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OCR Rendition - approximate
126 FINGER PRINTS CHAP. theless be a certain percentage of instances, due to pure chance, of the double event of whorls occurring in both ring-fingers, and it is easy to calculate their frequency from the above data. The number of possible combinations of 100 right ring-fingers with 100 left ones is 100 x 100, and of these 4 5 x 31 would be double events as above (call these for brevity " double whorls"). Consequently the chance of a double whorl in any single couplet is loo" oo, and their average frequency in 10 0 couplets, in other words, their average percentage is 4 ioo 1=13.9 5, say 14. If, then, the observed percentage of double whorls should be only 14, it would be a proof that the A. L. W. classes of patterns on the right and left ring-fingers were quite independent ; so their relationship, as expressed on the centesimal scale, would be 00. There could never be less than 14 double whorls under the given conditions, except through some statistical irregularity. Now consider the opposite extreme of the closest possible relationship, subject however, and this is the weak point, to the paramount condition that the average frequencies of the A. L. W. classes may be taken as pre-established. As there are 45 per cent of whorls on the right ring-finger, and only 31 on the left, the tendency to form double whorls, however stringent it may be, can only be satisfied in 31 cases. There remains a superfluity of 14 per cent cases in the right ring-finger which perforce must have for their partners either arches or loops. Hence the percentage of frequency that indicates the closest
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