Sounds are less delicately discriminated in intensity than lights. A certain difficulty has come from disputes as to the measurement of the objective intensity of the stimulus. Earlier inquiries made the perceptible increase of the stimulus to be about 1/3 of the latter. Merkel's latest results of the method of just perceptible differences make it about 3/10 for that part of the scale of intensities during which Weber's law holds good, which is from 20 to 5000 of M.'s arbitrary unit.[455] Below this the fractional increment must be larger. Above it no measurements were made.
For pressure and muscular sense we have rather divergent results. Weber found by the method of just-perceptible differences that persons could distinguish an increase of weight of 1/40 when the two weights were successively lifted by the same hand. It took a much larger fraction to be discerned when the weights were laid on a hand which rested on the table. He seems to have verified his results for only two pairs of differing weights,[456] and on this founded his 'law.' Experiments in Hering's laboratory on lifting 11 weights, running from 250 to 2750 grams showed that the least perceptible increment varied from 1/21 for 250 grams to 1/114 for 2500. For 2750 it rose to 1/98 again. Merkel's recent and very careful experiments, in which the finger pressed down the beam of a balance counterweighted by from 25 to 8020 grams, showed that between 200 and 2000 grams a constant fractional increase of about 1/13 was felt when there was no movement of the finger, and of about 1/19 when there was movement. Above and below these limits the discriminative power grew less. It was greater when the pressure was upon one square millimeter of surface than when it was upon seven.[457]
Warmth and taste have been made the subject of similar investigations with the result of verifying something like Weber's law. The determination of the unit of stimulus is, however, so hard here that I will give no figures. The results may be found in Wundt's Physiologische Psychologie, 3d Ed. i, 370-2.
The discrimination of lengths by the eye has been found also to obey to a certain extent Weber's law. The figures will all be found in G. E. Müller, op. cit. part ii, chap. x, to which the reader is referred. Professor Jastrow has published some experiments, made by what may be called a modification of the method of equal-appearing differences, on our estimation of the length of sticks, by which it would seem that the estimated intervals and the real ones are directly and not logarithmically proportionate to each other. This resembles Merkel's results by that method for weights, lights, and sounds, and differs from Jastrow's own finding about star-magnitudes.[458]
If we look back over these facts as a whole, we see that it is not any fixed amount added to an impression that makes us notice an increase in the latter, but that the amount depends on how large the impression already is. The amount is expressible as a certain fraction of the entire impression to which it is added; and it is found that the fraction is a well-nigh constant figure throughout an entire region of the scale of intensities of the impression in question. Above and below this region the fraction increases in value. This is Weber's law, which in so far forth expresses an empirical generalization of practical importance, without involving any theory whatever or seeking any absolute measure of the sensations themselves. It is in the
Theoretic Interpretation of Weber's Law
that Fechner's originality exclusively consists, in his assumptions, namely, 1) that the just-perceptible increment is the sensation-unit, and is in all parts of the scale the same (mathematically expressed, Δs= const.); 2) that all our sensations consist of sums of these units; and finally, 3) that the reason why it takes a constant fractional increase of the stimulus to awaken this unit lies in an ultimate law of the connection of mind with matter, whereby the quantities of our feelings are related logarithmically to the quantities of their objects. Fechner seems to find something inscrutably sublime in the existence of an ultimate 'psychophysic' law of this form.