562 CRITICAL NOTICES : two lengths," he says, " become the object of our judgment, they do not therefore cease to be physical magnitudes : it is the latter that we measure, not our sensations or their differences " (p. 91). To apply this to sensational intensities generally, seems to me what Prof. Aliotta elsewhere calls " psychological nonsense ". In spite of our inability to measure sensations, we may yet allow ourselves the psychological possibility of comparing sensations and of comparing and equating sensation-differences : and this possibility is all that Weber's law requires. Prof. Aliotta is on surer ground when he insists that a sensation is indivisible into parts and that Fechner's conception of measur- ing it by the sum of the just perceptible differences which are contained within it is psychologically unjustifiable. To juggle with sensations or sensation differences by addition, subtraction and other algebraical operations is, as he well says, " psychological nonsense". The following is a familiar but excellent example of the kind of treatment he has in mind, culled from Ebbinghaus's Grundziige der Psychologie (cf. Fechner's Elemente, Bd. ii., S. 38). Let eje 2 , e 2 /e 3 represent the differences between sensations e v e 2 , e 3 ; and let r v r 2 , r s be the magnitudes of the corresponding f* stimuli. Then since on experimental grounds e^je^ =/(-) and T -2 T e 2 /e s =/(-), where / is the symbol of functional dependence, r s /V> Of therefore (by summation) e-^fe^ = f (- ) + / (- 2 ). This operation r 2 r a implies that the sum of two sensation differences (those of the first two equations) must necessarily be equivalent to a single sensation difference, an arbitrary and psychologically unwarrantable as- sumption. Even while admitting that sensations cannot be divided into parts, it is nevertheless open for us to doubt that they are therefore immeasurable. Meinong urged that such physical quantities as work, velocity and the like, although indivisible into parts, were nevertheless capable of measurement. Prof. Aliotta replies (p. 75) that velocity is conceived as the distance traversed in unit time, and only thus is capable of measurement conceptually : similarly, too, in regard to work. But in order that measurement may be extended to the psychical sphere, he insists that we must have perceptual not conceptual measurement. Here lies the criix of the whole problem. What is perceptual measurement ? Where is it to be found ? We look in vain to Prof. Aliotta for an answer to these questions. For what he has denied to sensations, he denies also to other psychological processes. According to him, " the size of the error in the estimation of any magnitude, the longer or shorter duration of the process, in general every numerical difference in the objective results of a mental function [hence any quantitative result in experimental psychology] af- fords no measurement of psychical phenomena, but serves only
