42 Mr. W. Baily on Starch and Unannealed 



p = 45° and <7 = in (5), we get r 2 -j-=l. But in this case 



the emerging light is circularly polarized, and consequently 

 /3=45°, whence sin 2/3 also equals unity. Hence in every 

 case 



2 dd . ap> 



Hence dt ~~ 



sin 2/9 cos 2 cr— cos 2p sin 2 cr sin 20— sin 2/3 = 0. . (7) 



The locus of points at which the major axis of the ellipse of 

 polarization is inclined at a constant angle to the radius HP 

 will be called an " isoclinal line," and will be denoted by the 

 symbol K(a), where a is this angle. K(a) and K(a — 90°) 

 are both included in the equation (6), as that equation does 

 not distinguish between major and minor axes. 



The locus of points at which the line joining the extremities 

 of the axes makes a constant angle with the major axis will be 

 called an " isomorphal line/' and will be denoted by the sym- 

 bol M(/3), where /3 is this angle. Equation (7) is the equation 

 to M(/3). 



The direction of rotation of the sether is positive or negative 

 according as sin 2/3 is positive or negative — that is, according 

 as /3 is positive or negative, since we need only give /3 values 

 lying between ±45°. 



In figs. 2, 3, 4, 5 these loci are represented — the isomor- 

 phals by continuous lines, and the isoclinals by dotted lines. 

 The Arabic numerals indicate the values of a in degrees, and 

 the Roman numerals those of (3 in degrees. 



The value given to a is RP + 90°, a function which has been 

 assumed solely for convenience in drawing the figures. The 

 figures are drawn between the limits o-=180° and a- = 360°. 

 An extension beyond these limits would give merely a repeti- 

 tion of the portion within them, since an addition of 180° to 

 the value of <r makes no difference in the equations to the loci. 

 Directions from the centres of these figures will be referred to 

 by means of the lines in fig. 1. 



The values of p are in fig. 2, 45°, in fig. 3, 30°, in fig. 4, 

 15°, and in fig. 5, zero. Accordingly the incident light is 

 circularly polarized in fig. 2, elliptically in figs. 3 and 4 (the 

 eccentricity of the ellipse being less in fig. 3 than in fig. 4), 

 and plane-polarized in fig. 5. 



The isomorphals and isoclinals drawn are those for which 

 the values of a and /3 are 45°, 30°, 15°, and zero. The thick 

 continuous lines are branches of M(0), which is the locus of 

 plane- polarized light. The round spots are loci of circularly 

 polarized light, or M(±45). 



