Magnetic Induction in Iron and other Metals. 333 



in which F(a) is an arbitrary function giving the initial 

 conditions corresponding to # = 0. 



When H is positive x* 



J o cos{2n(H-a)-^^}6-^».d»=^|^-p 7r - (5) 



and =0 when H is negative. 



Thus we can write, as a solution o£ (3), 



x/4ttJo v j 



xe 4(H ~ a > 



(6) 



(H-a) 3 ' 2 ' 



Let us now take for the arbitrary function the following 

 values : — 



F(a)=a« between the limits a=0 and a=/i, where h is 

 definite and finite and a is a constant ; thereafter F(a) = 

 •constant =c, between the limits a = h and a=co , 



Fig. 2. 



Thus the initial conditions (# = 0) are expressed by such a 

 form as fig. 2 (c/. E wing's ' Magnetic Induction in Iron and 

 other Metals/ 3rd ed. fig. 144). 



