Page:Climatic Cycles and Tree-Growth - 1919.djvu/86

The first assumption in regard to conservation was that the ring-growth in any one year was built up by contributions from the current year and previous years in diminishing proportion. For example, it would be proportional to

$R_{n}+{\tfrac {1}{2}}R_{n-1}+{\tfrac {1}{4}}R_{n-2}$ etc.

in which R_n is the rainfall for the current year, R_n-1 that for the year preceding, etc. This may be called an additive correction. It did not

Fig. 15.—Relation of tree-growth and rainfall at Prescott, Arizona.
⁠Tree-growth and rainfall uncorrected.

Fig. 16.—Five-year smoothed curves of growth and rainfall.

Fig. 17.—Accumulated rain and smoothed tree-growth.

Fig. 18.—Actual tree-growth and growth calculated from rain.

Fig. 19.—Actual rain and rain calculated from tree-growth.

give satisfactory results for the Prescott trees, although a formula of this general type has been applied with some success to the sequoia, which grows in more moist soil.

The variations in the Prescott trees were seen to be proportional both to the rainfall of the year and to the average growth or activity