[Footnote 5: Jahrbuch Geol. Reichsanstalt, xxviii, 1878, 600.] Löwl questions the conclusion reached by Tietze and ascribes the transverse gaps to the backward or headwater erosion of external streams, a process which he has done much to bring into its present important position, and which for him replaces the persistence of antecedent streams of other authors.[6] [Footnote 6: Pet. Mitth., 1882, 405; Ueber Thalbildung, Prag, 1884.] A brief article[7] that I wrote in comment on Löwl's first essay several years ago now seems to me insufficient in its method. It exaggerated the importance of antecedent streams; it took no sufficient account of the several cycles of erosion through which the region has certainly passed; and it neglected due consideration of the readjustment of initial immature stream courses during more advanced river-life. Since then, a few words in Löwl's essay have come to have more and more significance to me; he says that in mountain systems of very great age, the original arrangement of the longitudinal valleys often becomes entirely confused by means of their conquest by transverse erosion gaps. This suggestion has been so profitable to me that I have placed the original sentence at the beginning of this paper. Its thesis is the essential element of my present study. [Footnote 7: Origin of Cross-valleys. Science, i, 1883, 325.] Phillipson refers to the above-mentioned authors and gives a brief account of the arrangement of drainage areas within our Appalachians, but briefly dismisses the subject.[8] His essay contains a serviceable bibliography. [Footnote 8: Studien über Wasserscheiden. Leipsig, 1886, 149.]