This method of obtaining the value of 100 deg. is open to grave objection in the present example. We have no right to consider that the 45 per cent of whorls on the right ring-finger, and the 31 on the left, can be due to pre-established conditions, which would exercise a paramount effect even though the whorls were due entirely to causes common to both fingers. There is some self-contradiction in such a supposition. Neither are we at liberty to assume that the respective effects of the special causes X and Z are equal in average amount; if they were, the percentage of whorls on the right and on the left finger would invariably be equal. In this particular example the difficulty of determining correctly the scale value of 100 deg. is exceptionally great; elsewhere, the percentages of frequency in the two members of each couplet are more alike. In the two fore-fingers, and again in the two middle fingers, they are closely alike. Therefore, in these latter cases, it is not unreasonable to pass over the objection that X and Z have not been proved to be equal, but we must accept the results in all other cases with great caution. When the digits are of different names,--as the thumb and the fore-finger,--whether the digits be on the same or on opposite hands, there are two cases to be worked out; namely, such as (1) right thumb and left fore-finger, and (2) left thumb and right fore-finger. Each accounts for 50 per cent of the observed cases; therefore the mean of the two percentages is the correct percentage. The relationships calculated in the following table do not include arches, except in two instances mentioned in a subsequent paragraph, as the arches are elsewhere too rare to furnish useful results. It did not seem necessary to repeat the calculation for couplets of digits of different names, situated on opposite hands, as those that were calculated on closely the same data for similar couplets situated on the same hands, suffice for both. It is evident from the irregularity in the run of the figures that the units in the several entries cannot be more than vaguely approximate. They have, however, been retained, as being possibly better than nothing at all. TABLE VIII. _Approximate Measures of Relationship between the various Digits, on a Centesimal Scale._ (0 deg. = no relationship; 100 deg. = the utmost feasible likeness.)