Distance constancy was clearly defined with Thouless and B1~nswik 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.
* I wish to express my thanks to Professor u
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 Hashiguehi 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.