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on the diffraction image (vspot and ring) of one single aperture. 

 With tliree apertures which form an arbitrary triangle, we observe 

 three systems of lines A, respectively perpendicular to the sides of 

 this triangle. They cross each other in the neighbourhood of the 

 centre (). 



With four or more apertures a similar phenomenon is observed 

 and so on. 



We get the impression that always line-systems, each perpendicular 

 to a line connecting two apertures (of which systems the number 

 always increases with the number of apertures) cross each other 

 near the centre. This would be the reason why near the centre 

 no pronounced lines are observed and instead of these a sunflower- 

 like structure. But at a greater distance from the centi'e the line- 

 systems must diverge. This suggested to me the conception that these 

 are tiie tibres of the phenomenon of Lauk. Working with 50 aper- 

 tures, the diffraction image has already quite the same aspect as 

 for a glass-plate covered with lycopodium ; the only difference is, 

 that in the first case the fibrous structure is coarser than in the 

 second. With a small number of apertures even when they are 

 distributed in an "accidental" way. it is however possible that among 

 all lines of connexion some directions are more represented than 

 others. 



3. This conception may be elucidated by a simple mathematical 

 consideration. 



Before the objective of a telescope focussed on a light-source at 

 an infinite distance a screen has been placed over which a great 

 number 7i of equal circulai- a[)ertures is distributed. The screen is 

 placed |)erpeiidicular to the axis of the telescope. Let 7^^ be the 

 principal focus of the objective, and let us consider the distribution 

 of the light in the focal plane F passing through F. According to 

 a well-known theorem of the diffraction theory the intensity at a- 

 point P of the plane can be represented by the product of two 

 factors. The fii'St of these is the intensity that would be due to one 

 single aperture, while the second is the intensity i that would 

 be observed if instead of the given apertures we had at their 

 centres ii equal apertures so small, that they might be considered 

 as points. Both factors are functions of the position of P in V. 

 The first determines the intensity in the diffraction image B of 

 one single aperture, where the intensity changes relatively slowly 

 from point to point. Into this diffraction image B the factor intro- 

 duces irregular fluctuations, by which the intensity changes much 



