In the seventh chapter an attempt is made to appraise the evidential value of finger prints by the common laws of Probability, paying great heed not to treat variations that are really correlated, as if they were independent. An artifice is used by which the number of portions is determined, into which a print may be divided, in each of which the purely local conditions introduce so much uncertainty, that a guess derived from a knowledge of the outside conditions is as likely as not to be wrong. A square of six ridge-intervals in the side was shown by three different sets of experiments to be larger than required; one of four ridge-intervals in the side was too small, but one of five ridge-intervals appeared to be closely correct. A six-ridge interval square was, however, at first adopted, in order to gain assurance that the error should be on the safe side. As an ordinary finger print contains about twenty-four of these squares, the uncertainty in respect to the entire contents of the pattern _due to this cause alone_, is expressed by a fraction of which the numerator is 1, and the denominator is 2 multiplied into itself twenty-four times, which amounts to a number so large that it requires eight figures to express it.
A further attempt was made to roughly appraise the neglected uncertainties relating to the outside conditions, but large as they are, they seem much inferior in their joint effect to the magnitude of that just discussed.
Next it was found possible, by the use of another artifice, to obtain some idea of the evidential value of identity when two prints agree in all but one, two, three, or any other number of particulars. This was done by using the five ridge-interval squares, of which thirty-five may be considered to go into a single finger print, being about the same as the number of the bifurcations, origins, and other points of comparison. The accidental similarity in their numbers enables us to treat them roughly as equivalent. On this basis the well-known method of binomial calculation is easily applied, with the general result that, notwithstanding a failure of evidence in a few points, as to the identity of two sets of prints, each, say, of three fingers, amply enough evidence would be supplied by the remainder to prevent any doubt that the two sets of prints were made by the same person. When a close correspondence exists in respect to all the ten digits, the thoroughness of the differentiation of each man from all the rest of the human species is multiplied to an extent far beyond the capacity of human imagination. There can be no doubt that the evidential value of identity afforded by prints of two or three of the fingers, is so great as to render it superfluous to seek confirmation from other sources.