ON SMALL DIFFERENCES OF SENSATION. 



JtEA r> nCTORElt 17, 1884. 



By C S. Prtrce and J. JASTRfiW. 



The physiological psychologists assunie that two nerve excitations alike in quality will only 

 ])ro(luce distinguishable sensations provi<le(l they differ in intensity by an amount greater tiian a 

 lixe<l ratio. Tlie least pereejitible dift'ereu'ce of the excitations divided by half their sum is what 

 they call the UnterschiedsHchwelle. Fechner* gives an experiment to prove the fact assumed, 

 namely: He finds that two very dim liglits placed nearly in line with the edge of an opaque body 

 show but one shadow of the edge. It will be found, however, that this phenomenon is not a clearly 

 marked one, unless the lights are nearly in range. If the experiment is performed with lateral 

 .shifting of one of the lights, and with a knowledge of the effects of a telescope upon the appear- 

 ance of terrestrial objects at uight, it will be found very far from conclusive. 



The conception of the psychologists is certainly a difficult one to seize. According to their 

 own doctrine, in which the observed facts seem fully to bear them out, the intensity of the sensa- 

 tion increases continuously witli the excitation, so that the least increase of the latter must pro- 

 duce a corresponding increase of the former. And, indeed, the hypothesis that a continuous in- 

 crease of the excitation would be accompanied by successive discrete increments of the sensation, 

 gratuitous as it would be, would not be sufficient to account for a constant Unterschiedsschwelle. 

 We are therefore forced to conclude that if there be such a phenomenon it has its origin, not in 

 the faculty of sensation, but in that of comparing sensations. In short, if the phenomenon were 

 established, we should be forced to say that there was a least perceptible dift'erence of .sensation — 

 a difference which, though existing in sensation, could not be brought into consciousness by any 

 eftbrt of attention. But the errors of our judgments in comparing our sensations seem sufficiently 

 accounted for by the slow and doubtless complicated process by which the impression is conveyed 

 from the periphery to the brain ; for this must be liable to more or less accidental derangement at 

 every step of its progress. Accordingly we find that the frequencies of errors of different magui- 

 fudes follow the probability curve, which is the law of an effect brought about by the sum of an 

 infinite number of infinitesimal causes. This theory, however, does not a<lmit of an Unterschieds- 

 schirdlt. On the contrary, if leads to the method of least squares, according to which the multipli- 

 cation of observations will indefinitely reduce the error of their mean, so that if of two excitations 

 one were ever so little the more intense, in the long run it would be judged to be the more intense 

 the majority of times. It is true that the astronomers themselves have not usually supposed that 

 this would be the case, because (apart from coustaut errors, which have uo relevancy to the pres- 

 ent question) they have supposed this extreme result to be contrary to common sense. But it has 

 .seemed to us that the most satisfactory course would be to subject the tpiesfiou to the test of direct 

 ex])eriment. If there be a least perceptible difference, then when two excitations differing by less 

 than this are presented to us, and we are asked to judge which is the greater, we ought to answer 

 wrong as often as right in the long run. Whereas, if the theory of least squares is correct, we uot 



' Elemente der Psychopliysik, I, p. 242. 



