The absolute increase in reaction time produced by a given decrease in intensity of stimulus, increases as the duration of the preparatory interval is increased beyond 2 secs., and this increase takes place at first more rapidly than later, as the interval is uniformly increased in length. Stated more definitely, if y represents the increase in reaction time produced by a decrease in the intensity of stimulus, and r the duration of any preparatory interval of 2 secs. or over, then y = A + B. log x, in which A and B are determinable constants. This law shows that the increase in reaction time produced by a decrease in intensity may be regarded as made up of two factors, one of which will vary with variation in the duration of the preparatory interval, and hence with variation in the degree of attention, while the other will remain constant.

As regards the absolute prolongation in reaction time produced by increase in the duration of the preparatory interval beyond 2 secs., it may be said that this prolongation increases markedly with decrease in the intensity of the stimulus. Since I did not measure the intensities of the stimuli I have not attempted a mathematical formulation of this law.

The relative increase in reaction time produced by a given decrease in intensity may not vary with prolongation in the preparatory interval beyond 2 secs. Similarly, the relative increase over the reaction time with a 2 sec. interval obtained with a longer preparatory interval, may remain the same for widely different intensities of stimulus.

In Chapter I, the conclusion was reached that the effect of variation in the preparatory interval upon reaction time, is due solely to the effect of variation in the interval upon the degree of adaptation of attention; so that the different reaction times obtained with the different intervals correspond to different degrees of attention. Now since the data show that the absolute effect of a given decrease in intensity varies with the duration of the interval, it follows, in accordance with the laws already stated, that the effect of variations in intensity varies with the degree of attention. And any factor which has a greater or less effect on

efficiency as the degree of attention involved is greater or less, is a condition of attention. Consequently, intensity of stimulus is a condition of attention. Similarly, since the unfavorable intervals may be regarded as detractors solely of attention, and since their effect was found to vary with intensity of stimulus, we may conclude that intensity of stimulus is a condition determining the effect that a given detractor of attention will produce, in other words, that intensity of stimulus is a condition of attention. The data of this chapter, therefore, assuming the conclusions of the preceding chapter, constitute an experimental proof that intensity is a condition of attention, and that different degrees of intensity condition different degrees of attention. What correspondence between intensity and degree of attention exists, is of course positive, not inverse. Data which corroborate this conclusion are given in Chapter IV.

Now, since the absolute increase in reaction time produced by the use of unfavorable preparatory intervals increases with decrease in the intensity of the stimulus, and since variation in the intensity of the stimulus results, as just pointed out, in corresponding variation in the degree of attention, we may conclude that the absolute increase in reaction time produced by the use of unfavorable preparatory intervals varies inversely with the degree of attention. Or, the degree of attention varies inversely with the absolute prolongation produced by unfavorable intervals. In other words, attentions may be measured or ranked, by equating them with the reciprocal of the absolute (but not the relative) prolongation in reaction time produced by the use of unfavorable preparatory intervals. We may use any two given conditions of intervals, one more favorable than the other, as a 4 sec. interval and a 20 sec. interval, both regularly repeated, or a 2 sec. interval regularly repeated and a given set of irregularly mixed intervals. The difference in the reaction times obtained under the two chosen conditions will vary inversely with the degree of attention.

By regarding the effect of unfavorable intervals and of weak intensities upon attention as typical of the effect of detractors in

general, we may state the following general law of detraction: The absolute detraction effect of a given detractor of attention varies inversely with the degree of attention upon which the detractor acts. This law not only furnishes the basis for the measurement of attention but gives a description resting upon experimental data of one of the most important functions of attention, namely, the increase in efficiency which results from the resistance to distracting or detracting conditions. It points out that attention varies inversely as the ability to resist conditions that are unfavorable to attention and that this ability is measurable in its effect upon efficiency. Indirectly, then, increase in efficiency is a function of attention. Were it practically important to have an absolute measure of attention instead of a relative one, I believe that we could very well substitute increase in efficiency for the function usually regarded as the most essential, namely, clearness, and instead of equating the absolute degree of attention with clearness equate it with the absolute increase in the reciprocal of efficiency produced under specified conditions by a specified detractor.

