Magnetic Hysteresis with Frequency. 107 



The factor /'can then be deduced from c. as equations (1) 

 above give us the relation 



By this method we obtain for the experiment in hand 



e= -00008178, /=29'8, 



which agree satisfactorily with the values obtained above by 

 the other method. 



The latter method of obtaining c and / is the one usually 

 adopted. 



The factors (h and b say) to be applied to <y and 3 in order 

 to obtain H and B. where H is "'the M.M.F. round the ring 

 divided by its mean circumference I, and B is the total flux 

 F divided by the iron cross-section a, are 



bnn x c , / 



It— — = — , b—-. 



t a 



Substituting the values of n lf L and a given in the details of 

 ring 1. in § 3, and those of c and /just obtained, we find 

 that 



A = -0056\ 6 = 17-52; 

 so that 



H = "00567, B = 17-52/8. 



Hence the final expressions for the pair of associated waves 

 investigated are 



H=l-81[sm©*--0317sin3(©*-7) + -004 sin 5(«t— 23-4)] 



B = 3802[sin (^-51-76) + -1382 sin 3(^- 63-1) + -0265 sin 5(^-69-2)] 



7. It is easy to show that as the secondary (galvanometer) 

 current is inappreciable, the energy (D say) dissipated per 

 cycle in the iron of the ring is given by 



J T dF 



which becomes (see § 6) 



D=n lC fV yd/3. 



Jo 



Hence when the galvanometer readings for {3 are plotted as 

 ordinates against the corresponding ones for y as abscissae 

 for a complete period a closed curve Is obtained, whose area 

 when multiplied by nycf gives D the total energy dissipated 

 per cycle in the iron of the ring. 



