﻿490 Mr. M. H. Belz on the Heterodyne Beat Method 



Before this formula can be applied it is necessary to 

 investigate several corrections. The absorption in the 

 platinum shield which covered the tube on which L 2 was 

 wound, and the eddy current effect, have been discussed and 

 shown to produce no correction terms. But there remain 

 two further corrections to be investigated, (i.) due to the 

 demagnetizing effect of the specimen, and (ii.) due to the end 

 correction term in the calculation of the self-inductance of 

 the coil and the effect on this due to the position of the 

 specimen. 



(i.) The demagnetizing effect on the magnetic field due 

 to the magnetism induced in the specimen. 



By treating the specimen as an elongated ellipsoid of 

 revolution, of semi-minor and semi-major axes a and c 

 respectively, with its long axis parallel to the field, Ewing * 

 has shown that if H is the value of the magnetic force 

 within the specimen, and H' the original value of the 

 magnetic force before the specimen was inserted, then 



where N is given by 



N = 4,r(l/« 2 -l)|l.log«(l+<>)/(l-<0-l}, 



e being the eccentricity and equal to ^/l — a 2 /c 2 . 



In a typical case, that of cobalt chloride in solution, 

 which had a value of K v approximately 20 x 10~ 6 c.g.s., 

 2a = 0'507 cm., 2c = S'0 cm. Hence <? = 0'998. This gives 

 N = 0-126, and hence 



H = H'(l-0-126x20xl0- 6 ) 



= H / (l-2-52xlO- 6 ), 



so that this correction is negligible. 



To get the effect on the external field, consider the 

 resultant magnetism induced on the ends and sides of 

 the specimen. Ewing f shows that the free magnetism, 

 although densest at the ends, extends towards the middle, 

 and it is only on the equatorial line that there is none. 

 Also the total quantity of free magnetism on any narrow 

 zone taken perpendicular to the direction of magnetization 



* Ewing, ' Magnetic Induction in Iron and other Metals/ pp. 23-25. 

 + Ewing, he. cit. pp. 25-27. 



