5. Thus, the relating function is brought into activity through associations, wherever they themselves or their products are made the objects of voluntary observation. This function is always connected, as the examples mentioned show, with the function of comparing, so that the two must be regarded as interdependent partial functions. Every act of relating includes a comparison of the related psychical contents, and a comparison is, in turn, possible only through the relating of the contents compared with one another. The only difference is that in many cases the comparison is completely subordinated to the end of reciprocally relating the contents, while in others it is in itself the end. We speak of a process of relating in the strict sense in the first case, and of a process of comparing in the second. I call it relating when I think of a present impression as the reason for remembering an earlier experience; I call it comparing, on the other hand, when I establish certain definite points of agreement or difference between the earlier and the present event.
6. The process of comparing is, in turn, made up of two elementary functions which are as a rule intimately interconnected: of the perception of agreements on the one hand, [p. 252] and of differences on the other. The erroneous view still frequent acceptance that the existence of psychical elements and compounds is the same as their apperceptive comparison. The two are to be held completely apart. Of course, there must be agreements and differences in our psychical processes themselves, or we could not perceive them; still the comparing activity by which we perceive, is different from the agreements and differences themselves and additional to them.
7. Psychical elements, the sensations and simple feelings, are compared in regard to their agreements and differences and thus brought into definite systems, each of which contain such elements as are closely related. Within such a system, especially a sensational system, two kinds of comparison are possible: that in respect to quality, and that in respect to intensity. Then, too, a comparison between grades of clearness is possible when attention is paid to the way in which the elements appear in consciousness. In the same way comparison is applied to intensive and extensive psychical compounds. Every psychical element and every psychical compound, in so far as it is a member of a regular graded system, constitutes a psychical quantity. A determination of the value of such a quantity is possible only through its comparison with some other quantity of the same system. Quantity is, accordingly, an original attribute of every psychical element and compound. It is of various kinds, as intensity, quality, extensive (spacial and temporal) value, and, when the different states of consciousness are considered, clearness. But the determination of quantity can be effected only through the apperceptive function of comparison.
8 . Psychical measurement differs from physical measurement in the fact that the latter may be carried out in acts of comparison separated almost indefinitely in time, because its objects are relatively constant. For example, [p. 253] we can determine the height of a certain mountain to-day with a barometer and then after a long time the height of another mountain and if no sensible changes in the configuration of the land have taken place in the interval, we can compare the results of our two measurements. Psychical compounds, on the other hand, are not relatively permanent objects, but continually changing processes, so that we can compare two such psychical quantities only under the condition that they axe presented in immediate succession. This condition has as its immediate corollaries: first, that there is no absolute standard for the comparison of psychical quantities, but every such comparison stands by itself and is of merely relative value; secondly, that finer comparisons are possible only between quantities of the same dimension, so that a transfer analogous to that by which the most widely separate physical quantities, such as periods of time and physical forces, are reduced to spacial quantities of one dimension, are out of the question in psychical comparisons.
9. It follows that not every relation between psychical quantities can be established by direct comparison, but this is possible only for certain particularly favorable relations. These favorable cases are 1) the equality between two psychical quantities, and 2) the just noticeable difference between two such quantities, as, for example, two sensational intensities of like quality, or two qualities of like intensity belonging to the same dimension. As a somewhat more complex case which still lies within the limits of immediate comparison we have 3) the equality of two differences between quantities especially when these quantities belong to contiguous parts of the same system. It is obvious that in each of these three kinds of psychical measurements the two fundamental functions in apperceptive comparison, the perception of agreements and of differences, are both applied together. In the [p.
254] first case the second of two psychical quantities A and B is gradually varied until it agrees for immediate comparison with A. In the second case A and B are taken equal at first and then B is changed until it appears either just noticeably greater or just noticeably smaller than A . Finally, the third case is used to the greatest advantage when a whole line of psychical quantities, as, for example, of sensational intensifies, extending from A as a lower to C as an upper limit, is so divided by a middle quantity B, which has been found by gradual variations, that the partial distance AB is apperceived as equal to BC.