A single instance has shown that the minutiae are _not_ invariably permanent throughout life, but that one or more of them may possibly change. They may also be destroyed by wounds, and more or less disintegrated by hard work, disease, or age. Ambiguities will thus arise in their interpretation, one person asserting a resemblance in respect to a particular feature, while another asserts dissimilarity. It is therefore of interest to know how far a conceded resemblance in the great majority of the minutiae combined with some doubt as to the remainder, will tell in favour of identity. It will now be convenient to change our datum from a six-ridge to a five-ridge square of which about thirty-five are contained in a single print, 35 x 5{2} or 35 x 25 being much the same as 24 x 6{2} or 24 x 36. The reason for the change is that this number of thirty-five happens to be the same as that of the minutiae. We shall therefore not be acting unfairly if, with reservation, and for the sake of obtaining some result, however rough, we consider the thirty-five minutiae themselves as so many independent variables, and accept the chance now as 1 to 2{35}. This has to be multiplied, as before, into the factor of 2{4} x 2{8} (which may still be considered appropriate, though it is too small), making the total of adverse chances 1 to 2{47}. Upon such a basis, the calculation is simple. There would on the average be 47 instances, out of the total 2{47} combinations, of similarity in all but one particular; (47 x 46)/(1 x 2) in all but two; (47 x 46 x 45)/(1 x 2 x 3) in all but three, and so on according to the well-known binomial expansion. 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 2{6}, 2{10}, 2{14}, 2{18}, etc. Hence the roughly approximate chances of resemblance in all particulars are as 2{47} to 1; in all particulars but one, as 2{47-6}, or 2{41} to 1; in all but two, as 2{37} to 1; in all but three, as 2{33} to 1; in all but four, as 2{29} to 1. Even 2{29} 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.