The expression "absolute detraction effect," in the law of detractors that I have just stated, is necessary, for I have shown that the relative effect cannot be used for the purpose of measurement of attention. The relative effect may remain constant while attention varies, as in the case of the relative prolongation of reaction time caused by the use of unfavorable intervals as detractors, where the relative prolongation remains constant while the degree of attention is varied by varying the intensity of the stimulus.

The phrase "a given detractor" conceals many difficulties, but the conditions determining a satisfactory detractor as well as an analysis of the conditions which must be complied with if the detraction effect is to be adequately measured has already been given in the introductory chapter.

THE MEASUREMENT OF ATTENTION BY REACTIONS TO A

CHANGE IN INTENSITY

The general subject of this chapter is the value of reactions to a change in intensity for the measurement of attention. More specifically, the object of the experiments reported in this chapter is twofold. The first set of experiments was made with the purpose of determining whether it is possible to find a form of reaction the time of which is unaffected by variations in retinal sensitivity, and so to get a method of measuring attention apart from its dependence upon retinal sensitivity. The second set of experiments here reported had for its principal object the verification of the law of detraction, as stated in the last chapter, namely, that the absolute effect of a given detractor varies inversely as the degree of attention detracted from; but in the present instance the different degrees of attention were not produced by change in the absolute intensity of the stimulus, as in the preceding chapter, but by changes in the size of the change in intensity, the reaction being to the change in intensity.

The sensitivity of the sense-organ, whether the eye or ear, would quite certainly affect the result of the measurement of attention by the method so far suggested. Decreasing the sensitivity of the sense-organ is the equivalent of decreasing the intensity of the stimulus, and since intensity is a condition of attention this would certainly affect the result. Consequently, by the method used in the last chapter, a person with a low retinal sensitivity as regards intensity would be very likely to have very bad attention, and a person with normal vision, comparatively good attention. For certain purposes such a result would be unsatisfactory. It seems desirable for the purpose of comparing the attention of different individuals to be able to measure an individual's attention, as it occurs in the reaction process, independently of the variations which might be pro

duced in that attention as the result of variation in the condition of the sense organ involved.

Individuals' attentions under the conditions of the reaction experiment, vary in part because of variation in the sensitivity of their sense organs, but there is nothing indefinite in the concept of measuring these attentions in so far as they differ only because of other factors than the factor of sensory sensitivity. Retinal sensitivity, or any other sensory sensitivity, is capable of separate measurement, possibly, and a correction for it might perhaps be worked out, but this would be too difficult and uncertain. I accordingly sought a method of ranking attentions considering them as different only to the degree they would be different as the result of all conditions other than sensory sensitivity.

Simple reaction times, such as I used in the experiments so far reported, are evidently not suited to my purpose.

Since the result of any detracting influence, e.g., the unfavorable intervals, varies with the intensity of the stimulus, it presumably varies also with the sensitivity of the retina. We know that increasing the sensitivity of the retina, as for instance by adaptation to darkness, has the same effect as increasing the intensity of the stimulus, that is, results in an increase in apparent brightness; and while I have not experimented in the way reported in the last chapter with different retinal sensitivities substituted for different intensities of stimulus, there is every reason to believe that the effect produced by unfavorable intervals would vary with variations in retinal sensitivity in a way corresponding to that in which it varies with variation in intensity of stimulus.

A single visual stimulus, then, undoubtedly has the effect of its intensity reduced by a decrease in the sensitivity of the retina. But what is the effect of a decrease in sensitivity on the apparent difference in intensity of two light stimuli? The variation in sensitivity of the retina in different people may be due to various causes, but the result here considered is simply variation in the effect of the intensity of the stimulus. In so far as these variations in the eyes of different people do not affect the intensity effect