Since it had been noted that in the desensitization treatment of phobias the number of presentations of a scene required to bring the anxiety level down to zero is not uniform but tends to increase or decrease on the way up a hierarchy, an attempt was made to establish quantitative relations by a study of those phobias that vary along a physical dimension. It was found that in claustrophobias and phobias in which anxiety rises with increasing proximity to a feared object the number of scene presentations to zero anxiety is low at a distance and increases with proximity, the cumulative curve corresponding to a positively accelerating function. In agoraphobias as in phobias increasing with number of objects the number of presentations needed is initially high and progressively falls as distance grows, the cumulative curve corresponding to a negatively accelerating function. In both cases the number of prestations to advance a segment of given size varies inversely with the distance of that segment from the central "safe zone" (as in agoraphobia) or "danger zone" (as in claustrophobia) in accordance with a simple power function such as has been constantly found to be the functional relation between stimulus magnitude and psychological magnitude.Abstract Teaser