[11] According to Mr. Jules Andrieu, the idea that nature must be tortured to reveal her secrets is preserved in the name crucible—from the Latin crux, a cross. But, more probably, crucible is derived from some Old French or Teutonic form, as cruche, kroes, krus, etc., a pot or jug (cf. Modern English crock, cruse, and German Krug).—Trans.
[12] Xenophon, Memorabilia iv, 7, puts into the mouth of Socrates these words: οὔτε γὰρ εὑρετὰ ἀνθρώποις αὐτὰ ἐνόμιζεν εἶναι, οὔτε χαρίζεσθαι θεοῖς ἂν ἡγεῖτο τὸν ζητοῦντα ἃ ἐκεῖνοι σαφηνίσαι οὐκ ἐβουλήθησαν.
[13] Galilei, Discorsi e dimostrazione matematiche. Leyden, 1638. Dialogo Primo.
[14] In the same way, the pitch of a locomotive-whistle is higher as the locomotive rapidly approaches an observer, and lower when rapidly leaving him than if the locomotive were at rest.—Trans.
[15] A kilometre is 0.621 or nearly five-eighths of a statute mile.
[16] Observe, also, the respect in which the wheel is held in India, Japan and other Buddhistic countries, as the emblem of power, order, and law, and of the superiority of mind over matter. The consciousness of the importance of this invention seems to have lingered long in the minds of these nations.—Tr.
[17] This effect is particularly noticeable in the size of workmen on high chimneys and church-steeples—"steeple Jacks." When the cables were slung from the towers of the Brooklyn bridge (277 feet high), the men sent out in baskets to paint them, appeared, against the broad background of heaven and water, like flies.—Trans.
[18] See Joh. Müller, Vergleichende Physiologie des Gesichtssinnes, Leipsic, 1826.
[19] Delivered before the German Casino of Prague, in the winter of 1871.
A fuller treatment of the problems of this lecture will be found in my Contributions to the Analysis of the Sensations (Jena, 1886), English Translation, Chicago, 1895. J. P. Soret, Sur la perception du beau (Geneva, 1892), also regards repetition as a principle of æsthetics. His discussions of the æsthetical side of the subject are much more detailed than mine. But with respect to the psychological and physiological foundation of the principle, I am convinced that the Contributions to the Analysis of the Sensations go deeper.—Mach (1894).