296 Messrs. H. E. Ives and E. F. Kingsbury on the 



This point illustrates the remark made in the introduction, 

 that the cases to be treated in this paper demand definite 

 numerical values which are not in all cases known, and call 

 for simplifying assumptions which are not completely justi- 

 fied. We may state in regard to this quantitative discrepancy 

 between the calculated and observed facts that : 



1. We do not actually know what the value of the Fechner 

 fraction is for successively presented impressions ; it may be 

 much lower than for the cases so far studied experimentally. 



2. Our theoretical treatment is for a simple sine curve 

 stimulus, while the experimental work was done with disks 

 having an abrupt dividing edge. 



3. Any unevenness of the surface of disks such as we 

 used will tend greatly to increase the speed called for at 

 all points except at what is the left-hand end of the diagram 

 shown. This point will be treated in detail under another 

 section. 



Whether these considerations are entirely sufficient to 

 account for the apparent exaggeration of the experimental 

 over the calculated conditions we are unable to determine. 

 However, it is evident that the theory does account extra- 

 ordinarily well for the principal facts regarding the sensi- 

 bilitjr of the flicker photometer. 



Before leaving the question of sensibility we may call 

 attention to an apparent consequence of the theory of some 

 practical importance. It has to do with the character of 

 the transition from one stimulus to the other. Should this 

 be abrupt or gradual ? Referring to fig. 1, it is to be noted 

 that if the transition, which is there considered as gradual, 

 is made abrupt, the limiting critical speeds, where either 

 light is reduced to zero value, will, for fairly obvious reasons, 

 be increased. Since the lower limit of speed is fixed (zero), 

 this means that the no-flicker region will be narrower with 

 the abrupt transition. In short, the sensibility for a given 

 speed should be greater for an abrupt transition than for a 

 gradual ; for instance, it should be greater for a sharp tran- 

 sition flicker-photometer field in focus than for the same 

 field out of focus. We are informed that some recent 

 experimental work confirms this. Where, however, the 

 speed is adjusted to the minimum set by the disappearance 

 of colour flicker, it is probable that the minimum will be so 

 much lower with the gradual transition as to leave the 

 ultimately attained sensibility about the same with either 

 type of transition. 



