cated. 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 + m2 and u' = u + m2. 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.
The cerebellum, as is well known, is not considered by our contemporary physiology to have any special connection with consciousness, but is treated as a co-ordinator of sensory and locomotor functions exclusively.
