have recently been made in Germany. Professor Ebbinghaus, in a really heroic series of daily observations of more than two years' duration, examined the powers of retention and reproduction. He learned lists of meaningless syllables by heart, and tested his recollection of them from day to day. He could not remember more than 7 after a single reading. It took, however, 16 readings to remember 12, 44 readings to remember 24, and 55 readings to remember 26 syllables, the moment of 'remembering' being here reckoned as the first moment when the list could be recited without a fault.[599] When a 16-syllable list was read over a certain number of times on one day, and then studied on the day following until remembered, it was found that the number of seconds saved in the study on the second day was proportional to the number of readings on the first—proportional, that is, within certain rather narrow limits, for which see the text.[600] No amount of repetition spent on nonsense-verses over a certain length enabled Dr. Ebbinghaus to retain them without error for 24 hours. In forgetting such things as these lists of syllables, the loss goos on very much more rapidly at first than later on. He measured the loss by the number of seconds required to relearn the list after it had been once learned. Roughly speaking, if it took a thousand seconds to learn the list, and five hundred to relearn it, the loss between the two learnings would have been one half. Measured in this way, full half of the forgetting seems to occur within the first half-hour, whilst only four fifths is forgotten at the end of a month. The nature of this result might have been anticipated, but hardly its numerical proportions. Dr. Ebbinghaus says:
"The initial rapidity, as well as the final slowness, as these were ascertained under certain experimental conditions and for a particular individual,... may well surprise us. An hour after the work of learning had ceased, forgetting was so far advanced that more than half of the original work had to be applied again before the series of syllables could once more be reproduced. Eight hours later two thirds of the original labor had to be applied. Gradually, however, the process of oblivion grew slower, so that even for considerable stretches of time the losses were but barely ascertainable. After 24 hours a third, after 6 days a fourth, and after a whole month a good fifth of the original labor remain in the shape of its after-effects, and made the relearning by so much the more speedy."[601]
But the most interesting result of all those reached by this author relates to the question whether ideas are recalled only by those that previously came immediately before them, or whether an idea can possibly recall another idea with which it was never in immediate contact, without passing through the intermediate mental links. The question is of theoretic importance with regard to the way in which the process of 'association of ideas' must be conceived; and Dr. Ebbinghaus's attempt is as successful as it is original, in bringing two views, which seem at first sight inaccessible to proof, to a direct practical test, and giving the victory to one of them. His experiments conclusively show that an idea is not only 'associated' directly with the one that follows it, and with the rest through that, but that it is directly associated with all that are near it, though in unequal degrees. He first measured the time needed to impress on the memory certain lists of syllables, and then the time needed to impress lists of the same syllables with gaps between them. Thus, representing the syllables by numbers, if the first list were 1, 2, 3, 4,... 13, 14, 15, 16, the second would be 1, 3, 5,... 15, 2, 4, 6,... 16, and so forth, with many variations.
Now, if 1 and 3 in the first list were learned in that order merely by 1 calling up 2, and by 2 calling up 3, leaving out the 2 ought to leave 1 and 3 with no tie in the mind; and the second list ought to take as much time in the learning as if the first list had never been heard of. If, on the other hand, 1 has a direct influence on 3 as well as on 2, that influence should be exerted even when 2 is dropped out; and a person familiar with the first list ought to learn the second one more rapidly than otherwise he could. This latter case is what actually occurs; and Dr. Ebbinghaus has found that syllables originally separated by as many as seven intermediaries still reveal, by the increased rapidity with which they are learned in order, the strength of the tie that the original learning established between them, over the heads, so to speak, of all the rest. These last results ought to make us careful, when we speak of nervous 'paths,' to use the word in no restricted sense. They add one more fact to the set of facts which prove that association is subtler than consciousness, and that a nerve-process may, without producing consciousness, be effective in the same way in which consciousness would have seemed to be effective if it had been there.[602] Evidently the path from 1 to 3 (omitting 2 from consciousness) is facilitated, broadened perhaps, by the old path from 1 to 3 through 2—only the component which shoots round through this latter way is too feeble to let 2 be thought as a distinct object.
Mr. Wolfe, in his experiments on recognition, used vibrating metal tongues.
"These tongues gave tones differing by 2 vibrations only in the two lower octaves, and by 4 vibrations in the three higher octaves. In the first series of experiments a tone was selected, and, after sounding it for one second, a second tone was sounded, which was either the same as the first, or different from it by 4, 8, or 12 vibrations in different series. The person experimented upon was to answer whether the second tone was the same as the first, thus showing that he recognized it, or whether it was different, and, if so, whether it was higher or lower. Of course, the interval of time between the two tones was an important factor. The proportionate number of correct judgments, and the smallness of the difference of the vibration-rates of the two tones, would measure the accuracy of the tone-memory. It appeared that one could tell more readily when the two tones were alike than when they were different, although in both cases the accuracy of the memory was remarkably good.... The main point is the effect of the time-interval between the tone and its reproduction. This was varied from 1 second to 30 seconds, or even to 60 seconds or 120 seconds in some experiments. The general result is, that the longer the interval, the smaller are the chances that the tone will be recognized; and this process of forgetting takes place at first very rapidly, and then more slowly.... This law is subject to considerable variations, one of which seems to be constant and is peculiar; namely, there seems to be a rhythm in the memory itself, which, after falling, recovers slightly, and then fades out again."[603]
This periodical renewal of acoustic memory would seem to be an important element in the production of the agreeableness of certain rates of recurrence in sound.