56 Mr. H. R. Hasse on the Equations of 



in to, and it is interesting to note that it is the specific 

 inductive capacity perpendicular to the direction of motion 

 of the medium which enters into the equation. 



To find an expression for the angle of rotation from (19),. 

 we have 2ir 



where t is the period of vibration, and is the same for both 

 rays, whence we can easily show that the angle of rotation 

 per unit length of the medium is 



Yj and V 2 being the velocities of the two waves *. 



Substituting for s its value ^-, and writing J for £' 



L for — — — , then the equation (19) becomes a quadratic 



. 1 . 

 in y, viz., 



1 2iv—J 

 ~2ys _ — y {K + e 2 ivJ + Le- \ =0, 



so that 



^=e{2ic-^)+{e\2w- J)* + 4(K + eW + Le*)}*, 



the two different wave-velocities being obtained by giving 

 positive and negative values to J and L. 



Taking the case of a structural rotation alone L = 0, and 

 we have 



^y = e(2w - J) + { 4feV + 4K + JV p, 



(vrvi)= 2 ^ 



~ir =e(2io + J) + {4w 2 € 2 + 4K + JV 



€V 2 



therefore 



2 f 



€ 



and the rotation 6 is 



there being no need to consider the constant JY as smalL 

 * Lorentz, Proc. Eov. Acad. Sci. Amsterdam, 1901-02. 



