200 DOUBLE REFRACTION AND CIRCULAR POLARIZATION 



according as a revolution from p l to p 2 appears clockwise or counter- 

 clockwise to one looking in the direction of the wave-normal. Since 

 p 1 and p z are determined by displacements in planes one-quarter of 

 a wave-length distant from each other, and the plane to which the 

 latter relates lies on the side toward which the wave-normal is drawn, 

 it follows that 9 is positive or negative according as the combination 

 of displacements has the character of a right-handed or a left-handed 

 screw. 



10. The kinetic energy of the medium, which is to be estimated 

 for an instant of no displacement, may be shown as in 7 of the 

 former paper (page 185 of this volume) to consist of two parts, of 

 which one relates to the regular flux ( rj, ), and the other to the 

 irregular flux (', tf, f). The first, in the notation of that paper, is 

 represented by 



J/(Potf+*?Pot 



which reduces to 



By substitution of the values given by equations (1), we obtain for 

 the kinetic energy due to the regular flux in a unit of volume 



. (10) 



11. The kinetic energy of the irregular part of the flux is repre- 

 sented by the volume-integral 



/* (f p ot f + if Pot f + f Pot n dv. 



Now, since ' rf t f are everywhere linear functions of f i\, f and 

 diff. coeff. (see 4), and since the integrations implied in the notation 

 Pot may be confined to a sphere of which the radius is small in 

 comparison with a wave length,* and since within such a sphere r\, f 

 and diff. coeff. are sufficiently determined (in a linear form), by the 

 values of the same twelve quantities at the center of the sphere, it 

 follows that Pot ', Pot if, Pot f must be linear functions of the values 

 of *7, f and diff. coeff. at the point for which the potential is sought. 

 Hence, 



will be a quadratic function of TJ, and diff. coeff. But the 

 seventy-eight coefficients by which this function is expressed will 

 vary with the position of the point considered with respect to the 

 surrounding molecules. 



* See 9 of the former paper, on page 187 of this volume. 





