538 



The agreement between (14) and (15) is good as long as — ^ is 



small because this assures the approximation of vf,(0,(/) bj a probability 



4jtV 

 integral, if (J.^l and c^O.Ol cm. thequantity -^S.^yClO't. 



The series for i>, (0,g) is then approximately 2[g-io''+(«-io'')'+ • •]• 

 Tiius t must be considerably less than 10~-^ sec. if (14) is to be a 

 good approximation. 



If now we should deal with a magnetic field which is periodi- 

 cally applied and removed from the cylinder the above calculation 

 must enable one to form an idea as to the average electrical resistance 

 of the cylinder used with a current passing longitudinally. In fact 

 the method of calculation which we used last applie.s not only in 

 the case of a uniform initial state but also if this state is variable. 

 The solution of any specitic case would be connected of course with 

 further calculations. 



Case 111. Sudden reversal of field. 



Fixing our attention again on Fig. 2 let us suppose that just 

 before < = the field has the uniform value H^^Hc- At t = 

 the field at x r= is suddenly changed to — H, where H, ]> He- 



After the lapse of a time t we may expect to find three regions 

 in the metal. These will be separated by two critical values of 

 X, say Xc,,x,^, {-x.^.v.J). In the intervals (0,Xc^), (.r,.,, «cj, (■'',■,, °°) <* ''^^ 

 the values i"f,,/i,,(i, respectively. 



We shall try to satisfy the conditions of the problem by letting the 

 magnetic field in these three intervals have the following expressions : 



H 



= H, = A, + B,&^^^^-fj ^v,<^< 



The equality between ^, and H, at x<.j and the equality between 

 H^ and H, at .c,., leads to the conclusion that 



Xc^ = n^V^ t , Xc, =z a^V t 



where «,, «, are constants. Thus the boundary and initial conditions 

 become ; 



