MR. J. S. TOWNSEND ON MAGNETIZATION OF LIQUIDS. 
541 
The equation determining the secondary current i 2 is 
i, § + - 
UN 
at ’ 
where c7N/a£ consists of a number of terms of the form — A. Be M . 
The solution of L 3 ~ = XBe“ w is 
X.B (e A/ — e p ') , , R (0) 
h = —B-Ur-> where p = 
-Llo /V-L^ ±J y 
and the quantity q 2 1s 
B 
<h = 
(1 - e- M ) - J (1 - e-''*) 
l\n X.t.1 
Let us consider the combined effect of the increase in permeability, and the currents 
generated in the liquid, on the quantity q. 2 . 
The first gives rise to the term inkMi, and the second to the series 
Hence 
SB„,e '" wt + Bpe pt in N, 
r/N 
clt 
4ttZ-ME 
R 
pz ,d 
2hnB ;/i e mat — 7>B /; e pl 
Substituting and bearing in mind that SB,„ -f- B ;J = 0, we get 
( 2 ) <h = 
47rMIE 
R 
(1 - e-P‘) - (1 - e~P' 1 ) 
JL 
/ 
P 
B„ 
■lb - rL 2 
+ 
ma 
V 
—p't _ f — inat 
R, — via L., 
+ 
M p< e ~ p l e ~ rl 
R 2 ~P L 2 
In order to select the important terms from this equation we must find the 
approximate values of m, p, and p. 
The smaller values of the roots of J 0 (x) = 0 are* 
2-404, 
5‘520, 
8-654, 
11-792. 
So that the smallest value of m is given by the equation 
* Lord Rayleigh, ‘ Theory of Sound,’ Yol. 1, section 206. 
