  We study the ratio $p=\eta_1/\eta_2$ of the pseudo-periods of the Weierstrass
$\zeta$-function in dependence of the ratio $\tau=\omega_1/\omega_2$ of the
generators of the underlying rank-2 lattice. We will give an explicit geometric
description of the map $\tau\mapsto p(\tau)$. As a consequence, we obtain an
explanation of a theorem by Heins who showed that $p$ attains every value in
the Riemann sphere infinitely often. Our main result is implicit in the
classical literature, but it seems not to be very well known.
  Essentially, this is an expository paper. We hope that it is easily
accessible and may serve as an introduction to these classical themes.
