The common report that the horizon moon looks "larger and closer" than the zenith moon means that the perceived visual angle (V' rad) for its diameter is greater, the perceived distance W' m) to it is less, and the perceived linear size (8' m) for its diameter is either greater or the same (size constancy), all in accord with the rule S'/D' = V' rad. These majority moon illusions remain unexplained because published descriptions use only one "perceived size" variable, rather than both V' and S'; and some create paradoxes by using the standard rule, 8'IV' = Vrad, which omits V'. Complete paradox-free redescriptions are offered, and the oculomotor explanation is outlined.THE s=dv THEORY APPROACH Although some investigators have used the variable V' deg (Baird, 1982;Enright, 1975;Restle, 1970;Rock & Kaufman, 1962a, 1962b, most have agreed with the predominant theoretical assumption that V is not perceived (Gilinsky, 1980;Hershenson, 1982;Reed, 1984).Moreover, many descriptions have been based upon the "size-distance invariance hypothesis" (SDIH), written as S'IV' = kV rad, in which k is an observer constant, nominally 1.0 (Gogel, 1977). Because the SDIH omits V', and because kV rad is constant for the moon, the popular report "looks larger and closer" does not fit the SDIH and seemed to create a "size-distance paradox" (Epstein, Park, & Casey, 1961). Recent explanations attempt to avoid that paradox but, by not using all three response variables, they often inadvertently recreate it.New explanations will not be reviewed in detail here because the main purpose is simply to fully describe moon illusions using V', S', and V'. Therefore, it is necessary to use an unconventional theory of spatial perception. I use the s=dv theory (McCready, 1965(McCready, , 1983(McCready, , 1985.(1) V'rad.
S'IV'The full moon at the horizon often appears about 1.5 times wider than it does at its zenith, and a ratio as high as 2.0 is not uncommon (Enright, 1975; Holway & Boring, 1940a, 1940bRock & Kaufman, 1962a;Taylor & Boring, 1942). Of course, the visual angle, V = 0.52°, subtended at the eye by the moon's azimuth diameter, remains virtually constant in accord with the ruleS is the moon's linear size (its diameter of 3,475 km), and V is its essentially constant distance from the eye (about 384,400 km). For simple examples, V (the optical direction difference) henceforth is rounded off to 0.01 rad.To most observers, the larger looking horizon moon also looks closer than the smaller looking zenith moon. New attempts to explain this "larger and closer" illusion continue to appear, with each writer noting how previous explanations (theories) fail (