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



In order to include in the constitutive relations for matter 

 at rest the phenomena of structural rotation and rotation 

 due to an external magnetic field, the first equation in (3) 

 must be modified by the addition of terms containing 

 differential coefficients of the first order of the electric 

 force E 1# Let us consider the case of a crystalline medium, 

 and let the axes of coordinates coincide with what would be 

 the axes of optical symmetry of the crystal if it were not 

 optically active, then we have for matter at rest * 



Di=K 1 B 1 +[L b ^] + [J 1 V 1 ,B 1 ]. . . . (16) 



where K 1? J l5 and Li are vector constants, the latter being- 

 proportional to the external magnetic field, while J x is the 

 coefficient of structural rotation. Kt is not necessarily 

 the specific inductive capacity, as this may be altered when 

 the external magnetic field is put on, though only to the 

 second order f. Vi is the vector operator 



B.t-i' a yi ' a*!- 



so that the last term in the above expression is a vector 

 whose components are 



Ji ^ Bl <" Ji *^ Ei *' ' 



We must first of all express the quantities D 1 and E x in 

 terms of D, E, and H by means of the equations (5), which 

 for case (B) above may be written in the form 



B = {l,e, e }{E 1 -[ w , BJ}, 1 



B=H = {l, e ,e}{B 1 + [,r,B 1 ]}, 

 D={l, e ,6}{D 1 -[«,,H ] ]} ) 

 H_ [D-E, w] = {l, e, e}{H I + [«, D,]}. 



Solving for E x and D 2 we find 



B 1 -.{l,«,«}{B-[«,H]} = {l,.,€}B', 

 D 1= {1, 6, «}{D-E[«, H]+[«, [D-E, «,]]<■ 

 = {l, e, e}{D-E-[>, [w, D-E]] + E'}. 



* Larmor, ' ./Ether and Matter," Section iv. Chap. xii. 

 t Larmor, ' ^Ether and Matter,' p. 197. 



(17) 



