Let \(q(t)= a_0t+\cdots+ a_nt^{n+1}\), \(a_0\neq 0\) real, be a polynomial univalent in the unit disc \(\Delta\). Let \(D= q(\Delta)\) and \(p(z)= \frac{1}{\pi} \int_D \frac{d\mu(\xi)}{z-\xi}\) be the potential of the domain \(D\). Then for large \(z\), \(p(z)= \frac{c_0}{z}+ \frac{c_1}{z^2} +\cdots+ \frac{c_n}{z^{n+1}}\) with \(c_0\neq 0\) real and \(c_k\) polynomials in \(a_0, a_1,\dots, a_n, \overline{a}_1,\dots, \overline{a}_n\). Thus, one sets up a map \(\eta\) by defining \(\eta(q)= p\). In this note, by calculating the Jacobian of \(\eta\), the author makes some interesting remarks about the nature of \(\eta\), useful in the inverse problem of recovering \(D\) from \(p(z)\).