The fractions (1) and (2) being both greater than (3), it follows that the relationships between the two thumbs, or between the two fore-fingers, are closer than that between the thumb and either fore-finger; at the same time it is clear that neither of the two former relationships is so close as to reach identity. Similarly as regards the other couplets of digits. The tabular entries fully confirm this deduction, for, without going now into further details, it will be seen from the "Mean of the Totals" at the bottom line of Table VI_b_ that the average percentage of cases in which two different digits have the same class of patterns, whether they be on the same or on opposite hands, is 59 or 57 (say 58), while the average percentage of cases in which right and left digits bearing the same name have the same class of pattern (Table VI_a_) is 72. This is barely two-thirds of the 100 which would imply identity. At the same time, the 72 considerably exceeds the 58. Let us now endeavour to measure the relationships between the various couplets of digits on a well-defined centesimal scale, first recalling the fundamental principles of the connection that subsists between relationships of all kinds, whether between digits, or between kinsmen, or between any of those numerous varieties of related events with which statisticians deal. Relationships are all due to the joint action of two groups of variable causes, the one common to both of the related objects, the other special to each, as in the case just discussed. Using an analogous nomenclature to that already employed, the peculiarity of one of the two objects is due to an aggregate of variable causes that we may call C+X, and that of the other to C+Z, in which C are the causes common to both, and X and Z the special ones. In exact proportion as X and Z diminish, and C becomes of overpowering effect, so does the closeness of the relationship increase. When X and Z both disappear, the result is identity of character. On the other hand, when C disappears, all relationship ceases, and the variations of the two objects are strictly independent. The simplest case is that in which X and Z are equal, and _in this_, it becomes easy to devise a scale in which 0 deg. shall stand for no relationship, and 100 deg. for identity, and upon which the intermediate degrees of relationship may be marked at their proper value. Upon this assumption, but with some misgiving, I will attempt to subject the digits to this form of measurement. It will save time first to work out an example, and then, after gaining in that way, a clearer understanding of what the process is, to discuss its defects. Let us select for our example the case that brings out these defects in the most conspicuous manner, as follows:--