f>72 DR EDWIN H. BARTON ON THE TEMPERATURE VARIATION 



V. Discussion of Apparent and True Susceptibilities. 



17. Susceptibility: Apparent and Real Values. — This curve does not, however, 

 give the variation in the true susceptibility of the specimen, as might be at first 

 supposed. On the contrary, it gives only a first approximation to the susceptibility, 

 because, hitherto, the reaction of the specimen on the impressed field has not been 

 considered. The ordinates of (vi.) would have been proportional to the true values of 

 the susceptibility if the actual magnetic field H, within the specimen, had been main- 

 tained constant throughout. Instead, however, of this being the case, the impressed 

 magnetic field, H 7 , has been constant. Now we have # (for an ellipsoid) 



H = H'-i\ri, 



where N is a constant depending on the relation of the length of the ellipsoid and its 

 transverse dimensions, and I is the intensity of magnetisation of the specimen. The 

 above equation may be written 



H = H'-i\ 7 "/cH, 



where k is the magnetic susceptibility, hence we get 



H(l+i\fe) = H' (1) 



Again, since the two secondary coils balance each other, we may write 



/cH = (induction effect) x (a constant) = k'H' .... (2) 



k being the first approximation to the susceptibility alluded to (Art. 16, vi.). Hence 

 H' having been constant, we have k' proportional to the induction effects. Now, to get 

 k in terms of k' and N, we must eliminate H and H 7 between (1) and (2). It will be 

 convenient to express the relation thus obtained in several ways, viz. : — 



w=- < 3 > 



JSFkk'-k+k'=0 (4) 



(5) 



l-i\V 



K+ w)( K -jr) = -W> ■ ... (6) 



18. If the variables k and k' be regarded as mutually rectangular coordinates, the 

 above relation between them represents a rectangular hyperbola whose asymptotes may 

 be written 



(•+y)('-y-° (7) 



* Magnetic Induction in Iron and other Metals, by J. A. Ewing, F.R.S., pp. 24, 25. 





