1281 



more (|iiickly from [»oint lo point. We maj' say that these fluctu- 

 ations are seen on the background formed by the image Z). If really 

 there are radially directed light and dark fibres, these flncfnations 

 must necessarily be caused by the second factor /. Therefore we 

 can conline ourselves to the consideration of the diffraction image 

 of n point-like apertures. 



4. Let P be a point of the focal plane and let the vibrations 

 (monochromatic light) reaching that point from the different apertures 

 be represented by: 



cos {rt -{- ((\), cos {vt -\- rf\) .... cos {vt -\- if^^), 

 where y', , . . . </„ denote the phases and where for the sake of 

 simplicity the amplitude has been put equal to 1. It will be known 

 that we may write for the resulting intensity 



i=zn y^ 2cos{(pa—ipb) (1) 



or 



i=^n -\r 2 inb . . (2) 



The summation has to be taken over all combinations of two 

 apertures. 



Thus it is evident that the intensity can be obtained by superposing 

 many fields viz. by simply adding their intensities. 



The fust field is uniform : n. 



On this there are superposed \n{ii — 1) other fields, each of them 

 belonging to one pair of apertures. 



The intensity of one of these pairs is 



iab^'^COs{(f^a — (f>h) . (3) 



which value varies between -f- 2 and —2. 



The negative intensities in each of the ^ ^M^*^ — 1) "elementary fields" 

 do not cause trouble, as the intensity ii of the uniform field is great 

 enough to neutralize even very many iab^- The expression (1) namely, 

 being derived from 



{E cos (fu,y -f {^ sin (paY 

 can never be negative. 



In each elementary field (3) we have a line-system as has been 

 described in ^ 2. It can be proved that along every line perpendicular 

 to the line connecting the apertures a and h (3) has a constant 

 value. From one line in that direction to the other ^„6 fluctuates. On 

 the line through the centre <fa = To, iab = -f- 2. There are equidistant 

 maximum and minimum lines, iab = 4-2, iab = — 2. 



5. It is interesting lo remark the following: if homogeneous light 



