  This work presents a classification of all smooth 't Hooft-Jackiw-Nohl-Rebbi
instantons over Gibbons-Hawking spaces. That is, we find all smooth SU(2)
Yang-Mills instantons over these spaces which arise by conformal rescalings of
the metric with suitable functions.
  Since the Gibbons-Hawking spaces are hyper-Kahler gravitational instantons,
the rescaling functions must be positive harmonic. By using twistor methods we
present integral formulae for the kernel of the Laplacian associated to these
spaces. These integrals are generalizations of the classical Whittaker-Watson
formula. By the aid of these we prove that all 't Hooft instantons have already
been found in a recent paper.
  This result also shows that actually all such smooth 't
Hooft-Jackiw-Nohl-Rebbi instantons describe singular magnetic monopoles over
the flat three-space with zero magnetic charge moreover the reducible ones
generate the the full L^2 cohomology of the Gibbons-Hawking spaces.
