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202   Life and Letters of Francis Galton

"(b) The core may be a circumflex or 'staple'; then, the shoulder* of the staple that is farthest from the delta is taken for the inner terminus, the nearer shoulder counting as a separate ridge (Fig. b).

delta

Inner Terminus   Outer Terminus
Fig. 34. Inner and Outer Termini for Ridge Counting.

"Outer terminus. Here also are two cases

"(c) Where the upper and lower sides of the delta are formed by the bifurcation of a single ridge. Here the point of bifurcation forms the outer terminus. It sometimes happens that successive forks or branches are thrown off from the same ridge first at an acute angle and progressively becoming more obtuse. In this case the branch to be considered as forming one side of the delta is the first that makes not less than a right angle with the stem (Fig. c).

"(d) Where the upper and lower sides of the delta are formed by two ridges that had previously run side by side, and then suddenly diverge. Here the base of the delta is the outer terminus. The nearest ridge in front of the place where the divergence begins, even if it be a mere dot, and whether or no it is independent of, or springs from one of the divergent ridges, is considered to form the base of the delta, and the outer terminus.

"If scrupulous care is taken by the beginner, first in selecting the termini that best fulfil the above conditions, and afterwards in counting the ridges, his eye will soon become accustomed to the work, and the process may then be effected both quickly and trustworthily f. It is usually easy to determine narrow limits within which the number of ridges will always be held to lie."

Galton tells us that the 156 (ull, ull, ii, ll)'s of his collection of 2632 sets showed, counting as above, all numbers of ridges from 3 to 16 with fairly equal frequency. He had also a few "under 3" and eight cases above 16; roughly these 15 groups would reduce the 156 to groups of about 10 sets. But Galton considers we must search not only the observed count-number, but -two count-numbers on either side of it, or practically (having regard to

central ridge. If it had been, then, I think, it is clear that with the delta in relatively the same position as in Fig. b one less ridge would be counted in Fig. a' and two less in Fig. a2. It is possible that the engraver erred in carrying the ridges quite up to the staple. Or, it may be, remembering what Galton has said about cols, i.e. that we cannot be certain whether a ridge terminates or forks, we ought always to put the inner terminal, as in Figs. a' and 0 above, not where the central ridge meets the staple, but at about a ridge interval from the meet.

* The term "shoulder" is somewhat vague; the ridge-counts might well differ according to the choice of "shoulder." If the word means where the sides of the staple become parallel, then the engraver of Fig. b has hardly hit this off. I believe it would be preferable to define the shoulder as about a ridge interval below the summit. Galton's Plate 4 (our Plate XXVI), entitled "Counting Ridges," hardly seems to meet my difficulties in this and in the previous footnote. 'If Fig. 82 be a case of Fig. a', then Galton does not appear to put the inner terminus at the top of the central ridge ; had he done so, I think the ridges would be 12 instead of 13.

t Galton's illustrations of ridge-counting are given on our Plate XXVI and would have been more helpful with a finer counting line. A thick line runs into the stem and occasionally obscures the finer parts of the delta.

b

C