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Abstract. Hack's law, an empirical, power law relationship between drainage basin area and the length of the main stream channel, has long been taken to imply that drainage basins become more elongate (relatively longer and narrower) with increasing basin size. A study of the geometry of 38 basins from three distinct geomorphic settings shows that this geometric interpretation of Hack's law is only occasionally true: Even though Hack's power law relationship holds between basin area and main channel length, these basins do not necessarily become more elongate with increasing size. Rather, Hack's law is an expression of a balance between changes in basin shape and changes in channel planform geometry. For the basins in this study, changes in channel sinuosity play the most important role in this balance; changes in basin shape are far less regular. Local conditions appear to determine the partitioning of importance between changes in basin shape and channel sinuosity.

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Active arc‐continent collision in Taiwan is an example of a typical collisional orogen, with a deformed continental margin (Foothills Belt, Hsueshan Range, and Central Range) separated from an accreted island arc (Coastal Range) by a collapsed forearc basin (Longitudinal Valley). The geomorphology of the eastern Central Range reflects spatial and temporal variations in uplift rate and pattern along the orogen during late Quaternary time. Digitized drainage basin perimeters, stream channels, and the mountain‐piedmont junction of a 200‐km‐long segment of the eastern Central Range provide data for calculating quantitative geomorphic parameters. Statistical analyses of these parameters define four domains of distinct landscape character. The northern domain extends northward along the coast from the northern end of the Longitudinal Valley (LV) and has landscape characteristics suggesting uplift near the mountain front. The central two domains are adjacent to the LV and show evidence of uplift concentrated in the interior of the range, away from the front. The boundary between the two central domains occurs near the middle of the LV. The southern domain extends southward along the coast from the southern end of the LV and has characteristics suggesting a transient response to increased uplift rate. Analysis of fluvial terrace profiles in the Central Range adjacent to the southern half of the LV indicates a change in uplift pattern through time, with migration of maximum uplift rate from the mountain front to the interior of the range. This change probably occurred just prior to late Pleistocene time.