Turning now to the explanation of the special experiments, we may begin with the _Vexirfehler_.[2] It seems to me that the _Vexirfehler_ is a very simple phenomenon. When a person is stimulated with two objects near together he attends first to one and then to the other and calls it two; then when he is stimulated with one object he attends to it, and expecting another one near by he hunts for it and hits upon the same one he felt before but fails to remember that it is the same one, and hence thinks it is another and says he has felt two objects. Observers agree that the expectation of two tends to bring out the _Vexirfehler_. This is quite natural. A person who expects two and receives one immediately looks about for the other without waiting to fixate the first, and therefore when he finds it again he is less likely to recognize it and more likely to think it another point and to call it two. Some observers[3] have found that the apparent distance of the two points when the _Vexirfehler_ appears never much exceeds the threshold distance. Furthermore, there being no distinct line of demarcation between one and two, there must be many sensations which are just about as much like one as they are like two, and hence they must be lumped off with one or the other group. To the mathematician one and two are far apart in the series because he has fractions in between, but we perceive only in terms of whole numbers; hence all sensations which might more accurately be represented by fractions must be classed with the nearest whole number. A sensation is due to a combination of factors. In case of the _Vexirfehler_ one of these factors, viz., the stimulating object, is such as to suggest one, but some of the other conditions--expectation, preceding sensation, perhaps blood pressure, etc.--suggest two, so that the sensation as a whole suggests _one-plus_, if we may describe it that way, and hence the inference that the sensation was produced by two objects. [2] Tawney, Guy A.: 'Ueber die Wahrnehmung zweier Punkte mittelst des Tastsinnes mit Rücksicht auf die Frage der Uebung und die Entstehung der Vexirfehler,' _Philos. Stud._, 1897, Bd. XIII., S. 163. [3] See Nichols: 'Number and Space,' p. 161. Henri, V., and Tawney, G.: _Philos. Stud._, Bd. XI., S. 400.