The Saint Venant torsion problem for an elastic cylindrical bar, with cross section \(\Omega\), leads to the following elliptic equation \(-\Delta u=1\) in \(\Omega\), \(u=0\) on \(\partial\Omega\). Saint Venant's study led to the following conjecture: (C) For plane convex domains, which are symmetric about both the axes, \(| \nabla u(x)|\) attains its maximum at those points on \(\partial\Omega\) which are at minimal distance from the origin. Recently \textit{G. Sweers} [J. Elasticity 22, No. 1, 57-61 (1989; Zbl 0693.73005)] constructed a convex domain \(\Omega\), for which he showed that the following alternative holds: Either (C) fails for \(\Omega\) or it fails for \(\Omega_ \varepsilon=\{(x,y): u(x,y)>\varepsilon\}\), for some small enough \(\varepsilon\). In a companion article [ibid. 27, No. 2, 183-192 (1992)], we gave a different proof of the same result, bringing the ideas out further. This also allowed us to construct other examples of domains \(\Omega\), for which a similar alternative holds. However an example of a concrete convex domain for which (C) fails, was still open. In particular, whether or not (C) holds for the domain \(\Omega\), was considered by Sweers and not answered. In another article [(*) Differ. Integral Equ. 3, No. 4, 653-662 (1990; Zbl 0718.73021)], we settled this question in the negative. The main tool used there was the moving plane method, considered by \textit{J. Serrin} [(**) Arch. Ration. Mech. Anal. 43, 304-318 (1971; Zbl 0222.31007)]. We present here a short and elegant proof of the main result of (*). Namely we show that out of the four points on \(\partial\Omega\) which are at minimal distance from the origin, \(|\nabla u|\) at two of them is strictly larger than \(| \nabla u|\) at the other two. This proof is the outcome of a thorough analysis of the technique in (*). Our only tool now is Hopf maximum principle. Thus the use of Serrin's boundary point lemma (see (**) lemma 1), which was crucial in (*), can be avoided. But still (*) contains more results and to extend our results to more general domains, we have to appeal to (*). However this paper is self-contained.