the Electrical Conductivity of Metals. 453 



Thus 

 = Ae^!! c 3^ f 1 + ^( 1 + L tan 2 f + % . ^)\ e'^'K sin ^ cos * d^ dR. 



The remainder of the work is now exactly analogous to 

 that carried out on pages 445 and 449, and we obtain 



Integrating the second term by parts we finally obtain 



2Ae' 

 6 m 



Jo 



= ^Ae 2 h\ 6~ 



Thus, using (21) we have 



a L= 2« 2 ^ 

 <t 3 e 2 



The result is thus independent o£ the manner in which 

 X c varies with the velocity. 



Appendix. 

 Problem (1). 



To show that cos ty= < 1 + ^-^ tan 2 > cos 0. 



Substituting in (6) from (4) and (5) we have, neglecting 

 second-order quantities, 



( v cos 0+^-t)t 

 cos^ = 



( v 2 * 2 cos 2 -f- — t z cos + r 2 * 2 sin 2 \ " 



\ zmv cos u J \ mv J 



Putting ^cos^ = «i', we readily obtain 



cos^= { 1+ ^',tan 2 j cos 0. 



mmm^^ma^^^^^m^m 



