( 11 ) 



6. To return to the explanation of the optical illusion described 

 above, it seems not impossible to me that we should have to look for 

 it in the influences by contrast as mentioned in 4., starting for instance 

 from the hypothesis that each element of the field in general in- 

 fluences the observed briglitness of any definite element under 

 consideration, an influence depending in a definite way on the 

 distance between the two elements and on the brightness both of 

 the „inducing" and the „reacting" element. But then we are not 

 allowed, as we might be inclined to do at first sight, to assume that 

 this influence increases as continually the distance between the inducing 

 and the reacting element diminishes and as the difterence in bright- 

 ness between these two elements increases. For the peculiarity of 

 the appearing of the lines mentioned in 5. sub 2". would be 

 incompatible with an influence acting in this manner. Moreover 

 Lehmann's ^) investigations have already brought to light that the 

 influence by contrast reaches its maximum at a definite value of 

 the proportion between the brightness of the inducing and the 

 reacting field. If we may as seems quite natural apply this law to 

 the contrast between any two elements of the field and if at the 

 same time further investigations might prove this „critical" propor- 

 tion between inducing and reacting brightness to decrease as the 

 distance between these two elements diminishes, it may be con- 

 ceived that the optical illusion we have described and the ordi- 

 nary effects of contrast will be found to obey the same laws. 

 Accurate investigations will however be required^), especially con- 

 cerning the influence of the distance between two contrasting fields 

 on the amount of the influence, before we can arrive at exactly 

 formulating these laws. 



7. Among the methods which may be used to produce the optical 

 illusion described I may still mention a very simple one: we send 

 a beam of light through a not too narrow slit, so that it falls on a 

 second slit parallel with the first, and receive the beam on a screen. 

 If the second slit is tcider than the first, a middle zone on the 

 screen will be illuminated by all the elements of the first slit; on 

 either side this middle zone transition-zones will be found illuminated 

 by continuously decreasing parts of the first slit, and these zones will 

 pass into other zones not at all illuminated by light through the slit. 



1) Lehman 1. c. S. 525. 



^) KiRSCHMANN announces in his treatise alhided to above the puljlioation of his 

 investigations already partly made on this influence of distance; but tjie ])ub]ication 

 seems not to have taken place yet. 



