26 CLIMATIC CYCLES AND TREE GROWTH 



records, because in fact, so far as cycles are concerned, the various curves 

 have entered the average with weights proportional to their mean sizes. 

 Hence in practise, to combine curves for cycle analyses we must bring them 

 to the same mean value, which for convenience is unity. (These curves, it 

 will be remembered, represent departures from a zero line and not from a 

 mean.) This process is easily done by reducing each curve to percentage 

 departures from its own mean ; that is, each separate value is divided by the 

 mean of the curve. This brings the new mean of each curve to unity, and 

 variations expressed in percentage give an illuminating view of what is hap- 

 pening in the curve. The average of the equalized curves gives equal im- 

 portance to the variations of each curve and is in proper form for analysis. 



There are further points for consideration in this usage. When a tree 

 ring is absent and its measure goes to zero, that value tells something impor- 

 tant, but whatever it tells is greatly exaggerated. Again, when we examine 

 the shorter cycles going on near a minimum of a long cycle, such as short 

 cycles in monthly sunspot numbers at minimum of the 11-year sunspot cycle, 

 variations from a mean fail to tell the story. Thus we reach the need for 

 local equalizing within a curve, which is a more difficult task but absolutely 

 necessary if we are to get the cyclical facts. In the case of trees, we are try- 

 ing to find the variations common to many trees in identical dates over a 

 large area. Obvious idiosyncrasies in individual trees must be removed if 

 each tree is to contribute its best to the common result. The western yellow 

 pine is an isolated tree and its early rings are very thick to build a framework 

 and give it strength. The change in mean ring thickness with age is called 

 the age curve. Douglas fir and pinyon usually begin under protection of 

 other trees, and their early rings are small and grow larger before beginning 

 to diminish regularly with age. These different age curves are easily removed 

 by plotting each tree record and drawing the apparent mean age curve as 

 nearly straight as possible through it. This mean line or age curve is called 

 the standardizing line and at each abscissa is divided into the corresponding 

 measured ordinate to produce the standardized value. 



The standardizing line is drawn only by someone of much experience. 

 It is made straight or with an irreducible minimum of curving or bending so 

 as to avoid inserting or taking out any cycles. A curve with such line is 

 shown in figure 12 together with the effect of standardizing. The process of 

 standardizing has received specially careful application in connection with 

 very long curves in order to disclose long cycles if present. The methods 

 developed will be described below under compressed curves. 



The big sequoias are in rare cases subject to "gross" rings or a limited 

 succession of rings of greatly exaggerated thickness. They are best examined 

 on top of a stump and may be due to a strain or fire injury and a vigorous 

 effort of the tree toward recovery. The growth curve of a sequoia becomes 

 far more normal when such gross rings are greatly diminished by moving the 

 standardizing line upward. Complete removal, however, is never practised. 



