Since the curve of the California trees is the only continuous and detailed record yet available for the climate of the last three thousand years, it deserves most careful study. It is especially necessary to determine the degree of accuracy with which the growth of the trees represents (1) the local rainfall and (2) the rainfall of remote regions such as Palestine. Perhaps the best way to determine these matters is the standard mathematical method of correlation coefficients. If two phenomena vary in perfect unison, as in the case of the turning of the wheels and the progress of an automobile when the brakes are not applied, the correlation coefficient is 1.00, being positive when the automobile goes forward and negative when it goes backward. If there is no relation between two phenomena, as in the case of the number of miles run by a given automobile each year and the number of chickens hatched in the same period, the coefficient is zero. A partial relationship where other factors enter into the matter is represented by a coefficient between zero and one, as in the case of the movement of the automobile and the consumption of gasoline. In this case the relation is very obvious, but is modified by other factors, including the roughness and grade of the road, the amount of traffic, the number of stops, the skill of the driver, the condition and load of the automobile, and the state of the weather. Such partial relationships are the kind for which correlation coefficients are most useful, for the size of the coefficients shows the relative importance of the various factors. A correlation coefficient four times the probable error, which can always be determined by a formula well known to mathematicians, is generally considered to afford evidence of some kind of relation between two phenomena. When the ratio between coefficient and error rises to six, the relationship is regarded as strong. Few people would question that there is a connection between tree growth and rainfall, especially in a climate with a long summer dry season like that of California. But the growth of the trees also depends on their position, the amount of shading, the temperature, insect pests, blights, the wind with its tendency to break the branches, and a number of other factors. Moreover, while rain commonly favors growth, great extremes are relatively less helpful than more moderate amounts. Again, the roots of a tree may tap such deep sources of water that neither drought nor excessive rain produces much effect for several years. Hence in comparing the growth of the huge sequoias with the rainfall we should expect a correlation coefficient high enough to be convincing, but decidedly below 1.00. Unfortunately there is no record of the rainfall where the sequoias grow, the nearest long record being that of Sacramento, nearly 200 miles to the northwest and close to sea level instead of at an altitude of about 6000 feet.