BISHOP'S RING AROUND THE SUN. 



469 



the thread will be just opposed at B, the crest of one will fall with the 

 trough of the other ; they are thus extinguished by interference, and 

 darkness will result. Take another point, D, on the screen, such that 

 D H differs from D T by a whole wave-length. Now the diffracted 

 waves will agree in phase at D, and this point will be illuminated, 

 like A. The screen will therefore be marked by a bright band behind 

 the thread, and by dark and bright bands, blending together and par- 

 allel to it on either side. Their breadth will vary directly as the wave- 

 length, and inversely as the diameter of the thread. The redder the 

 ray and the finer the thread, the broader the bands. 



Next consider the case of a single small particle of diameter greater 

 than the wave-length in the path of the monochromatic beam. The 

 same figure now may represent a plane parallel to the rays, passing 

 through the particle in any direction. The parallel bands become con- 

 centric rings with a bright central spot behind the particle. The 

 diameter of the rings varies, as above stated for the bands. The bluer 

 the light and the larger the particle, the narrower the rings. 



The next step makes an approach to the actual case by supposing 

 a great number of one-sized particles floating in the space traversed 

 by the waves, and considers their effect as perceived by an observer at 

 A (Fig. 2). The unaltered light is seen in the direction of the rays 



FiQ. 2. 



A R. Interference of the waves diffracted from B causes a dark cir- 

 cle on the surface V T, of diameter A H ; from C, a circle A J ; from 

 D, a circle A N. Hence all the particles situated on the surface of a 

 cone whose axis is A R, and apical angle is F A G, give no light to A, 

 and the luminous center R seems to be surrounded by a dark ring at 

 an angular distance RAF. This may be called a subjective ring in 



