368 Mr. H. E. Ives on a 



If for one of the brightness ratios is taken that of light 

 against darkness the corresponding logarithmic term drops 

 out, being zero. Measurements of the critical speeds for 

 the ratios 1 : and '34 : '66 were made by the writer on 

 several different occasions during the work, each consisting 

 of four to six alternated series of ten settings each, from 

 which the following values of log $ were found : — 



log 3= -3-0 

 -4*2 

 -3*7 

 -4*2 

 -5-0 



These figures, all obtained for the same mean brightness, 

 show that 8 varies over quite wide limits, for these variations 

 represent rather bigger differences in the critical speed 

 ratios than can be ascribed to the lack of precision of the 

 determinations, considerable though this is. There is clear 

 indication of a progressive decrease in S during the progress 

 of the work. 



In order to secure additional light on this point, similar 

 measurements were secured from other observers who had 

 not been working with the apparatus. 



Their results are as follows : — 



log 8= -4-2 (E. K.) 



-30 (E. F. K.)\ , 1 



-3-2 (E. F. k.) J sev }S ap ' 



-3 2 (E.R.M.') 



indicating that the fraction varies from individual to indi- 

 vidual, as well as from time to time with any one observer. 

 The mean value of all these determinations is 



log 8 = -3-74 or 8 = '00018. 



Remembering that the Fechner fraction, as ordinarily 

 understood and determined for juxtaposed fields, is of the 

 order of magnitude of 1 per cent., this value of S appears 

 extraordinarily low. It is well known, however, that the 

 greatest sensibility to small brightness difference is obtained 

 when the compared fields are most closely juxtaposed, but 

 even then the comparison must be made between impres- 

 sions received by different retinal elements. In the case of 

 successive impressions the comparison is made of impres- 

 sions on the same element, and there is nothing inherently 

 improbable in the sensibility to such impressions being higher 

 than the greatest sensibility attainable by juxtaposition. It 



