46 Mr. W. Baily on Starch and Unannealed 



We have already obtained a branch of K(0). Draw from 

 (23) the part of a branch of K(/>) which lies on one side of 

 M(0) between the limits <£ = and = 45°, and from (22) 

 obtain a similar part of a branch of K(±«) — for example, 

 K(15) in fig. 3 and K(30)'in fig. 4. 



Complete these branches by (14). 



Complete the other branches between the same limits by 

 (18). 



Draw the figure between <p = and </>= —45° by (11), and 

 complete the figure by the symmetry about UU' and VV. 



Draw straight lines in the direction UU' and VV to give 

 K(±45), for which the equation is 



sin2<£ = (24) 



To number the isoclinals : — 



Note in (6) that when cr = n7r, tan 2<z= — tan2(/>, ora= — (f>; 

 and when cr=(n + i)'7r, tan 2a=tan 2</>, or #=+<£. Hence 

 the intersections of the isoclinals with the circles of K(p) 

 graduate that circle in the negative direction, and their in- 

 tersections with the circle of K( — p) graduate that circle in 

 the positive direction. Graduate these circles accordingly, 

 taking care to deduct 180° from the graduation when it ex- 

 ceeds 90°, and 360° from it when it exceeds 270°, and the 

 readings will give the values of a. 



The deductions are made to keep the readings low, and for 

 the sake of symmetry. 



From the figures 3 and 4 it appears that M(±p) divides 

 the figure into regions of two kinds : one kind, which I will 

 call the " segments," contains all the points at which the light 

 is more circularly polarized than the incident light ; and the 

 other kind, which I will call the "rings," contains all the 

 points at which the light is more plane-polarized. 



In the segments the isomorphals are closed curves surround- 

 ing the circular points ; and in the rings the isomorphals are 

 closed curves surrounding the centre of the figure. 



It also appears that K(±p) divides the figure into regions 

 of two kinds — one containing all the points at which both 

 the axes of the ellipse are inclined to the radius by a greater 

 angle than p, and the other containing all the points at which 

 one of the axes is inclined at a less angle than p. Both 

 kinds of regions are four-cornered, and have two opposite 

 corners on circular points ; but in the first kind both these 

 circular points lie on the same radius, and in the second the 

 circular points lie on different radii. The isoclinals in each 

 region pass from one circular point to the other. 



