Nevertheless, the attempt to measure intensive magnitude is not so desperate as it appears. Clearly we cannot take one intensive quantity as the unit of measurement of others ; but we may take as unit of measurement the difference or interval between two intensities. Suppose that we are considering, instead of two sounds, two pairs of sounds. Symbolise the one pair by A and B, the other by a and β. We find that we are able to judge whether the difference in loudness between A and Β is or is not equal to the difference in loudness between a and β. Thus, if we have a scale of increasing gradations of intensity, we may take as our point of departure any given intensity in the scale. We can then arrange other intensities in relation to this, proceeding by intervals which we judge to be equal. By counting these equal intervals we can assign a numerical value to any intensity in the scale. The unit which is of most use is the least perceptible difference, viz. that difference between two intensities which makes it just possible for us to be aware that there is a difference at all. All least perceptible differences in the same class of intensities are regarded as equal to each other, because they appear equal when compared.
Instead of measuring psychical process, we may measure its external manifestations or conditions, and we may also measure the objects which are presented by means of it. As an example of the first kind of procedure, we may refer to the measurement of variations in the circulation of the blood, and in the action of the lungs, under varying phases of emotion and pleasant or painful feeling. The measurement of the presented object is of value when it can be brought into definite relation with varying conditions of presentation. The best example is supplied by recent attempts to measure certain geometrical illusions of visual perception. The following is a good illustration. Two lines in reality parallel are each intersected by slanting crosslines, the crosslines of the one being opposed in direction to the crosslines of the other. The parallel lines are then not perceived as parallel, but as diverging in the direction in which the crosslines would meet if produced, and converging in the opposite direction.
Now, to measure the amount of illusion, we have only to substitute for parallel lines lines really convergent in such a manner and degree that they appear parallel under the same conditions. The degree of convergence required for this purpose measures the amount of the illusion. By this means it is possible to trace the variations which take place in the amount of the illusion with variations in the conditions. It is found to varyaccording to the number and obliquity of the crosslines. It exists in a fainter degree when the crosslines merely meet the parallels without intersecting, or when they approach them without meeting. By establishing definite quantitative values for these varying cases valuable data are supplied for discovering the process on which the illusion depends. Actual experiments of this kind of course require a specially contrived apparatus. The lines may be represented by moveable threads, which can be readily adjusted at will so as to be parallel or to deviate from parallelism in varying degrees, the deviation being accurately measured by a scale. In this particular case, the solution of the problem has not been definitely reached, but there is no doubt that the quantitative method has far the best chance of success.