( 10 ) 



tions, which might still exist, seem to fall within the limits of 

 probable error in the determination of the place of those lines. 



2". If we examine successively several drawings in which a tran- 

 eitionzone occurs and which differ only in this regard that the 

 transitionzone gels narrower and narrower, we see the bright and 

 the black line growing finer and finer without there being any conti- 

 nuous increase in their distinctness ; on the contrary the distinctness 

 diminishes when the iransitionzones are very narrow and it seems 

 as if the narrowing transitionzone were a zone of almost constant 

 brightness, with sharply defined limits towards the other zones. 

 (Besides it seems to me that there is a general tendency to take 

 the middle part of a transitionzone in the above sense, for a zone 

 of uniform intermediate illumination). This gradual fading away 

 of the lines at a narrowing of the transitionzone may easily be 

 seen by slightly extending (for instance V2 cM.) the opening in 

 the middle of the rotating disc (fig. lb), by means of which the 

 disc is mounted on the axis, in the direction of one of the radial 

 borders ot the white paper and then causing the disc to rotate, it 

 being mounted on the axis first as excentrically as possible after- 

 wards with gradually decreasing excentricity. Indeed we get in this 

 way a gradual narrowing transitionzone and at the same time the 

 experiment shows very clearly the just mentioned fading away of 

 the lines. 



3^. Not only do the two lines appear when in the transition- 

 zone the brightness varies in a direction perpendicular to the border 

 of the zone with constant gradient, but also under quite diffe- 

 rent laws of intensity-variation as may be gathered from the 

 fact that also the photographs of the rotating discs show the lines 

 clearly; they are very prominent for instance when this gradient 

 is infinite on the brighter border and becomes finite and diminishes 

 gradually towards the other border, where it attains a minimum 

 differing from zero. 



40. The lines can also be very conspicuous when the gradient 

 continuously approaches zero on the borders of the transitionzone. 



5". Lastly the lines appear in some cases even where the zones 

 of equal brightness on either side the transitionzone are replaced 

 by zones of which the brightness gradually decreases (resp. increases) 

 towards the transitionzone. It may easily be stated by means of 

 a rotating disc that the brightness between the two transitionzones 

 still may appear to have two maxima as in fig. 5, two minima as 

 in fig. 6 the real brightness having even a faint maximum, resp. a 

 faint minimum, in the middle tietween the two transitionzones. 



