, Volume 34, Issue 3, pp 199-219

Distance constancy: Functional relationships between apparent distance and physical distance

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Distance constancy was clearly defined with Thouless and Brunswik indexes by examining its previous definitions. The typical functions expressing the relationships between apparent distance and physical distance were derived from; 1. much available data obtained by many researchers, 2. Thouless and Brunswik indexes (formulas), 3. Luneburg's theory. These derived functions were classified into type I, II and III according to their psychological significance. The validity of the classification was verified by experiments showing that the functions of type III were available in poorly articulated spaces with a long viewing distance, that is, on a housetop and a road, with the method of equal appearing intervals. Moreover, the relationships between distance constancy and personal constants in Luneburg's theory were clarified.


In der vorliegenden Arbeit wird die Entfernungskonstanz nach Überprüfung ihrer früheren Definitionen mit Thouless' und Brunswiks Indexen genau definiert. Die typischen Funktionen, die die Beziehungen zwischen scheinbarer Entfernung und physikalischer Entfernung zeigen, werden abgeleitet aus 1. den verfügbaren Forschungsergebnissen zahlreicher Gelehrter, 2. Thouless' und Brunswiks Indexen (Formeln), 3. Luneburgs Theorie. Diese abgeleiteten Funktionen werden ihrer psychologischen Bedeutung entsprechend in Typus I, II und III eingeteilt. Die Gültigkeit dieser Klassifikation wurde durch Experimente verifiziert, die mit der Anwendung der Methode von gleich erscheinenden Abständen zeigen, daß die Funktionen vom Typus III in ungenügend artikulierten Räumen mit einer langen Beobachtungsentfernung, d.h. auf einem Dach und einem Weg, gültig sind. Außerdem werden die Beziehungen zwischen Entfernungskonstanz und Personalkonstante in Luneburgs Theorie festgestellt.

I wish to express my thanks to Professor Yoshiharu Akishige for his guidance in this field of work, and Dr. Katsumi Ishii, the retired professor of Kyushu University, for his invaluable suggestions, especially for constant guidance in the problems of Luneburg's theory. Thanks are also due to Assistant Professor Masao Hashiguchi of Kagoshima University for his valuable advice and generous help concerning the mathematical problems. I am also indebted to the students of our department for their help in carrying out the experiments.