316 



E. Sissingh on Kerr's 



amplitudes or phases he attaches more weight to the rotations 

 themselves, and determines fully the changes of sign. More- 

 over, the principal angle of incidence of magnetized iron and 

 the singular angle of incidence are introduced. These hold 

 good, as we have already seen in § 16, only for one particular 

 plane of polarization of the incident light. 



19. The observations recorded in this paper furnish an 

 accurate representation of magnetic reflexion, which, on com- 

 parison with theory, assumes a simple form. In order to 

 demonstrate this clearly, I have given a table of the constant 

 quantities, and the relations between these and the observed 

 quantities, which suffice to fully determine metallic and 

 magnetic reflexion. 



Ordinary Metallic Eeflexion. 



Jamin's Constants : — 



J = Principal Angle of Incidence. 

 H= Principal Azimuth. 



Magnetic Eeflexion. 

 Constants of Equatorial Eeflexion 



= l-5xlO~ 3 ; S=85°*. 



Quantities used in presenting the Theories :— 



<£= Difference of phase between the 

 light polarized parallel and and 

 perpendicular to the plane of inci- 

 dence . 

 /=Amplitude of the reflected com- 

 ponent, polarized parallel to the 

 plane of incidence. 

 A=Amplitude of the reflected com- 

 ponent, polarized perpendicularly 

 to the plane of incidence. 

 Cauchy's Formulas for calculating the 

 ratios of amplitudes and the dif- 

 ferences of phase for an angle of 

 incidence a. : — 



A = Phase of the magnetic component 

 of the light. 



fi — Amplitude of the magnetic com- 

 ponent of the light. 



an $ = sin (r+w) tan \ 2 arc tan 



sin 2 a "1 

 arp COS a J 



cos < 2 arc tan — f 



=cos (t+«) sin { 2 arc tan sm2flS \ 

 I <rp cos a J ' 



Formula for calculating the ampli- 

 tude, the form of which is borrowed 

 from theory : — 



<r 3 sin a _ 

 fX. = fl = — _ 0. 



* PPiPi cos a 



Formula for calculating the difference 



of phase : — 



A = A + S. 

 A =3r-wj- !_2^ 1 -£ 4 -(S 2 -fl 1 ). 



* is the ratio of the observed to the calculated amplitude, and S is the 

 constant difference between the observed and calculated phases. 



