Hackett — The Twist and Magnetisation of a Steel Tube. 425 



Experimentally, we can make the two fields develop simultaneously by 

 shunting the solenoid across a short section of the circuit carrying the 

 current in the central wire. This current was controlled by a wire-resistance 

 frame, with Fleming anti-inductive coils, arranged in parallel, as in a lamp 

 resistance. The solenoid was in parallel with one of these coils, which was 

 permanently in the circuit. Owing, however, to the self-induction of the 

 solenoid, absolute simultaneity in the growth of the currents in each branch 

 cannot be secured. The circular magnetic field will develop a little more 

 rapidly than the longitudinal field. This effect will prevent (1 a) from being 

 completely satisfied. 



The results obtained by this method are shown in fig. 4. The theoretical 

 linear relation is approximately satisfied, though apparently not quite so 

 completely as in the case of anhysteretic spiral magnetization. But it is 

 possible to assign a reason for the deviation observed by taking account of 

 the demagnetizing factor. 



Let Ii a = longitudinal intensity for the applied spiral field *S" at pitch- 

 angle a. 

 I L = longitudinal intensity for longitudinal field S'. 

 dH' = average demagnetizing force. 

 S' - dS' = net resultant spiral field. 



(—) -* 



Then H = H' - NI. 



dH' dH 



dH' 



~ = JT(1 + NK) « iTapprox. 

 on 



The demagnetizing force dH' arises from the longitudinal magnetization, 



and may be written NIi a , where N is of the order 10" 3 . The following relations 



can be easily written down from a diagram of the applied and resultant 



fields : — 



dS' = dH'silla, 



dH' = NIia, 



ha = II sin a(approx. from graph fig. 4), 



dH' = NI L sin a. 



The resulting intensity I a for the resultant field S' - dS' for any pitch- 

 angle a, assuming a constant susceptibility at all angles, is given by 

 /» = I L + K[S' - 35" - (8' - NI L )-\ 

 = I L [1 + KNcos'a]. 



3 y2 



