Given a sequence of polynomials \(Q_n\) of degree n with zeros on \([-1,1]\) , we consider the triangular table of derivatives \(Q_{n, k}(x)=d^k Q_n(x) /d x^k\) . Under the assumption that the sequence \(\{Q_n\}\) has a weak* limiting zero distribution (an empirical distribution of zeros) given by the arcsine law, we show that as \(n, k \rightarrow \infty \) such that \(k / n \rightarrow t \in [0,1)\) , the zero-counting measure of the polynomials \(Q_{n, k}\) converges to an explicitly given measure \(\mu _t\) . This measure is the equilibrium measure of \([-1,1]\) of size \(1-t\) in an external field given by two mass points of size \(t/2\) fixed at \(\pm 1\) . The main goal of this paper is to provide a direct potential theory proof of this fact.