( s ) 



at continuously increasing distances in the transitionzones between 

 the lastnamed and the two firstnamed. (The law of increase of the 

 distances has been chosen so tliat the proximity of the stripes in the 

 transition zones varies as a linear function). 



3. This phenomenon may be produced even more obviously and 

 in a simpler way by means of revolving discs, as are often used 

 in physiological optics. If we paste a piece of white paper of 

 suitable shape on a black disc and cause the disc to turn very fast 

 in its plane we may get on the surface any distribution of light 

 in which the brightness of tlie observed plane diifers only for points 

 situated at different distances from the centre of rotation and so we 

 may compare it with the corresponding distribution of apparent 

 brightness. We can also photograph tlie discs first in rest, afterwards 

 in rotation, and then the first photograph gives an auxiliary figure, 

 from which the real distribution of light on the figure given by 

 the second photograph may be known. 



Fig. 2, 3 and 4 show (reduced to ± Vr, of their real size) some 

 of the discs used by me ; the outlines of the white parts of thé 

 discs are partly radii pointing towards the centre of rotation, and 

 partly arcs of spirals of Archimedes, for wliich, as is wellknown, 

 the variation of the length of the radius- vector is proportional to 

 that of its angle of rotation; at a rapid rotating of the discs re- 

 presented by these figures we get in accordance with these curved 

 outlines transitionzones in which the apparent brightness varies as 

 a linear function. 



The maxima and minima of brightness on the limits of the tran- 

 sitionzones as mentioned in 1., are clearly seen especially by direct 

 observation of the discs while rotating, but also by examining the 

 photographs taken of them. Fig. 5 and 6 are reproductions of such 

 photographs ; fig. 5, corresponding to fisj. 3, shows pretty clearly 

 the maxima and minima, alluded to above (being circles in this 

 case); fig. 6, corresponding to fig. 4, shows them hardly at all. The 

 reproductions of several of the photographs made by me proved so 

 inadequate that I preferred not to have them inserted here at all ; 

 all those published, without an exception, show tlie phenomena in 

 question far less distinctly than the originals ^). 



4. Now the question arises whether this optical illusion cannot 

 be classed among phenomena already familiar to us. Although I 

 dare not give a definite answer to this question I may be allowed 

 to offer the followina' considerations. 



^) Before tlie assembly Prof. Haga lias demonstrated the plienoiiipua described by 

 me, as well by means of revolving discs as by photographs talken of tliem. 



