378 Magnetic Expansion of some Magnetic Metals. [May 22, 



Thus 



0-414 0-228 0-171 



11 = -- - I = ' 



In J n put z = V(/ 2 + a ) SSLi!, where a is defined by tan 2a = ? ; 

 cos (v a) t 



also let t = tan a. 



With the above values of a/I we have a = 8 5', * = 0-142. 



Clearly tf 3 is negligible except where it is divided by cos or sin 0, 

 which become of order / at one or other limit. This substitution 

 gives 



1 2t fi- 



o^ (1 mu-i I ( ! + ^ se c 2n ^) (cos ^ + J sin ^) 2)l ~ 2 (sin 6 - tcos 6) dd 



a J + ' tan "~ 1 - sec 



whence 



T T 0-242 0-097 



J = 1-484, J! = -- 



Hence we get 



Z~ 2 = H 2 [0-500 - 0-268 . a^ + 0'071 . fi 4 I 2 - 0'024aI 3 

 + 0-250 . J - 0-018 . 2 J! + 0-053 . a 4 J 2 ] 



= 0-77 . H 2 . 



Lastly, (1) gives the values at the ends of the bar, say Zj and Zr. 

 Resuming, we get the following values : 



Z = 0-867H, Z, = 0-495H, 



Z 2 = 0-77H 2 , Z/ 2 = 0-245H 2 . 



