It must be emphasised that it is in the minutiæ, and _not_ in the measured dimensions of any portion of the pattern, that this remarkable persistence is observed, not even if the measurements be made in units of a ridge-interval. The pattern grows simultaneously with the finger, and its proportions vary with its fatness, leanness, usage, gouty deformation, or age. But, though the pattern as a whole may become considerably altered in length or breadth, the number of ridges, their embranchments, and other minutiæ remain unchanged. So it is with the pattern on a piece of lace. The piece as a whole may be stretched in this way, or shrunk in that, and its outline altogether altered; nevertheless every one of the component threads, and every knot in every thread, can easily be traced and identified in both. Therefore, in speaking of the persistence of the marks on the finger, the phrase must be taken to apply principally to the minutiæ, and to the general character of the pattern; not to the measure of its length, breadth, or other diameter; these being no more constant than the stature, or any other of the ordinary anthropometric data.
The object of this chapter is to give an approximate numerical idea of the value of finger prints as a means of Personal Identification. Though the estimates that will be made are professedly and obviously far below the truth, they are amply sufficient to prove that the evidence afforded by finger prints may be trusted in a most remarkable degree.
Our problem is this: given two finger prints, which are alike in their minutiæ, what is the chance that they were made by different persons?
The first attempt at comparing two finger prints would be directed to a rough general examination of their respective patterns. If they do not agree in being arches, loops, or whorls, there can be no doubt that the prints are those of different fingers, neither can there be doubt when they are distinct forms of the same general class. But to agree thus far goes only a short way towards establishing identity, for the number of patterns that are promptly distinguishable from one another is not large. My earlier inquiries showed this, when endeavouring to sort the prints of 1000 thumbs into groups that differed each from the rest by an "equally discernible" interval. While the attempt, as already mentioned, was not successful in its main object, it showed that nearly all the collection could be sorted into 100 groups, in each of which the prints had a fairly near resemblance. Moreover, twelve or fifteen of the groups referred to different varieties of the loop; and as two-thirds of all the prints are loops, two-thirds of the 1000 specimens fell into twelve or fifteen groups. The chance that an unseen pattern is some particular variety of loop, is therefore compounded of 2 to 3 against its being a loop at all, and of 1 to 12 or 15, as the case may be, against its being the specified kind of loop. This makes an adverse chance of only 2 to 36, or to 45, say as 2 to 40, or as 1 to 20. This very rude calculation suffices to show that on the average, no great reliance can be placed on a general resemblance in the appearance of two finger prints, as a proof that they were made by the same finger, though the obvious disagreement of two prints is conclusive evidence that they were made by different fingers.