Elements of Psychophysics, Vol. I

...investigation by Volkmann Alfred Wilhelm Volkmann (1801–1877) was a German physiologist and a close friend and brother-in-law of Fechner. His empirical data on vision and touch were crucial for Fechner’s mathematical formulations. The willing participation of this sharp and refined researcher in the interests of this study—which, incidentally, led him onto his own paths far beyond the requirements initially set—and the growth of the empirical foundations of this work that resulted from it, truly place me under the greatest obligation of thanks.

At the same time, I venture to claim it as a favorable sign for the principle and character of the doctrine of this work that it can not only point to support in the exact investigations of the most excellent researchers, but is also able to provide points of connection for such studies. Indeed, apart from those theoretical and experimental investigations upon which it is based, and which have already attached themselves to it, the course of this writing has frequently offered occasion to point toward investigations to be undertaken or continued in the future. These are partly necessary for the further development of the science of psychophysical measurement German: psychophysische Masslehre; the systematic study of the relationship between physical stimuli and mental sensations, and partly enter into its applications. Despite the great interest these investigations hold, they would not have presented themselves without the perspective of this doctrine. The psychophysical experiment, which has until now only found an occasional place in either the physics or physiology laboratory, now claims its own room, its own apparatus, and its own methods. It is also certain that the field of these investigations will expand more and more the more it is cultivated. Thus, I seek the main fruit of our investigation thus far less in what it has yielded until now, than in what it once promises to yield. What lies before us is a scant beginning of a beginning.

Regarding the way in which mathematics is introduced in this writing, and notably how it will take its place in the following part, I wish that mathematicians might [consider] these elements...