20 



CLIMATIC CYCLES AND TREE GROWTH 



assumes an average horizontal direction and is the continued algebraic sum 

 of departures from the mean. This same thing has been called "accumulated 

 moisture" by the meteorologists. A defect in this sort of curve is that it 

 has a quite arbitrary point of beginning that modifies subsequent values. 

 Since it adds together successive departures in the same direction, it sums up 

 favorable or unfavorable conditions into extreme departures that greatly 

 exaggerate the trends; hence small variations in the original data tend to 

 disappear. 



-SCO <-> 



30 40 50 60 70 80 90 I900\/ 10 



Fig. 8 — Mass diagram and residual mass diagram. 



When applied to a cycle, it makes the maxima and minima far more 

 conspicuous and moves each forward a distance which for the sine curve is 

 one-quarter of the cycle length. In that capacity it was used in 1919 to 

 express a conservation effect in the relation of rainfall at Prescott, Arizona, 

 to the ring growth of trees nearby. In all usage of these mass diagrams for 

 cycle purposes it should be remembered that these are modified expressions 

 of the original data and hence what they show is more complex than the 

 original data, and special care is needed to see that something fictitious is not 

 introduced. I have personally hesitated to use them because they are not 

 a primary expression of data, but it is not easy to say why cycles derived 

 from this sort of curve are not to be given careful consideration. 



