Now, whatever the actual extent of this regression is in a group we need to know how uniformly it occurs for all the classes of different deviations from the general average, that is, we need to know whether the extreme groups regress to the same relative extent as do those nearer the general average; and, further, we need to know how nearly the sons of fathers of any certain height are grouped about their own average. In other words, we should know, first, whether the regression of the sons of 62 and 76 or 67 and 71 inch fathers is proportionately the same in each case, and, second, to what extent the sons of 62-inch fathers vary, whether they vary as do the fathers of 62-inch sons, and so for each group. This kind of information we get by calculating what is called the _coefficient of heredity_. The calculation of this coefficient is a complicated process which it is unnecessary to describe here. It must suffice to say that a numerical coefficient can readily be determined, which will express the average closeness and regularity of the relationship between all the plus and minus deviations from the group average in fathers and the corresponding plus and minus deviations from the group average of their sons with respect to a given characteristic. This coefficient of heredity may vary between 0.0 and 1.0. When it is 0.0 there is, on the whole, no regularity in the relationship, i. e., no heredity; when it is 1.0 there is, on the whole, complete regularity, i. e., heredity is complete. Neither of these values is ever actually found in determining coefficients of heredity in the parental relation; these are usually between 0.3 and 0.5. It should be emphasized again that this comparison is between whole groups and not between individuals, and that it fails to allow for the distinction between fluctuations and true variations. And, further, it should be noted that the information derived from such a coefficient is defective in that it takes into account only the relationship between the son and one parent; the maternal relation is just as important but this has to be determined separately. There is no satisfactory method of determining the relation between children and both parents at the same time. The coefficient of heredity is, therefore, an abstract numerical value which gives us a fairly precise estimate as to the probable closeness of the relation between deviations from the group average of any character in two groups of relatives. The coefficient of _correlation_ is, in general, a measure of the relation between two different characteristics or conditions in a single group of individuals. The method of its determination and its limiting values are the same as for the coefficient of heredity. By experience the coefficients of heredity and correlation in general are found to have the following significance: