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VII. On the Behaviour of Pleochroitic Crystals along Di- 

 rections in the Neighbourhood of an Optic Axis *. By 

 Professor W. Voigt, of Gottingen], 



1. A LL theories regarding the absorption of light in 

 JOL. crystals agree in recognizing the fact that on account 

 o£ absorption there is added to the characteristic triplet of 

 directed quantities corresponding to each colour in trans- 

 parent crystals a second triplet of' analogous properties. The 

 first triplet may conveniently, though not quite correctly, be 

 regarded as forming the system of the three mutually per- 

 pendicular axes of symmetry for the conservative forces, while 

 the second corresponds to the absorptive forces. To each of 

 these axes there corresponds a certain number, which in trans- 

 parent crystals represents, as is well known, the velocity of 

 all those plane waves for which Fresnel's vibration-vector is 

 parallel to the corresponding axis. If we use the term tensor- 

 triplet, proposed by myself, to denote a system of three two- 

 sided mutually normal directed quantities, then an absorbing 

 crystal will have to be characterized, for a given colour, by 

 two tensor-triplets. These two triplets may be denoted by 

 the symbols a l5 a 2 , a 3 and bi, b 2 , b- B , and we shall suppose that 



ai>a 2 >a 3 and bi>b 2 >b% (1) 



2. It is known that in the case of transparent cry.-tals 

 most characteristic properties correspond to those two direc- 

 tions A : and A 2 which, lying in the plane of the greatest and 

 the least tensors a x and a 3 , make an angle 3 with the latter 

 defined by the equations 



s i n 23=^3 cos^ = ^^ 3 . ... (2) 



a 1 — a s a l — a 3 



These directions are also of special importance in absorbing 

 crystals, and are also called optic axes in this case, although 

 on account of their altered properties they would be more 

 correctly denoted by some other term (e. g. polarization axes). 



Corresponding to the optic axes, we may conveniently 

 consider as absorption axes the directions B l5 B 2 which, lying 

 in the plane of the greatest and least tensors b x and b B , make 

 an angle S with the latter defined by the equations 



sin 2 S = ^4 2 , cos*S=^4 3 . ... (3) 



* A summary of the results contained in a paper presented on Feb. 8, 

 1902, to the Kgl. Gesellschaft der Wissenschaften zu Gdttingen (Gott. 

 Nachr. 1902, Heft 1). 



t Communicated by Lord Kelvin. 



