v PATTERNS : THEIR OUTLINES AND CORES 81
pattern must have arrived either from the Inner plot (I), the Outer plot (0), 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 0, and let u be a line that unites the two plots I and 0, 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.
This easy method of classification has much power. For example, the four possible kinds of simple spirals (see the 1st, 2nd, and the 5th and 6th diagrams in the lowest row of Plate 11) Fig. 17) are wholly determined by the letters oj, jo, ij, ji respectively. The two forms of duplex spirals are similarly determined by of and io (see 4th and 5th diagrams in the upper row of Fig. 17), the two slopes of loops by oo and ii (3rd and 4th in the lower row). It also shows very" distinctly the sources whence the streams of ridges proceed that feed the pattern, which itself affords another basis for classifi-
