not show variation when attention varied, and which would not accordingly show a parallelism with attention under the condition that "the work itself was not influenced by anything else but change in attention." But Geissler's work experimentally establishes the validity of this assumption.

66

Concerning the bearing of this correlation between estimated degrees of clearness and efficiency of work upon the measurement of attention, Geissler writes: we believe that our results have brought us within reach of a new and fairly definite method of measuring attention, for the results have shown that degrees of clearness are just as accessible to introspective determination as variations of the intensity of sensations. . . There is sufficient warrant in our results for the assumption that continued practice will lead at least to a differential clearness limen which may be just as definite as any other psychophysical limen, while on the other hand, it may be perhaps more difficult to establish the least possible or the highest possible clearness degree for any given mental process. However, the determination of a difference limen for clearness would be the most important step toward an exact measurement of the concentration of attention. It would enable one, by starting with a certain clearness degree of a given mental process under fixed experimental conditions, either to increase or decrease that clearness by just noticeable differences, until the maximum or the minimum of attention to the particular process is reached.”2

Concerning this differential limen, which Geissler says would be the most important step toward an exact measurement of the degree of attention, all that can be said in reply is that no such limen for clearness has as yet actually been measured, and that Dallenbach3 in his recent article which is avowedly a continuation of Geissler's work, does not even refer to the matter.

It is perhaps possible that, apart from the matter of a differential clearness limen, use may ultimately be made in the measurement of attention of the high correlation which both Geissler and Dallenbach have found to exist between efficiency

and estimates of clearness. Neither of the authors mentioned, however, deny that efficiency may vary as the result of other factors than attention; nor do they explain any procedure for keeping other factors than attention constant, though their statement of parallelism between estimated clearness and efficiency is limited by the condition that no factor other than attention shall vary.

Both Geissler and Dallenbach have paid so much attention to the matter of devising suitable distractors, that their work has considerable bearing upon the method proposed by Titchener. Titchener writes as follows: "If we knew, for instance, that a certain sensation may exist in ten different degrees of clearness: and if we had at our disposal ten stimuli which, introduced by way of distraction, would reduce this sensation from the corresponding degree of clearness to total obscurity: then we might calculate, from the effect of a particular distractor in the particular case, what fraction of maximal attention the observer was giving to the matter in hand. The method is cumbrous and difficult to work out; but the writer believes that it may, some day, be successfully applied." Such a method evidently requires above everything else a set of constant and reliable distractors. Indeed, while the theory of the distraction method of measuring attention has, in the rough, been known for many years, the rub has always been in finding suitable distractors-or, since as a matter of fact only one, and not a set, is necessary, a suitable single distractor. A method of distraction suitable to the measurement of attention has not hitherto been devised. Geissler found that even the most complex distractors, after a few days' work, were unable to induce great variations of attention,5 and Dallenbach writes: "In choosing the distractors, our ideal was that of Drew, 'to arrange a series of tasks of increasing degrees of complexity which should from the normal make ever greater demands on the mind until the attention should pass from a fully concentrated to a completely distracted state.' This is the prin

'A Text-Book of Psychology, 1909, 296. Cf. also his The Psychology of Feeling and Attention, 1908, 276-282.

Op. cit., 513.

ciple laid down by Stumpf in his Tonpsychologie, and by Titchener in his Psychology of Feeling and Attention. The results show that we were not successful in obtaining such a series of graded distractors.”

A quite different method of measuring clearness is that followed by Wirth. Wirth's method is exceedingly complicated and utilizes very elaborate apparatus. There exists serious doubt whether Wirth's method accomplishes its aim. Geissler, in a second review of Wirth's method after a reply9 by Wirth to his first criticism,10 concludes by still maintaining that Wirth "has failed to solve his problem" 11 and Gruenbaum in a criticism of the work of A. Kaestner u. W. Wirth entitled Die Bestimmung der Aufmerksamkeitsverteilung innerhalb des Sehfeldes mit Hilfe der Reaktionsversuche, concludes as follows: "Meiner Ansicht nach ist also weder der Vergleich der Resultate nach beiden Methoden [the reaction method and the differential brightness limen method] positiv ausgefallen, noch eine einwandsfreie Darstellung des Aufmerksamkeitsreliefs gelungen, noch die Durchfuehrung der Aufmerksamkeitsverteilung gesichert gewesen.

