# The Philosophical Review/Volume 1/Review: Angell - Untersuchungen über die Schätzung von Schallintensitäten

This essay, accepted by the University of Leipzig for the degree of Ph.D., begins with a brief consideration of the two classes of hypotheses underlying the considerations of Weber's law, namely, the hypothesis of absolute and that of relative differences. According to the former the absolute differences of sensation are the same as long as the relation of the variations of the stimulus are the same; according to the latter as long as the relation of the variation of a sensation to that sensation is the same the relation of the stimulus to its variation remains constant. The results of the method of successive gradations (mittlere Abstufungen) are regarded as the strongest proof against the relation-hypothesis; when three sensations are so arranged in intensity that the second occupies the middle position between the extremes it is evident that the differences between it and the extremes are considered equal. The relation-hypothesis is of a rather hyper-psychological character. As Dr. Angell has pointed out, according to its supporters the differences between strong sensations are greater than the corresponding (judged as the same?) differences between weaker sensations. It seems that the difference between sensations has been turned into a sensation — a difference-sensation. According to Merkel, a supporter of the relation-hypothesis, Weber's law would be confirmed if by the method of successive gradations the middle stimulus was the arithmetic middle; just how this could be, it is difficult to understand, and if such a result is required to prove that hypothesis, Dr. Angell's experiments have completely disproved it.
In his consideration of the relation-hypothesis Merkel was led to assert that we could determine the half of a given sensation or twice it just as well as the just perceptible difference. Aside from all theoretical considerations the question arises: is it possible to measure intensities ​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 21/2 or 21/3 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 ​complicated. This uncertainty as to what actually happens showed itself clearly when the energy of the colliding bodies was varied by using balls of different weights; as Dr. Angell says (p. 14), this method produces a change in quality as well as in intensity. It is at least possible that a variation of the energy by varying the height of fall also produces a change in quality. We can, to a certain degree, abstract from a consideration of anything but the intensity, but even an unconscious difference can influence the decision. Taking these facts into consideration, the amount of variation from the double of the stimulus corresponding to a double sensation is really less than would be expected. The great care exercised in this case has reduced the variation in general to less than 20%. Finally, it is no objection to the method of multiple stimuli that we have to learn to estimate intensities; the same is true of all estimations of length, time, etc.
The latter half of the dissertation is devoted to a proof of the applicability of the method of successive gradations to intensities of noise and to determining whether the estimated middle intensity follows any law.
The variation of the middle stimulus can be regular or irregular. If regular, the successive steps by which it is varied can be different in direction, in size, in number, and in the point of starting. The influence of the difference in size is shown in tables IV, V, and VI. To eliminate the influence of the point of starting this was varied as much as possible. The influence of these matters is so great that Dr. Angell remarks: "I am of the opinion that in all our experiments the factors of expectation and habit are within quite distant limits much more influential in the estimates than the intensity of the varied stimulus itself" (p. 36). Recourse was had to irregular variations of the middle stimulus in the manner employed by Lorenz. Various intensities between the two extremes were judged as above (o), at (m), or below (u) the middle; then o' and u' were taken thus: o' = o + m/2 and u' = u + m/2. This is, in fact, the only satisfactory form of the method of successive gradations as applied to successive stimuli. The results are excellently shown in the accompanying plate. The confirmation of Weber's law which here occurs is one of the most important contributions on that subject.
E. W. Scripture.
This work is in the public domain in the United States because it was published before January 1, 1929.
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