[660] These and also other coordinate diagrams will be found in Mr G. Heilmann’s book Fuglenes Afstamning, 398 pp., Copenhagen, 1916; see especially pp. 368–380.

[661] Cf. W. B. Scott (Amer. Journ. of Science, XLVIII, pp. 335–374, 1894), “We find that any mammalian series at all complete, such as that of the horses, is remarkably continuous, and that the progress of discovery is steadily filling up what few gaps remain. So closely do successive stages follow upon one another that it is sometimes extremely difficult to arrange them all in order, and to distinguish clearly those members which belong in the main line of descent, and those which represent incipient branches. Some phylogenies actually suffer from an embarrassment of riches.”

[662] Cf. Dwight, T., The Range of Variation of the Human Scapula, Amer. Nat. XXI, pp. 627–638, 1887. Cf. also Turner, Challenger Rep. XLVII, on Human Skeletons, p. 86, 1886: “I gather both from my own measurements, and those of other observers, that the range of variation in the relative length and breadth of the scapula is very considerable in the same race, so that it needs a large number of bones to enable one to obtain an accurate idea of the mean of the race.”

[663] There is a paper on the math­e­mat­i­cal study of organic forms and organic processes by the learned and celebrated Gustav Theodor Fechner, which I have only lately read, but which would have been of no little use and help to our argument had I known it before. (Ueber die mathematische Behandlung organischer Gestalten und Processe, Berichte d. k. sächs. Gesellsch., Math.-phys. Cl., Leipzig, 1849, pp. 50–64.) Fechner’s treatment is more purely math­e­mat­i­cal and less physical in its scope and bearing than ours, and his paper is but a short one; but the conclusions to which he is led differ little from our own. Let me quote a single sentence which, together with its context, runs precisely on the lines of the discussion with which this chapter of ours began. “So ist also die mathematische Bestimmbarkeit im Gebiete des Organischen ganz eben so gut vorhanden als in dem des Unorganischen, und in letzterem eben solchen oder äquivalenten Beschränkungen unterworfen als in ersterem; und nur sofern die unorganischen Formen und das unorganische Geschehen sich einer einfacheren Gesetzlichkeit mehr nähern als die organischen, kann die Approximation im unorganischen Gebiet leichter und weiter getrieben werden als im organischen. Dies wäre der ganze, sonach rein relative, Unterschied.” Here in a nutshell, in words written some seventy years ago, is the gist of the whole matter.

An interesting little book of Schiaparelli’s (which I ought to have known long ago)—Forme organiche naturali e forme geometriche pure, Milano, Hoepli, 1898—has likewise come into my hands too late for discussion.

INDEX.