It might be hastily inferred from the statistical identity of the connection between, say, the right thumb and each of the two fore-fingers, that the patterns on the two fore-fingers ought always to be alike, whether arch, loop, or whorl. If X, it may be said, is identical both with Y and with Z, then Y and Z must be identical with one another. But the statement of the problem is wrong; X is not identical with Y and Z, but only bears an identical amount of statistical resemblance to each of them; so this reasoning is inadmissible. The character of the pattern on any digit is determined by causes of whose precise nature we are ignorant; but we may rest assured that they are numerous and variable, and that their variations are in large part independent of one another. We can in imagination divide them into groups, calling those that are common to the thumb and the fore-finger of either hand, and to those couplets exclusively, the A causes; those that are common to the two thumbs and to these exclusively, the B causes; and similarly those common to the two fore-fingers exclusively, the C causes. Then the sum of the variable causes determining the class of pattern in the four several digits now in question are these:-- Right thumb A + B + an unclassed residue called X(=1=) Left thumb A + B + " " " X(=2=) Right fore-finger A + C + " " " Z(=1=) Left fore-finger A + C + " " " Z(=2=) The nearness of relationship between the two thumbs is sufficiently indicated by a fraction that expresses the proportion between all the causes common to the two thumbs exclusively, and the totality of the causes by which the A. L. W. class of the patterns of the thumbs is determined, that is to say, by A + B ----------------------- (1). A + B + X(=1=) + X(=2=) Similarly, the nearness of the relationship between the two fore-fingers by A + C ----------------------- (2). A + C + Z(=1=) + Z(=2=) And that between a thumb and a fore-finger by A --------------------------------------------------- (3). A + B + C + X(=1=) (or X(=2=)) + Z(=1=) (or Z(=2=))