Both separation and eccentricity can limit precise position judgements: a reply to Morgan and Watt

Weber's law is ubiquitous in position judgements. In a variety of position acuity tasks, the position threshold is proportional to the separation of the reference features. Recently, we (Klein & Levi, 1987; Levi, Klein & Yap, 1988) suggested that two sensory processes may serve to limit position acuity, and thus contribute to Weber's law for position. One is the target separation, and the other is the target eccentricity. In order to test this idea, we pitted separation against eccentricity by measuring spatial interval discrimination thresholds on an iso-eccentric arc (Levi et al., 1988). Over a 5-fold range of separations, we found that thresholds were independent of separation, and concluded that at large separations, eccentricity can limit precise position judgements. In the preceding article, Morgan and Watt (1989) have questioned this conclusion, and have shown that the effects of eccentricity are small in an arc length discrimination task. In the present article, we: (i) address the objections raised by Morgan and Watt; (ii) show that our data and 2-mechanism model are consistent with many previous studies; and (iii) show that Morgan and Watt's task is inherently difficult, so that rather than tapping the sensory limits imposed by the target eccentricity, performance on the arc length task is constrained by the cognitive demands of the task, or by the difficulty of reconstruction. In contrast, the measurement of chord length (spatial interval discrimination on an iso-eccentric arc) can be simply done by calculating the distance between the endpoints. Thus, at large separations, thresholds for the chord length judgements are much lower than those of Morgan and Watt, and are proportional to the eccentricity of the targets.