Thus, in the experiments on the force of motion, by combining methods, the authors were able to show that the just observable difference meant a different thing to different observers, that the variable error of the j. o. d. was a better test of discrimination than the j. o. d. itself, and that the constant error cannot be taken as a measure of discrimination in experiments on the extent of movement by the method of average error. The investigation on extent of movement supplements Delabarre's work on sensations of motion in considering the relation of the variable error to the size of the movement. Indeed, the experimental part of the work abounds in acute observations of value to the student of the psychophysical methods.
For extent and force of movement it was not found that the error of observation increased as fast as Weber's law demands; instead of being proportional to the magnitude of the stimulus, it was more nearly proportional to the square root of the stimulus. Accordingly the authors, or more especially Professor Cattell, propose to substitute for Weber's law the following:—"The error of observation tends to increase as the square root of the magnitude, the increase being subject to variations whose amount and cause must be determined for each special case" (pp. 25 and 153). As an independent law and a generalization from the experiments under the given conditions, the statement is hardly to be criticised, but the conditions are scarcely such as to make it a substitute for Weber's law. The enormous complication of the sensations entering into the perception—sensations which arise in different parts of the limb in different parts of the movement—makes it almost impossible to consider Weber's law as bearing any relation to the perception. For the law expresses primarily the relation of a certain kind of sensation to a given intensity of stimulus. Experiments made by the writer's students indicate that the proportion of the square root holds true not only for movements in the same direction, but for consecutive movements in opposite directions—in which case, whatever the relation at issue, it is certainly not that of a certain sensation to a given amount of stimulus.
The treatise is enriched by descriptions and cuts of several pieces of apparatus devised by the authors—a dynamometer adjustable for force and extent of pull, apparatus for measuring the time (velocity) of movement, and an apparatus for comparing successive light stimuli.
