CHRONOLOGY DOUGLASS AND ANTEVS 309 



quarters, and fifths. A cycle of approximately 100 years emerges 

 in the longer records. Michelson considered that he found this 

 cycle in the sun-spot numbers. 



CYCLES IN ARIZONA PINES 



The records of Arizona pines, Pinus fonder osa^ have been extended 

 back in a continuous series to 700 A. D. by the aid of beams from 

 prehistoric ruins. A preliminary examination of this sequence in- 

 dicates well-developed long cycles of approximately 38 years and 

 100 years nearly continuous through the interval, together with 

 shorter cycles apparently related to the sun-spot cycle and one of 9.5 

 or 19 years (doubtless related to the 38-year cycle just mentioned) . 



The " Hellmann relation " is the name tentatively given to the 

 half sun-spot cycle having a length of about 5.5 years. It is pre- 

 sumably an 11-year cycle with two maxima usuall.y unequal. This 

 cycle was described and compared with the sun-spot cycle by Hell- 

 mann in his study of the North German drainage area, published 

 in 1908. It was observed by the speaker in 1908 in the California 

 rainfall and in tree growth in Arizona at the same time. In 1912 

 it was found in north European trees with one maximum often sup- 

 pressed. About 1915 it was found highly developed in the Arizona 

 trees during the century or more following 1420, and it is now 

 recognized to extend in a slightly modified form from 1300 to 1650, 

 and at other places. This is considered to form a basis for recon- 

 structing the sun-spot curve during that interval and such an attempt 

 is being made. This relation may easily be detected in recent Cali- 

 fornia tree growth and rainfall. 



A shorter cycle somewhat over two years in length was noted in 

 tree growth from the frequent occurrence of alternating sizes in suc- 

 cessive rings. Such a cycle had been noted years before by Clayton, 

 Arctowski, and others. From a study of rainfall near Windsor, 

 Vt., published in 1915, this appeared to average about two and one- 

 third years in length. The original cyclogram gives a suggestion of 

 composite character, as if there were really two cycles, one about 

 2.25 and the other about 2.55 yeare in length. 



PREHISTORIC DATING 



The influence of weather and especially rainfall on the size of rings 

 has individualized them with great uniformity over a wide extent of 

 country. This produces distinctive configurations of large and small 

 rings, which, like " fingerprints of Father Time," can be recognized 

 from tree to tree. Thus, cross dating is possible over at least the 

 northern half of the Pueblo area, and we are able to build up a long 



