_Supplementary Note_.--Professor Albrecht Penck of Vienna has published a valuable essay on "Die Bildung der Durchbruchsthäler" (Verein zur Verbreitung naturwissenschaftlicher Kenntnisse in Wien, 1888) from which the following historical notes are taken to illustrate the gradual overthrow of the fracture theory of cross valleys by the introduction of the idea that rivers can sometimes cut down their beds as fast as the land is uplifted or upfolded beneath them. Ferd. Römer. Die jurassische Weserkette. Zeit. d. deutsch. geol. Gesellsch., ix, 1857, 581. The deepening of valleys by rivers and streams must keep pace with the gradual elevation of continental masses. The Porta Westphalica has thus been cut by the Weser in the Wiehen-Weser range, in the northeastern part of Westphalia. A similar suggestion was briefly made a little later by Bischoff, to explain the gorge of the Rhine below Bingen. Lehrb. d. chem. u. phys. Geol., 2 Aufl., i, 374, 382; and again independently for the same river by Dücker. Zeitschr. d. Gesellsch. f. Erdk. Berlin, v, 1870, 183. Gümbel explained the course of the Altmühl, a branch of the Danube which crosses the Frankish Jura in northwestern Bavaria, by supposing its course was defined before and maintained during the deformation of the range. Bavaria: Landes- und Volkskunde des Königreichs Bayern, 1865, iii, 756. Medlicott recognized that many streams flowing from the inner Himalaya are older than the outer ranges, and showed reason for believing that they held their places while the outer ranges were tilted up. Mem. Geol. Survey India, iii, 1865, 6, 122, 127, 157, 163. A little later, he applied the same explanation to some Alpine rivers. The Alps and the Himalayas, a geological comparison. Q. Journ. Geol. Soc., London, xiv, 1868, 47, 52. Wynne explains the Indus and adjacent rivers as of greater age than the elevation of the Salt Range in northwestern India. Mem. Geol. Survey India, xi, 1875; xiv, 1878. Rütimeyer recognized the possibility of uprising ranges being cut down by transverse rivers, but regarded the occurrence as a rare one, thinking that lakes would generally appear behind such a growing barrier. He emphasized the idea that erosion works upstream, which Löwl has later developed farther. Ueber Thal- und Seebildung, Basel, 1869; 2 Aufl., 1874. Tietze regarded the persistence of rivers across growing ranges as the rule rather than the exception. Die Bildung von Querthälern, Jahrb. d. k. k. Geol. Reichsanst., 1878, 581. Hayden was perhaps the first to point out in this country the antecedent origin of certain headwaters of the Missouri in Montana, where the mountain ranges are frequently cut across by deep cañons. Amer. Journ. Science, xxxiii, 1862, 305. Hayden's Sixth Report, 1872 (1873), 85.