In [2], flows on the standard two-dimensional torus given by the differential equations \begin{equation*}\frac{dx}{dt}=a-Fy(x,y),\quad \frac{dv}{dt}=b+Fx(x,y)\end{equation*}were considered. It was assumed that $F(x,y)$ was real analytic and of period one in both $x$ and $y$. A key step in proving the results in [2] was to show that one could conclude topological transitivity for the flow provided one assumed:\begin{enumerate}\item[(a)] $a/b$ is irrational;\item[(b)] there does not exist a topological disc on the torus that is invariant under the flow.\end{enumerate}