of the Hall Effect and Allied Phenomena. 535 



and each integral in the two cases is directly evaluated after 

 substitution of the appropriate value of <f> by the usual 

 spherical polar transformation which reduces them at once 

 to single integrals with respect to u. In this way we find 

 that the ^-components of the electric and thermal currents 

 are exactly the same as would be obtained in the absence of 

 the magnetic field, whilst the other two components of the 

 electric flux are identical with the corresponding components 

 of the flux vector 



The same components of the heat flux are determined 

 similarly by the vector 



♦ if & m-i [HVlAWtHV],)"-^]. 



These expressions are quite general; by using the par- 

 ticular value of r n given above we can deduce the results 

 for the particular cases to be investigated. It will not, 

 however, be necessary for us to retain complete generality 

 as the limitations of the theory are probably not such as to 

 warrant any such rigour in the analysis. We shall therefore 

 neglect all powers of H beyond the second. Thus using 



i ' 



4:7rrifi 2 I 



» 00 



cos 2 Ootda 



that 



SO iu«i =-1 



T m =lmU* 



and introducing the ordinary expression for the conductivity 

 in these cases, 



we find that the y and z components of the electric flux are 



