72 HENET A. EOWLAND 



function of the magnetization, and hence a function of the magnetizing- 

 force; but the latter varies in different parts of the section, and hence 

 n must vary. But the correction will be small, because the average 

 value will be nearly the same as if it were a constant. We may estimate 

 the correction in the following manner. Let // and be the values of 

 those quantities at any point in the section of the ring, // and ' the 

 values at the centre of the section, and fjt t and , the observed values. 

 Then, by Taylor's theorem, 



But = 2n ' 1 and ft' = , and so we have 

 a x a 



\ 4 a* 2// dJQ r \ a 2 



Jp' 2 d z >j. I R* , q K 



But in my Tables I have already calculated 



Q 1 



A*J = 



a 



&c. . 



t / i T53 \ J 



,lfV (l + i ^ + fto.) 



and as ft l is very nearly equal to fjf, and $, to ^)', we have approximately 

 6, din. I IP 3 If . 



-- 



. 



2 4 a 4 



which will give the value of // corresponding to Q' and >'. Hence the 

 correct values of the quantities will be //, ', and S3' = ^V. 



The quantities -^- and ^/- can be obtained either by measuring a 



"/ **/ 



plot of the curve, or from the empirical equation 



= sn 



when we know the values of the constants. In this case 



dp _ , ft, 

 *$/ " 

 ^V/ 

 d? 

 in which 



