  The first irreducible solution of the $\mathrm{SU} (2)$ self-duality
equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and
Duff in 1977, only 2 years later than the famous BPST instantons on
$\mathbb{R}^4$ were discovered. While soon after, in 1978, the ADHM
construction gave a complete description of the moduli spaces of instantons on
$\mathbb{R}^4$, the case of the Euclidean Schwarzschild manifold has resisted
many efforts for the past 40 years.
  By exploring a correspondence between the planar Abelian vortices and
spherically symmetric instantons on ES, we obtain: a complete description of a
connected component of the moduli space of unit energy $\mathrm{SU} (2)$
instantons; new examples of instantons with non-integer energy (and non-trivial
holonomy at infinity); a complete classification of finite energy, spherically
symmetric, $\mathrm{SU} (2)$ instantons.
  As opposed to the previously known solutions, the generic instanton coming
from our construction is not invariant under the full isometry group, in
particular not static. Hence disproving a conjecture of Tekin.
