458 Dr. J. Buchanan on the Theory of 



equation required : 



T 2aR?r-l nr- %7rr/ \\ 



+ 4c-a(R-2\) ^ R • • • (16) 



7T 



in which r has only odd values. 



By comparison of the general terms of (15) and (16) with 

 one another, we get 



t. a aR . 2?n\ 4c-a(R-2\) 



D r cos r = ^- 2 sin -n-^+ — — ; 



r 7rV R irr 



D r sm0„=— o- 9 cos 2 ^X (17) 



Thus D r and # r can be expressed in terms of the constants 

 of the graph of I x= g> 



Now, as Dr. Ewing has pointed out*, " the curves (of 

 magnetization) . . . appear in all cases to start off tangent to a 

 line parallel to the axis on which H is measured whenever 

 the change of H is reversed in sign.'" 



In the notation of (15) and (16) above, such reversal takes 



TO 



place when H= j- . This w T ould suggest that in (16) a value 



for \ about ~- should give an approximation to the truth. 



■p 



Let us then take as an approximate value ^=j-. By 



substitution in (17) we get 



. aR. 



t-x a aR . irr , 2 

 D cos 6 r = -j- a sin — + ; 



i * ^j 2 irr 



D n aR 

 ,"»^fli (18) 



.-. tantf - aR 



irr\ 



(. aR\ _ . 7rr' 

 4c 3-l + aRsm — 



* Phil. Trans, pt, ii. 1885, p. 533. 