9912

Whether the main trouble with Wirth's method lies in his units of measurement or in his method of securing distributed attention, it is difficult to decide. Serious objections may certainly be made to both. Wirth's fundamental proposition, to limit myself to his first method, seems to be that the clearness of any point of the visual field with respect to intensity can be measured by determining, first, the intensive differential limen with maximal attention upon the point in question, and second, the same limen with less than maximal attention to the point in question, i. e., with distributed attention, and third, dividing the first mentioned limen by the second.

'Philos. Stud., 1902, 635-659. Psychol. Stud., 1906, 30-88; A. Kaestner und W. Wirth, Psychol. Stud., 1907, 361-392 and 1908, 139-200.

As for the third part of the procedure, I must confess that it seems to me the result of incorrect and confused reasoning. And while this part of Wirth's procedure is unjustified, it is impossible on the basis of the data he presents to outline any other which would give a correct result. In Chapter III it will be shown that a decrease in the favorableness of the conditions of attention, under certain conditions, exerts an absolute effect inversely proportional to the degree of attention, while the relative effect may remain the same. A theoretical explanation of this fact is there given. If such a law as this held under the conditions used by Wirth, one would have to use the difference between the normal and distraction limena, and not their quotient, as the measure of clearness. Wirth takes the quotient, but he has no data which prove the validity of this procedure. It is based on the hypothetical and unsound speculation that all the component factors involved in the discrimination of intensity would vary in the same direction as the result merely of a change in attention. Now either attention alone changed, in which case the non-attention factors involved in the process of discrimination did not change at all, or else other factors than attention varied and it would then be hopeless to attempt to get a measure of attention or clearness from the resulting change in the limen.

Moreover, it is very apparent that a measurement of clearness possessing any accuracy can not be obtained by such a method of securing distributed attention as that used by Wirth. If the clearness of different points in the field of vision is to be determined by Wirth's procedure, it is essential that throughout any set of measurements that are to be compared, the distribution of attention used to secure less than maximal attention shall remain constant. But the distribution was produced solely by the voluntary direction of the subject. It can not be said to have been brought under experimental control. We have no guarantee of its constancy, through a series of measurements, and consequently we can not make a valid comparison of the different measurements. The very great irregularity in the results obtained do not justify any faith in the reliability of such a method of securing a constant distribution of attention. That the method

was altogether inefficient is indicated by the result that the clearness of points in the area "attended to" was about as often either high or low as that of points in the area "distracted from," and that no reliable difference existed even on the average in the clearness of the points in the areas "attended to" and in the areas "distracted from."

Passing now to the method developed in the following pages, I wish to raise a question which is bound to occur sooner or later and so may as well be considered at the start. How can one claim to have a method of measuring attention when psychologists are not entirely agreed as to what attention is? One may arbitrarily define attention, a procedure which has the advantage of definiteness, or one may argue that the method is valid for any of a number of reasonable and generally accepted definitions of attention. Since what attention is, is more or less of a speculation, I prefer the latter course. It will be assumed that attention is a psychophysical process, the intimate nature of which is still in doubt, but which is known by certain of its functions. By a function of attention is meant something which varies whenever attention varies. Electricity is perhaps a roughly analogous illustration of a process known only by its functions. One of the most commonly accepted functions of attention is clearness. I do not regard clearness as a synonym of attention but as a function of attention. Another function is limitation or narrowing of the field of consciousness. Another function is efficiency in any psychophysical process, that is, the greater the degree of attention, the greater the efficiency, other conditions remaining constant. There are many other functions. Attention may be satisfactorily defined in terms of any of its essential functions. The function by which attention is defined must always vary when attention varies, providing other conditions remain constant.

The function of attention which I have chosen for the purpose of measurement of the degree of attention is efficiency in a psychophysical act. There is no more important function. Efficiency, has, morever, been shown to correlate very highly with clearness by Geissler and by Dallenbach. It is true that the effi