Size-constancy refers to the event that an object of constant physical size is judged to be such, regardless of its location within the three-dimensional physical environment. In the laboratory when size judgments are based upon information received by the visual sense, perfect size-constancy seldom occurs, a result not in keeping with certain functionalist theories of perception (Gibson, 1950; Taylor, 1962). Only a particular combination of instructions, stimulus, and response factors lead to size-constancy (Baird, 1965a;Carlson, 1962;Epstein, 1963), and these results probably can be treated as special cases within a more comprehensive theory (e.g., Akishige, 1961). Before such a theory can be operational, however, several key issues need to be settled. This paper describes some progress toward these prerequisite goals.First, we have extended the range of quantitative data collected for size and distance judgments under Objective instructions and full-cue conditions. The majority of previous results were gathered with a single method on a single value of a dimension such as relative distance or stimulus orientation. We used an extended stimulus series in three conditions. In one situation a relative-size judgment was made between a comparison stimulus at one distance and a standard stimulus at a number of different distances, when both were in a frontal plane. The second situation also involved relative size, but the stimuli were placed flat on a table extending away from the observer and beneath his primary lines of sight. In the third situation ratio estimates of distance along the table were obtained. The same two observers were used in all conditions, and the relative positions of the comparison and standard were varied.Our second concern was theoretical. Since the functionalist theory leading to size-constancy predictions is based upon metric measures of stimuli, and since this approach is inadequate when applied to most data on size and distance, we decided to explore an alternative measure-the subtended visual angle of stimuli at the eye. The task set the observer then is presumed to be the production or estimation of certain visual-angle ratios between the standard and comparison stimuli. The exact ratios depend upon the relative spatial positions of stimuli including their orientation to the eye and ground. Different stimulus and instruction variables require different ratio productions of visual angles. At present we cannot predict exactly which ratio is appropriate for each experimental condition. The important point is that the law of the visual angle is not restricted to a ratio of 1.0 in which the visual angles of the comparison and standard are equal, but is extended to include many other ratios as well.The next step is to defi~e quantitatively the relations among theoretical visual-angle ratios and those actually produced or estimated by observers. When metric measures (arithmetic) are used in graphic plots of theoretical and judged size, the resulting curves are not always linear. It is to our ...