376 Dispersal of Light by a Dielectric Cylinder, 



In our present notation the light dispersed in direction 6 

 depends upon 



TZ&W™?* (29) 



When # = 180°, i.e. in the direction of primary propa- 

 gation, 



J x (2^cos^) = zcos^O, 



and (29) reduces to ire?. In this direction every element o£ 

 the obstacle acts alike, and the dispersed light is a maximum. 

 In leaving this direction the dispersed light first vanishes 

 when 



cosi<9 = 3-8317/22, 



and afterwards when 



2z cos \e = 7-0156, 10-173, 13-324, &c. 



The factor (29) is applicable, whether the primary vibra- 

 tions be parallel or perpendicular to the axis of the cylinder. 

 The remaining factors may be deduced by comparison with 

 the case of an infinitely small cylinder. Thus for vibrations 

 parallel to the axis, we obtain from (6) 



+=(■*)*#«-»> x ( * W * c)Jl i ?* c C0S **> , . (30) 

 T \2ikrJ cos^0 



applicable however large c may be, provided (k' — k) be 

 small enough. 



In like manner for vibrations perpendicular to the axis 

 we get from (9) 



/ 7T \* ci(nt _ kr) x (kc - k' c) cos 0. J 1 (2kc cos JO) ^ n) 

 ^ \2ikr) cos \Q "> \ ) 



vanishing when 0=90°, whatever may be the value of Ice. 

 It will be seen that (30) and (31) differ only by the factor 

 — cos 6, and that this is unity in the direction of the 

 primary light. 



