Complete form of Fechner's law

Underlying vision, audition, and other sense perception is a fundamental quantitative relation between stimulus and sensation, between the objective and the subjective. From this fundamental relation, once established, may be derived another relation giving the least perceptible increment to the stimulus in terms of the whole. Fechner's law is such a relation derived from experimental data. It states that the least perceptible increment is proportional to the whole stimulus over quite a wide range of moderate intensities. That is, the ratio of least perceptible increment to total stimulus is a constant. This constant experiment shows to be of the order of about two per cent. Now, just at the threshold value of a stimulus, evidently the least perceptible increment is the whole, so that, calling >S this stimulus and SS the least perceptible increment, BS:S=i, while according to Fechner's law SS: S= constant= about 0.02, hence Fechner's law does not and can not hold in this form at low intensities for any sense organ. The general law must be such that BS : S= 1 for S=S ,