296 R. Sissingh on Kerr's 



The resulting intensity is 



{ -/&« + Hip cos $ + Pi cos m i} 2 +{ H ip sin * + ^ sin 7?i. } 2 . 

 This will be a minimum when fo , $ ip have the values 

 fc $£> gi yen by the following equations : — 



-/*S + Hi P c °s <& + /** cos m. = 0, 



(1) 

 Hr p -f<l>ia™s® + f*i cos (*-m.) = 0, J 



These equations can also be determined by a geometrical 

 construction for the resultant amplitude of the waves which 

 traverse the analyser. 



If the incident ray is polarized perpendicularly to the plane 

 of incidence, we obtain in the same manner : — 



-f4? P + Hia cos ® + Pi cos n h = °> 1 , 2) 



Hi -fh cos ^ + ^ cos (* - m i) = °>} 



In the above deduction quantities of the order (<f> ip ) 2 , A 6 ^^? 

 &c. are neglected, because the rotations <f> are only a few 

 minutes of angle, and /j, is less than 0*001*. 



4. If, on reversal of the magnetization, the amplitude /jl of 

 the magnetic component of the light also changes its sign 

 without any alteration of the phase m, it follows from the 

 formulae (1) and (2) that the minimum positions of the Nicol 

 prisms are only symmetrical with respect to the plane of 

 incidence and a plane perpendicular to it, in case the 

 incident or reflected ray is polarized in one of these planes. 

 (j) i} , <£. a , <f>. , cj) lu must be equal to zero. If we call the 

 angles between the minimum positions of the Nicol prisms for 

 positive and negative magnetization -fyf &c, it follows from 

 (1) and (2), with the above assumption : — 



1 sin<P/-v/r™ l 2cosm. 



tan m,= — cot <P— - — -=- -— : — ; /*.,= + ~- ' 

 1 sin <J>/^™ ' ^ 2cosw?, 



f. (3) 



J 



* cj)ip, <j)ia, 4>i P , 4>ia indicate the small angles between the plane of 

 polarization of the Nicol prisms and the plane of incidence or a plane at 

 right angles to it. The indices i and / mean that the incident light 

 is polarized nearly parallel or normal to the plane of incidence. The 

 analyser is set in a plane nearly perpendicular to the plane of incidence. 



