18 



CLIMATIC CYCLES AND TREE GROWTH 



an even change from the center of one year to the center of the next. This 

 has been regarded by the writer as a form of smoothing. It is the beginning 

 of that general process, the grouping of details together in order to bring out 

 the larger characters. 



Smoothed Curves — There are two methods of smoothing in current use, 

 the unweighted and the weighted running mean. An unweighted or com- 

 mon running mean of three is an average of each three successive terms placed 

 as a substitute for the middle term. The common weighted running mean 

 used for many years gives double weight to the central term. The formula 

 for it is: 



y' _ Y n _i -f- 2Y n 4- Y n+ i 



.1810 .1820 ,1830 .1840 .1850 .I860 .1870 



4, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i i I 1 1 1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 L 



1.0 



COLUMNAR PLOT 



■P 



TTTV 

 ' I ' 



1810 

 i ii ill n 



1820 

 1 1 1 1 1 1 



1830 

 I III Mil 



1840 



ii i iliin 



1850 



i ii i In ii 



I860 



HI I ll 1 1 1 



1870 

 llllLl 



LLQ 



Fig. 6 — Point and column plots of same data. 



In our usage this method is adopted to the complete exclusion of simple 

 running means because the latter in case of rapid alternations may bring a 

 maximum where a minimum should be and vice versa (fig. 7. See also fig. 30). 



This weighted running mean has long been called the "Hann" (the word 

 has also been used as a verb) because applied extensively by Julius Hann. 

 It is conveniently worked by actual figures as a "second intermediate." In 

 this process the average of each two successive values is placed between them, 

 but in a separate column, and then the process is repeated for the new column 

 thus formed. The quantities thus obtained give the exact values of this 

 weighted running mean and are often called Hanned values or second inter- 



