In the first line of Section A a correlation coefficient of only -0.056, which is scarcely six-tenths of the probable error, means that there is no appreciable relation between the rainfall of a given season and the growth during the following spring and summer. The roots of the sequoias probably penetrate so deeply that the rain and melted snow of the spring months do not sink down rapidly enough to influence the trees before the growing season comes to an end. The precipitation of two preceding seasons, however, has some effect on the trees, as appears in the second line of Section A, where the correlation coefficient is +0.288, or 3.2 times the probable error. When the rainfall of three seasons is taken into account the coefficient rises to +0.570, or 8.7 times the probable error, while with four years of rainfall the coefficient begins to fall off. Thus the growth of these eighteen sequoias on relatively dry slopes appears to have depended chiefly on the rainfall of the second and third preceding rainy seasons. The growth in 1900, for example, depended largely on the rainfall in the rainy seasons of 1897-1898 and 1898-1899.
Section B of the table shows that with 112 trees, growing chiefly in moist depressions where the water supply is at a maximum, the correlation between growth and rainfall, +0.577 for ten years' rainfall, is even higher than with the dry trees. The seepage of the underground water is so slow that not until four years' rainfall is taken into account is the correlation coefficient more than four times the probable error. When only the trees growing in moist locations are employed, the coefficient between tree growth and the rainfall for ten years rises to the high figure of +0.605, or 9.8 times the probable error, as appears in Section C. These figures, as well as many others not here published, make it clear that the curve of sequoia growth from 1861 to 1910 affords a fairly close indication of the rainfall at Sacramento, provided allowance be made for a delay of three to ten years due to the fact that the moisture in the soil gradually seeps down the mountain-sides and only reaches the sequoias after a considerable interval.
If a rainfall record were available for the place where the trees actually grow, the relationship would probably be still closer.