JAMIN ON METALLIC REFLEXION. 93 



of an undulation, and he placed the principal section of this plate 

 in a direction (w) which restores the rectilinear polarization. It 

 is hence clear that the experiment amounts to this : — 



The ray elliptically polarized by the metal decomposes itself 

 into two beams polarized in planes parallel and perpendicular to 

 the principal section of the thin plate ; the calculation of the in- 

 tensities and of the phases of these rays has already been pre- 

 viously effected ; the difference of route is expressed by the for- 

 mula 



tan (8' - 8") = ^. ^^" 8 sin 2 a ^ ^ 



' sin 2 CO cos 2 « — sin 2 a cos 2 m cos 8 * ' ^ 



In traversing the thin plate, these two rays acquire, in conse- 

 quence of the thickness traversed, a new difference of phase equal 

 to a quarter of an undulation, or to 90°, which is added to the 

 former, or subtracted from it. Now, in order that the polariza- 

 tion may be restored, it is necessary that the sum obtained should 

 equal 0° or 180°, which cannot take place unless (8' — 8") is 

 itself equal to + 90° ; this determination amounts then to the 

 investigation of a direction for which the two rectangular rays 

 into which the ellipse resolves itself, have a difference of route 

 equal to a quarter of an undulation ; this direction is that of one 

 of the axes of the ellipse ; it is obtained by putting 



tan (8'— 8") = oo , whence tan 2 w= tan 2 « cos 8. 



To obtain the intensities of the rectangular rays in the direc- 

 tion which M'e have found, it will suffice to calculate A'^ and B'^ 

 in the formulae (13.), replacing (w) by its value, and these inten- 

 sities will be proportional to the lengths of the axes. 



In the experiments of M. de Senarmont, the difference of 

 phase being reduced to zero and the polarization being restored 

 by the superposition of two rectangular rays whose intensities 

 are A'^ and B'^, the azimuth of restored polarization is given by 

 the formula 



Thus the experiments of M. de Senarmont measure two azi- 

 muths : — 



1st. The azimuth of the principal section of the plate of mica, 

 that is the direction of one of the axes of the ellipse : 



2nd. The azimuth of restored polarization, and the tangent of 

 this angle expresses the ratio of the lengths of the axes of the 

 ellipse of oscillation. 



