106 Professor Airy on the 



general expression) that the light is least when 



a „ a 



= 45° -5, 135"--, &c 



This shews that, with this value of a, the spot will be a darkish cross, its 

 arms in positions 



45 - |, 135° -J, &c. 



But these are exactly the angles at which the depression of the ring below 

 a circle is a minimum, or at which the points of the square are found. 

 Therefore, we may expect to find a cross-like spot in the center, its arms 

 in the diagonals of the square. This corresponds perfectly with the phe- 

 nomena. 



4. The succession of colours in the cross-like spot, it is easily seen, 

 depends only on this circumstance: that as \ is greater for red than for 

 blue rays, the value of a which allows no red rays to pass is less than that 

 which allows no blue rays to pass. That is, for a certain small value of a, 

 there are rays of the blue and only of the spectrum transmitted : for a 

 larger value, the rays only of the red end are transmitted. 



5. If the polarizing and analyzing plates are parallel, or a = 0. the 

 expression for the brightness becomes 





cos 5 2 0} sin 2 — . 



A 



It is easily seen that this indicates a series of rings, but there is now no 

 total darkness. When 



= 0,= 90°, = 180°, = 270°, 

 the expression is 



