Light by a Dielectric Cylinder. 



375 



and that marked N' to ('26). A few points have been 

 derived from values not tabulated. From the nature of 

 the functions represented both curves are horizontal at the 

 limits 0° amd 180°. 



When z = '8, the curves show the characteristics of a very 

 thin cylinder. At 90° N' nearly vanishes, indicating that in 

 this direction little light is scattered whose vibrations are 

 perpendicular to the axis. When 5 = 1*2, the maximum 

 polarization is still pretty complete, but the direction in 

 which it occurs is at a smaller angle 0. For 2 = 1'6 the 

 polarization is reversed over most of the range between 45° 

 and 90°. By the time z has risen to 2*4 a good deal of 

 complication enters, at any rate for the curve N. 



In fig. 2 are plotted curves showing the variation with z 

 at given angles of 6 = 0°, 60°, and 90°. At 0° the polariza- 

 tion is all in one direction over the whole range from to 2*4. 



Fiff. 2. 







0° 











60° 



r ~L^ 



S*~ 







**** | 







90° 



1 J 



■4 -8 1-2 J -6 2-0 2-4 



At 60° there are reversals of polarization at £ = 1*5 and 

 2 = 2 - 05. At y0° these reversals occur when z= 1*7 and 

 2 = 2-3. 



The curves stop at 2 = 2*4. It would have been of interest 

 to carry them further, but the calculations would soon 

 become very laborious. As it is, they apply only to visible 

 light dispersed by the very finest fibres, inasmuch as z is 

 the ratio of the circumference of the cylinder to the wave- 

 length of the light. 



When 2, or kc, is greater than 2*4, we may get an idea of 

 the course of events by falling back upon the case where the 

 refractivity (//,— 1) is very small, treated in my 1881 paper. 



