Quantitative judgments of color: 11Ie square root I1IIe I RICHARD M. WARREN UNIVERSITY OF WISCONSIN. MILWAUKEE Judgments of the appearance of colored papers blended with different proportions of white were obtained usillg a ro- tating color mixer. Responses consisted of a mark on a line labeled with the appropriate color name at one end and "white" at the other. Prior context was avoided by obtaining only smale judgments. It WllS found for aU six color displays that distance from the colored end of the line was proportion- al to the sqllllre root of the ｰｲｯｰｯｲｴｩｾｮ of white present in the mixture. This square root relation is in keeping with the physical correlate theory and with other experimellts involv- illg gray papers, point sources, and luminous fields. The appearance of pigments on paper has played an important part in the history of sensory scaling. The first attempt to measure any -sensation directly involved the selection of a gray appearing midway between white and black (Plateau. 1872). This was followed by a brief flurry of experimental papers on sensory magnitudes. By the late 19th and early 20th centuries, several influential critics contended that sensation by its nature could not be measured. and interest in scaling sensory magnitudes was almost nil for many years, until studies with colored papers by Richardson (1929) and by Maxwell (1929) marked the beginning of the flourishing modern phase of psychophysics. They showed that groups of experi- mentally naive Ss could quantify the appearance of a pink produced by blending red and white papers with a rotating color mixer. The present study has involved a re-examination of their data for color mixing. This new look was prompted by the outcome of a series of experiments on gray papers. It was demonstrated that a simple relation exists between reflectance and subjective lightness judgments (t.e., lightness is proportional to the square root of reflectance) under a variety of experimental conditions, including conditions which eliminated prior judgments and the influence of back- ground reflectance (Warren & Poulton, 1960, 1966; Warren & Warren, 1966). When the data of Richardson and of Maxwell were analyzed to determine if any similar rule existed for judgments withcoloredpapers, it appeared that their method of scoring responses had hidden from them a striking agreement of their data with a square root rule (i.e., the whiteness of a pink was proportional to the square root of white in the color mixture). In order to test the validity of this rule, the present study employed groups of Ss who knew nothing of psychophysical theory, and had never participated in any kind of psychophysical ex- periment. Since the second judgment may be pro- foundly influenced by the first (Warren & Poulton, 1960; Poulton et al, 1965), each S was presented with a single display and requested to make onlyone judgment. METHOD Sulljects The 180 Ss were students from the Introductory psychology course at the University of Wisconsin- Milwaukee. All had had no previous experience With, or knowledge of. sensory scaling. Ap,llfatus Disks for the rotating color mixer were prepared by flxlng colored paper on a rigid white background of cardboard. known as "railroad board." with Scotch brand "Double Stick Tape." The disks, shown in Fig. 1. had a radius of 108 mm, The arc of the larger colored circle was 30 mm from the rim, and the smaller colored arc was 60 mm from the rim. At a distance of 90 mm from the rim and extending to 18 mm from the center of the disk was a dark gray bolt fastening the disk to the motor plate and shaft. For Part 1, the arcs of the larger and smaller colored circles were 306 0 and 54 0 , respectively, and for Part 2. the corresponding values were 230 0 and 130 0 • When the disks were rotated rapidly (by a C. H. Stoelting Co. Electric Color Mixer, Model 12610), S saw an outer white ring enclosing a ring which blended white with the colored paper, which in turn sur- rounded a disk of the "pure" colored paper. Procedure All Ss read the same instructions except for dif- ferences in color names appropriate to their stimulus display: "In this experiment, a rapidly rotating disk called a color mixer is used. You will see a] ]* surface and a white surface separated by a band produced by mixing the [ ]* and the white. We are interested in the appearance of this band. "A slip will be given you marked 'white' at one end and ,[ ]*, at the other. Consider this line to represent a scale of all shades [ ]** progressing from pure white tor l-. You are to place a mark on this line to lndlcate where you think the mixture of white and [ ]* belongs on this scale." * ["red." "green," or ''blue''] as appropriate ** ["of pink"] when red paper employed, other- wise nothing inserted at this point. After reading the instructions, S was conducted to 448 COP7Iright 1967. PS7lchonomic Press. Goleta. Calif. Perception & Psychophysics, 1967. Vol. 2 (9)