and the boundary condition for $A_\varphi = 0 $ at infinity. The magnetic potential $\left(\int\mu d\Psi\right)$ changes its qualitative behavior in its spatial distribution when $m=-1$. If we adopt $m < -1$, as $\Psi$ decreases from its maximum to zero on the axis of the star the value of the magnetic potential increases unboundedly if $\epsilon\to 0$. As a result, the [*poloidal*]{} magnetic field lines are concentrated near the axis in order to fulfill such magnetic potential distributions. On the other hand, if we choose $m > - 1$, the value of the magnetic potential decreases as $\Psi$ decreases from its maximum to zero, which is realized on the axis. Then the [*poloidal*]{} magnetic field lines are distributed more uniformly than those for configurations with $m < -1$. If we choose $m=0$, we obtain $\mu = $ constant configurations. They are the same as those investigated by other authors.

It is remarkable that the only freedom that we can take in our formulation is related to the choices of functional forms and the values of the parameters which appear in those functions. It implies that degrees of freedom for choices for these functions and parameters correspond to degrees of freedom 