directly on one another? This can be answered only by experiment; one case of it, the determination of the double intensity of a given noise, is undertaken in the present essay. The noise was produced by a small ivory ball falling from a given height on a hard board. According to Starke's previous determinations on the same apparatus the intensity of the noise is proportional to the height of fall. The referee had the pleasure of serving as "Versuchsthier" in an investigation of the same problem and with the same apparatus, in which the leader of the investigation was unable to obtain any results on account of the difficulties connected with both apparatus and method. He, perhaps better than any one else, can appreciate the care and patience shown in Dr. Angell’s investigation (e.g. see p. 24). Indeed, the essay can be held up as a model to our American workers who are only too inclined to rush through an investigation per express.
The results obtained can be condensed by saying that for a noise produced by a ball falling 13.5 cm. the double intensity was found when the ball fell about 212 or 213 times as far, for a noise produced by a fall of 27 cm. the double was a little less than twice, for 40.5 cm. it was about 1.85 times, for 54 cm. about 1.85 times. Although these noises were neither very loud nor very weak, yet the variation of the relation between the double of the stimulus and the double of the sensation is considerable. This variation is well explained from the fact that the observer had to learn what was meant by a double intensity, also from the knowledge of the number of steps employed in approaching the double and from the influence of unconscious suggestion. The conclusion, however, is drawn (p. 58) that the method of double stimuli cannot count as a psychophysical method. This conclusion, it seems to the referee, is not quite justified by the experiments.
The concussion of two bodies produces an irregular periodic vibration of the air, generally starting with a maximum displacement and more or less rapidly and irregularly decreasing; see the figures in Hermann, Handbuch der Physiologie, III (2). To such a given vibration, there corresponds a percept having several characteristics, among which there are those called quality and intensity. When the two bodies meet in concussion with a different energy a vibration of an analogous kind is produced, but there is no proof that the amplitudes of each of the phases of displacement is correspondingly increased without other change. Even if this were so, yet we have no guarantee that the percept of the noise has not changed in quality as well as intensity. Moreover, for tones the intensity of the percept is a complicated function of the amplitude and the pitch. Even for a single simple tone the psychological intensity varies in the same sense as the amplitude, but is in no wise directly proportional to it, the relation being much more compli-
