334 Mr. W. Spottiswoode on the Rings produced by [May 2, 



In all these cases the light falling on the analyzer is plane polarized ; and 

 the following Table will give the angle through which the plane of polari- 

 zation has been turned in its passage through the system Q, C, Q x . 



Case/ 



Angle between 

 plane of polari- 

 zation and princi- 

 pal plane of A. 



Angle between 

 principal planes 

 of P and A. 



Sum = angle through 

 which plane of po- 

 larization is turned. 



I. 

 II. 

 III. 

 IV. 



TT . . e 



2 1 J ~ 2 



. . 



i — i 



J 2 





 2 



it __e 



2 2 



7T . . . 



a + b 







7T — - 



2 



- + a-f b-\- - 

 2 2 



- + a + b — - 

 2 2 



Cases I. and II. represent Fresnel's experiments, cases III. and IV. Airy's. 

 In all four the rotation depends upon 0, that is, upon the wave-length ; 

 and consequently if the analyzer be turned round, we shall have a succes- 

 sion of colours which recur after every 1 80°. Thus far the effects will re- 

 semble those produced by quartz, excepting that the tints will not be 

 exactly the same ; because in these cases the rotation of the plane of po- 

 larization is approximately proportional to \~\ while in that of quartz it is 

 proportional to X~ 2 . It may be noticed that if I., II., IV. represent a right- 

 handed, III. will represent a left-handed quartz. 



The result in case I., being independent of i and j, shows that if the 

 system of plates Q, C, Q x be turned round bodily in its own plane there 

 will be no change in the phenomena produced. 



The result incase II. shows that if the system of plates be turned bodily 

 in its own plane, we have a sequence of colours the reverse of those pro- 

 duced when the analyzer is turned round, and returning at every 90° instead 

 of every 180°. 



The results in cases III. and IV., being independent of the separate 

 values of a and b, but depending only upon the sum a + b, show that if 

 the system P, Q, Q„ A remain fixed, and the crystal C be turned in its 

 own plane, the phenomena will undergo no change. 



If the experiments be made with convergent light, two general results 

 are manifest : first, that rings are formed as with plane-polarized light, but 

 better defined, because in the absence of any constant term in the value of I 2 

 the minima values are absolutely zero ; and secondly, that no dark brushes 

 will exist. 



If we now consider the rings produced with convergent light and the 

 system Q, C, Q x , in which the axes of Q, Qj are crossed, and the axis of 



