FIG. 15. TRANSITIONAL PATTERNS--ARCHES AND LOOPS (enlarged three times).] [Illustration: PLATE 10. FIG. 16. TRANSITIONAL PATTERNS--LOOPS AND WHORLS (enlarged three times).] The chief theoretical objection to this threefold system of classification lies in the existence of certain compound patterns, by far the most common of which are Whorls enclosed within Loops (Plates 7, 8, Fig. 12, ~15~, ~18~, ~19~, and Fig. 13, ~20-23~). They are as much Loops as Whorls, and properly ought to be relegated to a fourth class. I have not done so, but called them Whorls, for a practical reason which is cogent. In an imperfect impression, such as is made by merely dabbing the inked finger upon paper, the enveloping loop is often too incompletely printed to enable its existence to be surely ascertained, especially when the enclosed whorl is so large (Fig. 13, ~23~) that there are only one or two enveloping ridges to represent the loop. On the other hand, the whorled character of the core can hardly fail to be recognised. The practical difficulties lie almost wholly in rightly classifying a few transitional forms, diagrammatically and roughly expressed in Fig. 11, ~4~, ~5~, and Fig. 12, ~8~, ~18~, ~19~, with the words "see" so and so written below, and of which actual examples are given on an enlarged scale in Plates 9 and 10, Figs. 15 and 16. Here Fig. 15, _a_ is an undoubted arch, and _c_ an undoubted nascent loop; but _b_ is transitional between them, though nearer to a loop than an arch, _d_ may be thought transitional in the same way, but it has an incipient curl which becomes marked in _e_, while it has grown into a decided whorl in _f_; _d_ should also be compared with _j_, which is in some sense a stage towards _k_. _g_ is a nascent tented-arch, fully developed in _i_, where the pattern as a whole has a slight slope, but is otherwise fairly symmetrical. In _h_ there is some want of symmetry, and a tendency to the formation of a loop on the right side (refer back to Plate 7, Fig. 11, ~4~, and Fig. 12, ~12~); it is a transitional case between a tented arch and a loop, with most resemblance to the latter. Plate 10, Fig. 16 illustrates eyed patterns; here _l_ and _m_ are parts of decided loops; _p_, _q_, and _r_ are decided whorls, but _n_ is transitional, inclining towards a loop, and _o_ is transitional, inclining towards a whorl. _s_ is a nascent form of an invaded loop, and is nearly related to _l_; _t_ and _u_ are decidedly invaded loops.