Page:Popular Science Monthly Volume 72.djvu/471

 and a commentary of even greater length. Such a procedure would be him to be of the size of a plate, a cart-wheel, or what not, and there's an end. His answer can not be challenged on the score of malobservation; one may impeach either his memory or his truthfulness, but not the accuracy of his observation or even of his judgment. In other words, if the man misunderstood the question, and was really answering this other: "How large does the moon instinctively appear to you?" his answer, "as large as a carriage-wheel" or "as large as a one-cent piece," is better than any that either the psychologist or the astronomer can supply for him. If, on the other hand, the student understood the question as it was "carefully explained" by Professor Münsterberg, he absolutely deceived himself if he imagined that his "perception" of the moon's size had anything to do with the answer. We do not, by direct perception, actually estimate the angle subtended by an object, nor do we perform any equivalent operation. For any object within a small distance, we automatically make absolutely complete compensation for the diminishing angle under which it is seen as the distance increases; a plate, a silver dollar or a pea, held at arm's length, looks precisely as large as it does when held at the distance of a foot—we have no consciousness whatsoever that the angle it subtends is only one third as great in the former case as in the latter. The moon subtends an angle of half a degree; a large pea at arm's length does the same; a large pin's head, perhaps, does the same a foot away from the eye. But the keenest observer in the world is no more aware of these things by direct perception than is the most ill-constructed member of Professor Münsterberg's class. Our automatic compensation for diminishing angle becomes very imperfect both at great distances and in unusual circumstances—such as looking down upon the floor of the rotunda of the capitol from the gallery at the top; and for celestial objects, like the sun and the moon, it of course falls infinitely short of requirements. We make some compensation, though immeasurably less than what is required; and the well-known fact that people differ enormously in their feeling of the apparent size of the moon merely shows that the amount of this compensation (which, in any event, has no simple relation to the actual size and actual distance of the moon) is very different with different persons. But, strangely enough. Professor Münsterberg seems to lose sight of all these facts, and actually to regard the question of the apparent size of the moon as identical with the mathematical question of the angle that it subtends—or, what comes to the same thing, the size of an object which, held at arm's length, will "just cover" it. For while he "carefully explained" the question as meaning the latter thing, his comments relate to the former; and, in particular, in the closing remarks of his article, he speaks of his students not knowing whether "the moon is small as a pea or large as a man." By "is," he of course means "seems";