The Arch-Loop-Whorl, or, more briefly, the A. L. W. system of classification, while in some degree artificial, is very serviceable for preliminary statistics, such as are needed to obtain a broad view of the distribution of the various patterns. A minute subdivision under numerous heads would necessitate a proportional and somewhat overwhelming amount of statistical labour. Fifty-four different standard varieties are by no means an extravagant number, but to treat fifty-four as thoroughly as three would require eighteen times as much material and labour. Effort is economised by obtaining broad results from a discussion of the A. L. W. classes, afterwards verifying or extending them by special inquiries into a few of the further subdivisions. [Illustration: PLATE 11. FIG. 17. ORIGIN OF SUPPLY OF RIDGES TO PATTERNS OF PRINTS OF RIGHT HAND. FIG. 18. Ambiguities in prints of the Minutiae.] The divergent ridges that bound any simple pattern admit of nine, and only nine, distinct variations in the first part of their course. The bounding ridge that has attained the summit of any such pattern must have arrived either from the Inner plot (I), the Outer plot (O), or from both. Similarly as regards the bounding ridge that lies at the lowest point of the pattern. Any one of the three former events may occur in connection with any of the three latter events, so they afford in all 3 x 3, or nine possible combinations. It is convenient to distinguish them by easily intelligible symbols. Thus, let _i_ signify a bounding line which starts from the point I, whether it proceeds to the summit or to the base of the pattern; let _o_ be a line that similarly proceeds from O, and let _u_ be a line that unites the two plots I and O, either by summit or by base. Again, let two symbols be used, of which the first shall always refer to the summit, and the second to the base of the pattern. Then the nine possible cases are--_uu_, _ui_, _uo_; _iu_, _ii_, _io_; _ou_, _oi_, _oo_. The case of the arches is peculiar, but they may be fairly classed under the symbol _uu_.