Different sets ofmagnitude estimation instructions were given to different subjects in order to see if this couldaccountfor the reported variation ofthe exponent in Stevens' power law. Subjects who were asked to give as an estimate of pulse rate (Experiment I) or loudness (Experiment II) the number 50 when it was 112 of the standard :md 150when~t was 1 1 12 times the standard y~elded exponents which were reliably smaller than those obtamed when subjects were asked to respond WIth 25 when it was 1f4, of the standard and 750 when it was 7 1 / 2~imes. th~standard. For the conditiongen?rating the larger exponent in each experiment, a power law relationship fits the data better than Fechner slaw. Both experiments were exactly replicated for comparison,with the same results obtained as mentioned above. The frequently observed variability of the exponent maybe a consequenceofbias introduced by numericalexamplesas part ofthe instructions in a magnitude estimation task.

In the present study, numerosity estimation was investigated. A two-parameter Stevens power law analysis was performed on a total of 944 subjects in six experiments. Two pulse ranges (2-17 or 17-253 pulses) and six pulse rates (either constant or randomly varied within trial blocks) were used, variously, in an unsuccessful attempt to find evidence for a psychological moment, under the supposition that the exponent (or, possibly, the measure constant) would become smaller as increasing numbers of pulses fell within the interval determined by each psychological moment. A single-parameter reanalysis of these six experiments under the initial value condition that a (standard) stimulus of one pulse be assigned a theoretical response (modulus) of one yielded single-parameter equations whose exponents were reliably less varied than those for conventional two-parameter equations in Experiments 1-4 (with randomly varying pulse rates from trial to triaD but not less varied in Experiments 5 and 6 (in which pulse rates were constant within trial blocks). It was concluded that the variable pulse rate condition, with its reduced exponent variability and presumed reduced temporal confounding, provides a more valid estimate of the singleparameter power law exponent for numerosity, which was found to be 0.80.Although we are intellectually aware that apparently continuous movie scenes are discontinuous, and that the visual field for each eye includes a sizable (but usually unnoticed) blind spot, the impression of visual continuity dominates our perception to the extent that such intellectual awareness does not disrupt the illusion. Presumably contributing in part to the illusion are insensitivity (in the case ofthe blind spot imaged onto an optic disk devoid ofphotoreceptor cells) and informational overload, wherein variations in sensory input occur at a rate exceeding the~en sory or perceptual capabilities of the sensory system (in the case of the apparently continuous movie). Stroud (1955) has suggested a perceptual moment hypothesis, which, although it is not specific with respect to the anatomical locus , represents an attempt to account for apparent informational limits in a variety of contexts, by means of the supposition that we can differentiate in psychological time repetitive physical events that we see or hear, provided that they are in separate psychological moments of time. This psychological (perceptual) moment corresponds to a typical duration ofapproximately 0.1 sec, but it may range from 0.05 to 0.2 sec for various circumstances. An implication of this hypothesis is illustrated by Stroud (1955, pp. 189-191) with reference to some preliminary unpublished work of Cheatham and White, who investigated subjects' ability to count repeated flashes Thanks are extended to Nancy B. Robinson for general assistance and to two anonymous reviewers for their comments on the manuscript. Correspondence may be addressed to

No abstract

Gustav T. Fechner (1801–1887), professor of physics at the University of Leipzig, sought to measure the mind quantitatively. In approaching this task he studied stimuli and the sensations they aroused. His interest was in ascertaining how sensations changed with changing stimulation. While lying in bed on the morning of October 22, 1850, he conceived the essential idea of what was later to be called Fechner's law. In his subsequent derivation of the law (which appears at the beginning of the second volume of Elemente der Psychophysik ), he began with Weber's law (that the just‐noticeable difference in stimulation is a constant proportion of the stimulus magnitude, or JND=kI) and the assumption that the sensation (R) of a stimulus is the cumulative sum of equal sensation increments. Translating this into differential form, he started with dR = dI/I and integrated, under the assumption that R = 0 at absolute threshold (I°), to get the equation R = clog (I/I°).

Ernst Heinrich Weber (1795–1878), professor of anatomy (1821–1871) and physiology (1840–1866) at the University of Leipzig, on the basis of experiments with stimuli of pressure, lifted weights, and visual distance (line lengths), along with reported observations of others, concluded that, rather than perceiving simply the difference between stimuli being compared, we perceive the ratio of the difference to the magnitude of the stimuli. A similar finding had already been made by the French physicist and mathematician Pierre Bouguer (1698–1758) for visual brightness. Gustav T. Fechner (1801–1887), formerly a student of Weber's and later also a professor at the University of Leipzig, translated this conclusion into the familiar mathematical form used today. Thus Weber's law is usually given as either Δ I/I = k or Δ I = kI, where Δ I is the change required for a just noticeable difference in stimulation (JND), I is the stimulus magnitude, and k is a constant for the particular sense. The value of k is termed the Weber ratio. The equation Δ I = kI shows more clearly the proportional change in stimulation required for a JND. If, for example, the stimulus magnitude is doubled, the amount of change required for a JND is also doubled.