A BRA UN TUBE HYSTERESIGRAPH 



295 



side by side are placed two equal search coils, connected in series 

 opposing. These coils are 10 inches long, and in one assembly carry 

 30,000 turns each, in another 7,000 turns each. The sample, about 

 40 inches long, is placed in the axis of one search coil, the other coil 

 serving to compensate for the air space of the first. This assembly is 

 mounted in a brass frame to which is attached a windlass and spring 

 scale for applying tension to the sample when so desired. The effect 

 of the earth's magnetic field on the specimen is made negligible by 

 either passing a direct current through one of the magnetizing windings 

 in series with a high inductance, or by passing a direct current through 

 the two coils from a battery in parallel with the electrolytic condenser. 



III. Mathematical Analysis of the Apparatus. 



The performance of the apparatus will be analyzed for two simple 

 cases representing extremes in the properties of the magnetic material. 

 In the first case it will be assumed that the flux in the search coil is 

 proportional to the magnetizing field, a condition that is approached 

 with hard materials at low field strengths. In the second case the 

 assumption will be made that the material becomes saturated perfectly 

 in the positive or negative direction, as the magnetizing field passes 

 through zero. This is the limiting case of soft materials at high 

 alternating field strengths. 



1. Circuit Corrections for the Case of Small Magnetizing 

 Fields. 



The circuit of the integrator is represented in Fig. 3. The condenser 



r r 



Fig. 3 — Equivalent circuit of the integrator. 



is shunted by an effective resistance r made up of the grid leak re- 

 sistance r' and the condenser resistance r" . The conductance of 

 condensers is a function of frequency and temperature and possibly 

 of other factors. As a function of frequency it may be written 



Z\ Zi 



C 



+ 



(3) 



