Opacity of Tourmaline Crystals. 117 



that the law of equality of power to absorb and emit radia- 

 tions extends to the ease of the light absorbed by the tour- 

 maline, which, when heated to redness, emits rays partially 

 polarized in a principal plane of section — that is to say, emits 

 those rays most freely which it most freely absorbs. 



II. Mathematical Theory. 



10. Let K, /n, and stand respectively for the dielectric 

 inductive capacity, the magnetic inductive capacity, and the 

 conductivity per unit of volume of a medium. In crystalline 

 media these quantities will, in general, have different values 

 in three principal rectangular directions, being no longer mere 

 scalar quantities, but linear (and vector) operators upon their 

 several functions. If these values be specified for any crystal, 

 then the optical properties of that crystal may be deduced 

 from the general equations of electromagnetic disturbances. 

 These equations are found in Maxwell's ' Electricity and Mag- 

 netism,' art. 783 (7), as follows:— 



<".+*&$ + &**+£.-* 



K^ c+ 4)(§+f)+v^ + f=o,> ..a) 



where 



J= dF da dR 



clx dy dz y 



and where F, Gr, H are the components of vector-potential at 

 the point (x. y, z) in three rectangular directions parallel to the 

 #, y, and z axes respectively, and where ^ represents the elec- 

 tric (scalar) potential of the possible free electricity. These 

 general equations apply to the case of a medium in which both 

 electric displacements and true conduction currents are simul- 

 taneously produced under the action of an impressed electro- 

 motive force. They cease to apply in strictness to the case 

 where the medium possesses movements of its own, which we 

 are not here considering. If the medium be homogeneous, 

 Avhether asolotropic or isotropic, and if its conductivity under- 

 goes no discontinuity in its values at any point (that is to say, 

 has the same continuous values in the same direction), there 

 will be no reason to expect the phenomenon of electric absorp- 

 tion to occur, or free electrification to appear at any internal 

 point of the medium. Hence, in considering steady periodic 

 disturbances such as light-waves, we may neglect terms invol- 



