JAMIN ON METALLIC REFLEXION. 



95 



light (m) times at these incidences, the differences of phase will 

 be multiplied by (m), and will become 



0, %, 2 TT, 3 TT, rmr. 



These will therefore be (m+ 1) incidences if 0° and 90° be taken 

 into the account, or (m— 1) between these limits, for which the 

 polarization will be restored, and which we can calculate from 

 the theoretical formulae. We observe further, that there cannot 

 be more of them ; for in order that the polarization may again 

 become plane, it is necessary and it is sufficient that the differ- 

 ence of phase be equal to a multiple of (tt) ; since it varies from 

 to TT between the limiting incidences for a single reflexion, it 

 Mill be comprised between and nnt after (m) reflexions, and 

 between these numbers (m— 1) multiples, only, of (tt) can be 

 found. There will therefore be only (m — 1) angles of restored 

 polarization between 0° and 90°. These theoretical consequences 

 are exactly in accordance with facts, the first point is therefore 

 completely disposed of. 



2nd. It will not be difficult to foresee the direction of the azi- 

 muths of polarization. 



Suppose the vibration of the incident ray to be performed in 

 the direction A D ; it will be decomposed into two vibrations in 

 the two principal planes A B, A C. After (m) reflexions, when 

 the polarization will be restored, the phases of the two compo- 

 nents will differ by a multiple of a semi-undulation ; if this mul- 

 tiple is even, the difference is a whole number of undulations : 

 the vibrations are in the same condition as if it were nothing, 

 they agree as before reflexion, and their resultant will lie in the 



