[334] Physiol. Psych., 2d ed. ii, 264-6.
[335] This was the original 'personal equation' observation of Bessel. An Observer looked through his equatorial telescope to note the moment at which a star crossed the meridian, the latter being marked in the telescopic field of view by a visible thread, beside which other equidistant threads appear. "Before the star reached the thread he looked at the clock, and then, with eye at telescope, counted the seconds by the beat of the pendulum. Since the star seldom passed the meridian at the exact moment of a beat, the observer, in order to estimate fractions, had to note its position at the stroke before and at the stroke after the passage, and to divide the time as the meridian-line seemed to divide the space. If, e.g., one had counted 20 seconds, and at the 21st the star seemed removed by ac from the meridian-thread c, whilst at the 22d it was at the distance bc; then, if ac: bc:: 1: 2, the star would have passed at 21 1/8 seconds. The conditions resemble those in our experiment: the star is the index-hand, the threads are the scale; and a time-displacement is to be expected, which with high rapidities may be positive, and negative with low. The astronomic observations do not permit us to measure its absolute amount; but that it exists is made certain by the fact than after all other possible errors are eliminated, there still remains between different observers a personal difference which is often much larger than that between mere reaction-times, amounting ... sometimes to more than a second." (Op. cit. p. 270.)
Fig. 35.
[336] Philosophische Studien, ii, 601.
[337] Physiol. Psych., 2d ed. ii, 273-4; 3d ed. ii, 339; Philosophische Studien, ii, 621 ff.—I know that I am stupid, but I confess I find these theoretical statements, especially Wundt's, a little hazy. Herr v. Tschisch considers it impossible that the perception of the index's position should come in too late, and says it demands no particular attention (p. 622). It seems, however, that this can hardly be the case. Both observers speak of the difficulty of seeing the index at the right moment. The case is quite different from that of distributing the attention impartially over simultaneous momentary sensations. The bell or other signal gives a momentary sensation, the index a continuous one, of motion. To note any one position of the latter is to interrupt this sensation of motion and to substitute an entirely different percept—one, namely, of position—for it, during a time however brief. This involves a sudden change in the manner of attending to the revolutions of the index; which change ought to take place neither sooner nor later than the momentary impression, and fix the index as it is then and there visible. Now this is not a case of simply getting two sensations at once and so feeling them—which would be an harmonious act; but of stopping one and changing it into another, whilst we simultaneously get a third. Two of these acts are discrepant, and the whole three rather interfere with each other. It becomes hard to 'fix' the index at the very instant that we catch the momentary impression; so we fall into a way of fixing it either at the last possible moment before, or at the first possible moment after, the impression comes.
This at least seems to me the more probable state of affairs. If we fix the index before the impression really comes, that means that we perceive it too late. But why do we fix it before when the impressions come slow and simple, and after when they come rapid and complex? And why under certain conditions is there no displacement at all? The answer which suggests itself is that when there is just enough leisure between the impressions for the attention to adapt itself comfortably both to them and to the index (one second in W.'s experiments), it carries on the two processes at once; when the leisure is excessive, the attention, following its own laws of ripening, and being ready to note the index before the other impression comes, notes it then, since that is the moment of easiest action, whilst the impression, which comes a moment later, interferes with noting it again; and finally, that when the leisure is insufficient, the momentary impressions, being the more fixed data, are attended to first, and the index is fixed a little later on. The noting of the index at too early a moment would be the noting of a real fact, with its analogue in many other rhythmical experiences. In reaction-time experiments, for example, when, in a regularly recurring series, the stimulus is once in a while omitted, the observer sometimes reacts as if it came. Here, as Wundt somewhere observes, we catch ourselves acting merely because our inward preparation is complete. The 'fixing' of the index is a sort of action; so that my interpretation tallies with facts recognized elsewhere; but Wundt's explanation (if I understand it) of the experiments requires us to believe that an observer like v. Tschisch shall steadily and without exception get an hallucination of a bell-stroke before the latter occurs, and not hear the real bell-stroke afterwards. I doubt whether this is possible, and I can think of no analogue to it in the rest of our experience. The whole subject deserves to be gone over again. To Wundt is due the highest credit for his patience in working out the facts. His explanation of them in his earlier work (Vorlesungen üb. Menschen und Thierseele, i, 37-42, 365-371) consisted merely in the appeal to the unity of consciousness, and may be considered quite crude.
[338] Note that the permanent interests are themselves grounded in certain objects and relations in which our interest is immediate and instinctive.
[339] Herbart: Psychologie als Wissenschaft, § 128.
[340] Sir W. Hamilton. Metaphysics, lecture xiv.