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OCR Rendition - approximate
112 FINGER PRINTS CHAP. appropriate, though it is too small), making the total of adverse chances 1 to 247. Upon such a basis, the calculation is simple. There would on the average be 47 instances, out of the total 247 combinations, of similarity in all but one particular ; 41X41 in all but two ; 4 1 x 2 x 3 5 in all but three, and so on according to the well-known binomial expansioli. Taking for convenience the powers of 2 to which these values approximate, or rather with the view of not overestimating, let us take the power of 2 that falls short of each of them ; these may be reckoned as respectively equal to 26, 210, 214, 218, etc. Hence the roughly approximate chances of resemblance in all particulars are as 24i to 1; in all particulars but one, as 247-6, or 241 to 1 ; in all but two, as 287 to 1 ; in all but three, as 238 to 1 ; in all but four, 'as 220 to 1. Even 229 is so large as to require a row of nine figures to express it. Hence a few instances of dissimilarity in the two prints of a single finger, still leave untouched an enormously large residue of evidence in favour of identity, and when two, three, or more fingers in the two persons agree to that extent, the strength of the evidence rises by squares, cubes, etc., far above the level of that amount of probability which begins to rank as certainty. Whatever reductions a legitimate criticism may make in the numerical results arrived at in this chapter, bearing in mind the occasional ambiguities pictured in Fig. 18, the broad fact remains, that a complete or nearly complete accordance between two prints of a single finger, and vastly more so between
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