92 



CLIMATIC CYCLES AND TREE GROWTH 



former oval and indicates a negative correlation between successive values. 

 This changed major axis indicates in the discarded residuals a strong zigzag 

 that we need so much for prediction purposes. The axes of the oval have a 

 ratio one to the other of 2.3:1.0 and suggest a negative correlation of about 

 75 per cent between successive departures from the smoothed curve. 



Information obtained in the last paragraph is important for prediction 

 purposes. But in using it we must not forget that random data treated in 

 similar manner always give theoretically a ratio over unity. Quoting Dr. 



Minus Plus 



The year itself- Departure from mean 



Fig. 39 — Conservation in successive years in Fort Defiance group, 

 shown by scatter diagram using departures from a mean 



Bartels, we may have a series of random values, but the differences between 

 those values are not entirely random, and if we smooth the data as usually 

 done, there is increased chance that successive values will be on opposite 

 sides of the smoothed sequence. In a scatter diagram of such random rela- 

 tion, the theoretical mean form of the oval should have a ratio of axes of 

 1.3:1.0. Therefore, to retain a clearer estimation of the situation we have 

 added three curves of the two-year reversal interference test on random 

 values in figure 38. They show no relation to each other and thus are very 

 different from the action of natural sequences in our western zones. We 



