A bar magnet of magnetic moment $M_1$ is suspended by a wire in a magnetic field. The tip of the wire is rotated through ${180}^{\circ }$, then the magnet rotated through ${45}^{\circ }$. Under similar condition, the magnet of magnetic moment $M_2$ is rotated through ${30}^{\circ },$ the ratio of $M_1$ and $M_2$ is