of the two corrective factors, which are to be discussed later, did not seem to apply. 



The annual rate of growth of trees is subject to variation for four chief reasons. In the 

 first place, trees grow at very different rates according to their age, young trees usually 

 growing rapidly and old trees slowly. In the second place, trees destined to have a long 

 life usually make haste slowly, being outstripped at first by their neighbors, which are 

 to die much sooner. These two types of variation can be calculated with mathematical 

 precision, and by the use of the proper formulae corrective factors can be obtained by 

 means of which errors due to them can be largely eliminated. The third reason for varia- 

 tion in the annual rate of growth of trees is the occurrence of non-climatic accidents such 

 as shading in youth, the breaking of branches, the slipping of the soil, the ravages of insects, 

 or the devastation wrought by fire. At first sight these appear to be of almost preponder- 



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