408 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912. 



are purely mathematical, and do not depend upon the individual 

 judgment of the investigator. While he is working out the calcula- 

 tions he can not have any idea of the exact results which will be 

 obtamed; nor can he make the results fit one theory rather than 

 another except by willful manipulation. 



The accompanying diagram, figiu^e 1 (p. 407) , shows the results of Mr. 

 Recknagel's tree analyses when computed according to the method 

 here described. The horizontal lines indicate the course of time 

 from 1590 to 1910 A. D. The height of the curves indicates the 

 relative rate of growth of the trees at any particular date. Figure 1 

 is given simply as an example to show the effect of the corrections. 

 It is based upon the 50 oldest trees, which began growth at periods 

 ranging from 1460 to 1590 A. D. The upper dotted Hne indicates 

 the actual average rate of growth of these 50 trees without any cor- 

 rection whatever. The lower dash hne is the same curve after the 

 correction for age has been apphed — that is, after allowance has been 

 made for the fact that young trees grow faster than old. The sohd 

 hne shows what happens to the curve when the correction for lon- 

 gevity is added to that for age — that is, when allowance is also made 

 for the fact that during their youth trees which are to Hve to a great 

 age regularly grow more slowly than the normal rate. 



Turnmg now to the mterpretation of the New Mexican curve, we 

 find a surprisingly close agreement with our conclusions based on the 

 evidence of terraces, archeology, and history. Before going on to 

 discuss the matter I would emphasize the fact that these conclusions 

 were all reached before the trees had been investigated. They have 

 been set down above exactly as they were reached, at a period of 

 from 15 to 5 months before any examination of the trees was made. 

 The importance of this lies in the fact that the agreement of the 

 mathematically derived tree curves with the conclusions derived from 

 entirely different methods furnishes the strongest possible confirma- 

 tion of the accuracy of those methods as employed both in America, 

 Asia, and southern Europe. From the rums of Gran Quivira, it will 

 be remembered, we concluded that at the time of the Spanish occu- 

 pation of New ]\lexico in the first half of the seventeenth century 

 climatic conditions were distinctly more favorable than at present. 

 About 1680 the ruins of Gran Quivha seem to have been fuially 

 abandoned at the time of the Pueblo rebellion. During the succeed- 

 ing century conditions appear to have been somewhat better than 

 durmg the one that ended in 1900, as appears probable from the ruins 

 of Buzani, and one or two other places not here mentioned. The 

 curve of the trees points to exactly the same conclusion. One reason 

 why the Spaniards were able to estabUsh themselves m New Mexico 

 almost without a blow may have been that from 1600 to 1645 the 

 amount of ram and the general conditions controlling the growth of 



