320 Professor Airy on a new Analyzer, 



ray polarized in one plane is more retarded than the ray polarized 

 in the plane at right angles to it. The position of these planes 

 however is not defined : that will be best found by observing 

 the dark brushes in the common apparatus. 



To give a mathematical form to the investigation, let us dis- 

 tinguish the two kinds of circularly polarized light by the letters 

 A and B. Suppose that light of the kind A is incident, and that 



its vibration is resolved into + a. sin — — (vt — x) for the ordinary 



ray, and +«.cos — - (vt — x) for the extraordinary. On emerging 



A 



from the crystal they may be represented by + a . sin — - (vt — *) 



2 7T 



for the ordinary ray, and + a. cos — - (vt— x + 0) for the extraordi- 



A 



nary. These will be separated by the analyzer into two pencils 

 of light of the kinds A and B ; these will be represented by 



+ p . sin — - (vt — x + q ) perpendicular to the principal plane 



A 



+ p . cos — - (vt — x + q) parallel to the principal plane 

 A 



and 



2 7T 



+ y.sin — - (vt — x + q) perpendicular to the principal plane 



A 



— p .cos — (vt — x + q) parallel to the principal plane 



constituting 

 light A, 



constituting 

 light B. 



Making the vibrations in each plane equal to those at emergence 

 from the crystal, 



a . sin — (vt — x) = p. sm — - (vt — x + q) + p . sin — - (vt — x + q ) 



\ \ A 



a .cos —~ (vt — x + 0) = p. cos-— (vt — x + q) — p' .cos —(vt — x + q). 



X A. \ 



