362 Dr. H. C. Pocklingtoii on Botatory 



and let the electric force be <ficr -when t = 0. Then when t 

 is not zero, the electric force is the sum of two terms, one 

 being that given above, and the other that due to the Hall 

 effect, viz. ^V(t4-t )o--=cVt o- if we neglect r in comparison 

 with t in this small term. 



The equations* of the electromagnetic field are now 



V.v(#o- + cYr a) = — t, 



Eliminating r these give 



.3. In order to discuss the case of plane waves, let 



<t = /jl expo)p(i-\- SX/o), (1) 



where a> is the scalar quantity ^( — 1), and p is the vector of 

 any point, so that X is the vector of wave-slowness, and the 

 locus of its extremity is the index-surface. The calculations 

 will be carried out with this imaginary value of cr, and at the 

 end we shall, in virtue of the linearity of the differential 

 equations, reject the imaginary parts of the various expressions 

 found for the electromagnetic forces. 



Wave-surface near axis. 



The operators v and djdt when the above expression is the 

 operand are equivalent to multipliers — <wpX and <op respec- 

 tively, hence the vector differential equation satisfied by <r 



* Cf. Basset, ' Treatise on Physical Optics,' p. 394. 



