Magneto-optic Phenomenon. 267 



of penetration *) is different for the two circular rays. Ac- 

 cordingly it is easily seen that the difference of optical path, 

 and therefore the difference of phase, may have the opposite 

 sign for reflexion or transmission respectively. In fact it is 

 only necessary that the swifter circular ray penetrate so much 

 deeper than the slower one, that the acceleration of phase, 

 which it would otherwise acquire, be thereby changed into a 

 retardation behind the phase of the slower ray. 



Generally speaking it is therefore possible that the rotations 

 on reflexion or transmission respectively have the same or 

 opposite signs. The former might even have different signs 

 according to wave-length, and vanish for particular values of 

 X. Experiment seems to point to a case of this kind with 

 magnetite (§ 22). The curves of dispersion for reflexion and 

 transmission of course need not show any analogy ; in any 

 particular case this depends upon the properties of the sub- 

 stance. The above considerations were hinted at by Voigt f , 

 though in a different form ; but they are not limited to any 

 particular optical theory, whether electric or elastic. They 

 are of a purely kinematical nature ; the hypothesis of circular 

 birefraction and " biabsorption/' on which they are based, 

 must, however, be retained. 



The contents of this paragraph have therefore to be con- 

 sidered apart from all that precedes ; with this sole exception 

 I have striven to cling to experiment and its immediate con- 

 sequences, free from any additional assumption. In conclusion, 

 I beg to tender my best thanks to Prof. F. Kohlrausch, in 

 whose laboratory these experiments were carried out. 



Phys. Inst, of Strasburg Univ., 

 Oct. 20, 1889. 



* The most general assumption is that part of each circular ray is re- 

 flected in the surface itself. The rest then penetrates into the metal, and 

 every elementary sheet of its substance again reflects a " circular element," 

 with amplitude the less, the greater the depth at which reflexion ensues. 

 The reflected pencil now consists of one circular vibration and an infinity 

 of circular elements vibrating in the same sense. Kinematic integration 

 gives a single circular vibration in this sense. This consideration, there- 

 fore, leads to the same result as the assumption, made above, of direct 

 penetration of the pencil as a whole, and subsequent reflexion at a defi- 

 nite depth. The two resulting opposite circular vibrations now possess 

 difference of phase, thence rotation, and slight difference of amplitude, 

 thence slight ellipticity in the reflected ray. (Compare the geometrical 

 method of circular elements by Dr. Wiener, Wied. Ann. xxxv. pp. 3-5, 

 1888.) J ™ ' 



t Voigt, Wied. Ann. xxiii. p. 508 (1884). 



X2 



