§5. Quantitative Methods.—A science becomes more exact in proportion as it deals with exactly measured quantities. Of late years, a strenuous effort has been made to measure the duration and intensity of psychical process. What are called reactiontime experiments are intended to measure the duration of simple mental operations. "It is agreed between two persons, the 'experimenter' and the 'reactor,' that on the occurrence of a certain sensory stimulus* (given by the experimenter) a certain movement shall be made (by the reactor)."* The time elapsing between the occurrence of the sensory stimulus and the execution of the movement in response to it is accurately measured. The responsive movement may follow at once upon the becoming aware of the effect of the stimulus, or "be restrained until certain connections have been formed in consciousness. In the former case, we speak of a simple, in the latter, of a compound, reaction."§ The simple reaction has two forms, the muscular and the sensory. ''In the muscular,......the reactor is directed to hold his attention from the outset upon the movement which is to be made in response to the stimulus."* In the sensory, "the reactor is directed to hold his attention from the outset upon the sensory stimulus, and to withhold the reaction movement until he has sensed that stimulus."+One result of these experiments is that the muscular reaction occurs in a distinctly shorter time than the sensory. When the attention of the reactor is fixed in preparation for a coming sensation, he waits until he is distinctly aware of the presence of the sensation before reacting. On the other hand, in the muscular reaction, the reactor, being preoccupied with making ready for his own reaction, need not wait till he is fully aware of the presence of the sensation. Hence he becomes with practice able to react before he has any distinct consciousness of it. The stimulus, as soon as it begins to operate, produces simultaneously sensation and reaction. The time taken by the simple reaction varies according to the nature of the stimulus. The sensorial reaction to light lasts about 270 thousandths of a second. A thousandth of a second is symbolised by the Greek letter σ. The muscular reaction to light lasts 180σ. The sensorial reaction to sound lasts 225 σ, and the muscular 120σ. The sensorial reaction to pressure lasts 210σ and the muscular 110σ.

* An Outline of Psychology, p 35

*Such as the sound of a falling body. A sensory stimulus is a stimulus acting on an organ of sense such as the eye or the ear. Op. cit., p. 319.                  § Ibid, p. 320.

Accuracy of measurement is secured by special apparatus. An electric clock or chronoscope, as it is called, marks thousandths of a second. The production of the stimulus sets this clock going. The finger of the reactor all the time rests lightly on the button. The movement he makes by way of reaction consists in a slight pressure on this button, which immediately stops the clock.

Op. cit., p. 325,

+ Ibid., p. 323,

In the compound reaction, various complications are introduced. The reactor may be called on to discriminate between two sensations, reacting only to one of them. Thus he may be told "that he will be shown either black or white, and that he is to react when he has cognised the black as black or the white as white; but he does not know which of the two brightness qualities to expect in each particular experiment."* In this case, he knows that either white or black is to be looked for. The conditions may be further varied, so that he has no definite knowledge of the alternatives which are to be submitted to him, although he is expected to react on one of them, and one only. "Thus he may be told that he will be shown a light stimulus, and that he is to react when he has cognised this stimulus as a particular brightness or a particular colour; but nothing more explicit is said."+

The measurement of the intensity of psychical states is attended by peculiar difficulties, due to the intrinsic nature of the quantity to be measured. The degree of loudness of a sound cannot be broken up into fractional parts which can be marked off from each other. We cannot say by direct comparison of two sounds that one is half, or a quarter, or a third, or twice as loud as the other. The two sounds cannot be superposed so as to make the fainter coincide with part of the louder, leaving a remainder which can be regarded as the quantitative difference between them. In this respect intensive differs from extensive quantity. The difference between two extensive quantities is itself an extensive quantity. The difference between two lines, one a foot long and the other ten inches long, is itself a line two inches long. But the difference between the loudness of two sounds is not itself a sound having a certain assignable loudness. "The difference between two intensive quantities, in fact, differs from each as much as the difference between two horses differs from a horse."*

*B. Russell : "On the Relations of Number and Quantity," Mind, N. S. vi., p. 334.