cannot do this, we must do the best we can and describe a sensation in terms of the number it most strongly suggests.  Subjects very often, as has been mentioned before, describe a sensation as ‘more than one but less than two,’ but when pressed for an answer will say whichever number it most resembles.  A person would do the same thing if he were shown spectral colors from orange to yellow and told to name each one either orange or yellow.  At one end he would be sure to say orange and at the other yellow, but in the middle of the series his answers would likely depend upon the order in which the colors were shown, just as in determining the threshold for the perception of two points by the method of minimal changes the answers in the ascending series are not the same as those in the descending series.  The experiments have shown that the sensation produced by two points, even when they are called one, is not the same as that produced by only one point, but the difference is not great enough to suggest a different number.

If the difference between one and two were determined by the distance, then the substitution of lines for knobs of the aesthesiometer ought to make no difference.  And if the sensations produced by two objects fuse when near together, then the sensations produced by lines ought to fuse as easily as those produced by knobs.

In regard to the higher numbers difficulties will arise unless we take the same point of view and say that number is an inference from a sensation which is in itself a unit.  It has been shown that four points across the ends of the fingers will be called four or less, and that four points, one on the end of each alternate finger and one at the base of each of the others, will be called four or more—­usually more.  In either case each contact is on a separate finger, and it is hardly reasonable to suppose there is no diffusion when they are in a straight row, but that when they are in irregular shape there is diffusion.  It is more probable that the subject regards the sensation produced by the irregular arrangement as a novelty, and tries to separate it into parts.  He finds both proximal and distal ends of his fingers concerned.  He may discover that the area covered extends from his index to his little finger.  He naturally infers, judging from past experience, that it would take a good many points to do that, and hence he overestimates the number.  When a novel arrangement was given, such as moving some of the weights back on the wrist and scattering others over the fingers, very little idea of number could be gotten, yet they were certainly far enough apart to be felt one by one if a person could ever feel them that way, and the number was not so great as to be entirely unrecognizable.

* * * * *

THE SUBJECTIVE HORIZON.

BY ROBERT MACDOUGALL.

I.