  We theoretically study the magnetism induced by the proximity effect in the
normal metal of ferromagnetic Josephson junction composed of two $s$-wave
superconductors separated by ferromagnetic metal/normal metal/ferromagnetic
metal junction (${S}/{F}/{N}/{F}/{S}$ junction). We calculate the magnetization
in the $N$ by solving the Eilenberger equation. We show that the magnetization
arises in the ${N}$ when the product of anomalous Green's functions of the
spin-triplet even-frequency odd-parity Cooper pair and spin-singlet
odd-frequency odd-parity Cooper pair in the ${N}$ has a finite value. The
induced magnetization $M(d,\theta)$ can be decomposed into two parts,
$M(d,\theta)=M^{\rm I}(d)+M^{\rm II}(d,\theta)$, where $d$ is the thickness of
$N$ and $\theta$ is superconducting phase difference between two ${S}$s.
Therefore, $\theta$ dependence of $M(d,\theta)$ allows us to control the
amplitude of magnetization by changing $\theta$. The variation of $M(d,\theta)$
with $\theta$ is indeed the good evidence of the magnetization induced by the
proximity effect, since some methods of magnetization measurement pick up total
magnetization in the ${S}/{F}/{N}/{F}/{S}$ junction.
