Glass under the Polariscope. 49 



When the incident light is elliptically polarized, the spots 

 will move round the curves M(0) ; but the rate and appearance 

 will vary (see figs. 3, 4, and 7). For on the circles of M(/o) 

 the major axis of the ellipse preserves a constant direction in 

 space, since (/> + a = ; but on the circles of M(-—/o) the major 

 axis rotates uniformly in space with an angular velocity double 

 that of the radius, since <j> — «=0. Hence in those portions 

 of M(0) which are near the circles of M(/o), the change in the 

 direction of the vibration will be slow ; so that in this part 

 the spot will be elongated, and will move more rapidly than 

 the analyzer is rotated: but in the parts of M(0) near the 

 circles of M(— /o), the change in the direction of the vibra- 

 tion will be rapid ; so that in these parts the spot will be 

 shortened, and will move more slowly than the analyzer is 

 rotated. 



When the" incident light is plane-polarized (see figs. 5 

 and 8), the slow-changing parts of M(0) have combined to 

 form the inner and outer circles of the figure and the diame- 

 ters S S' and T T'. Along these lines the direction of vibra- 

 tion has no change, but remains constantly the same as 

 that of the incident light ; but on the middle circle of the 

 figure, and on corresponding circles, the direction of vibration 

 rotates uniformly with a velocity double that of the radius. 

 Hence on the latter circles there will be spots moving uni- 

 formly round with a velocity double that of the analyzer ; 

 but on the other parts of the figure there will be no spots. 

 However, when the spots on the latter circles reach the 

 diameters, then the former circles and the diameters will 

 become black. 



If the light is not monochromatic, these appearances will 

 not be so distinctly seen, as the absence of one colour will not 

 occur exactly in the same place as the absence of another, 

 since the position of the isomorphal and isoclinal lines de- 

 pends upon the value of c, and this will differ for different 

 colours. But the position of diameters which give plane- 

 polarized light in figs. 5 and 8,. is not dependent on the value 

 of <r ; and hence with any light this cross will always appear 

 uncoloured, being black when the upper and lower Nicols are 

 crossed, and in full light when they are parallel. 



If a is constant, the isomorphals and isoclinals become 

 straight lines from the centre, and the state of the polariza- 

 tion may be conveniently represented by taking a series of 

 points in a circle round the centre, and drawing about each 

 point the ellipse of polarization at that point. The ellipse 

 will show the polarization along the radius on which it lies. 



Phil. Mag. S. 5. Vol. 7. No. 40. Jan. 1879. E 



