Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/114

on account of the molecules beginning to be transferred from the one cone to the other. This rapid increase, however, soon comes to an end as the number of molecules forming the negative cone diminishes, and at last the magnetization reaches the limiting value M.

If we were to assume that the values of L and of D are different for different molecules, we should obtain a result in which the different stages of magnetization are not so distinctly marked.

The residual magnetization, I' , produced by the magnetizing force X, and observed after the force has been removed, is as follows:

When X is less than L,

No residual magnetization.

When X is between L and D,

$I'=M\left(1-{\frac {L^{2}}{D^{2}}}\right)\left(1-{\frac {L^{2}}{X^{2}}}\right).$

When X is equal to D,

$I'=M\left(1-{\frac {L^{2}}{D^{2}}}\right)^{2}.$

When X is greater than D,

$I'={\frac {1}{4}}\left\{1-{\frac {L^{2}}{XD}}+{\sqrt {1-{\frac {L^{2}}{D^{2}}}}}{\sqrt {1-{\frac {L^{2}}{X^{2}}}}}\right\}^{2}.$

When X is infinite,

$I'={\frac {1}{4}}\left\{1-{\frac {L^{2}}{XD}}+{\sqrt {1-{\frac {L^{2}}{D^{2}}}}}\right\}^{2}.$

If we make

$M=1000,\quad L=3,\quad D=5,\,$

we find the following values of the temporary and the residual magnetization:—

Magnetizing Force.	Temporary Magnetization.	Residual Magnetization.
X	I	I'
0	0	0
1	133	0
2	267	0
3	400	0
4	729	280
5	837	410
6	864	485
7	882	537
8	897	574
≈	1000	810