the sensation-series 1 2 3 4 5 corresponds with
a stimulus-series of the type 1 2 4 8 16;
or, mathematically expressed, an arithmetical series of intensities of sensation is correlated with a geometrical series of intensities of stimulus. In the instance given, the exponent of the geometrical series is 2; but that is only an imaginary instance; in the case of noise the actual exponent is 4/3, so that
the sensation-series 1 2 3 4 5 corresponds with
the stimulus series 1 4/3 16/9 64/27 256/81;
or, if we take units of some sort, such as millimetres of height of fall,
the sensation-series 1 2 3 4 5 corresponds with
the stimulus-series 81 108 144 192 256.
This law of correlation was first formulated by the German physiologist E. H. Weber in 1834 as follows: “in comparing objects and observing the distinction between them, we perceive, not the difference between the objects, but the ratio of this difference to the magnitude of the objects compared.” Weber speaks of objects, because he was thinking of experiments that he had made with weights; he should have said sensations. His law holds, over a middle range of intensities of sensation, for lights, sounds, pressures, various kinæsthetic complexes, and odours. Its validity in the fields of taste and temperature is doubtful.
It is because of Weber’s law that we are able to ignore the manifold changes of illumination to which we are exposed in the course of the daylight hours; that the painter, who cannot at all reproduce by his pigments the absolute intensities of light in nature, can nevertheless give us a recognisably true copy of any natural scene; and that a large block of seats in the concert-room, at a moderate distance from the stage, can all be sold at the same price and all have equal advantages for hearing. You will readily find other instances of its working, if you are clear as regards the principle involved; namely, that the less you have of anything, the less need be added, and the more you have, the more must be added, to make an appreciable difference; or, on the negative side, that you are not likely to notice any difference in your surroundings, so long as the relations of the stimuli remain unchanged. So Weber’s law furnishes yet another reason for the apparent stability of the landscape that we discussed on p. 63.