  We investigate the relationship between colour confinement and the monopoles
derived from the Cho-Duan-Ge decomposition. These monopoles, unlike Dirac and
't Hooft monopoles, do not require a singular gauge field and are defined for
any choice of gauge (and are not just restricted to, for example, the maximum
Abelian gauge). The Abelian decomposition is defined in terms of a colour field
$n$; the principle novelty of our study is that we have used a unique
definition of this field in terms of the eigenvectors of the Wilson Loop. This
allows us to investigate the relationship between the gauge invariant monopoles
and confinement both analytically and numerically, as well as retaining the
maximal possible symmetry within the colour field so that it is able to see all
the monopoles in an SU($N_C$) calculation.
  We describe how the Abelian decomposition is related to the Wilson Loop, so
that the string tension may be calculated from the field strength related to
the decomposed (or restricted) Abelian field. We discuss the structures in the
colour field which may cause an area law in the Wilson Loop, which turn out to
be magnetic monopoles. If these monopoles are present, they will lead to an
area law scaling of the Wilson Loop and thus be at least partially responsible
for confinement.
  We search for these monopoles in quenched lattice QCD. We show that the
string tension is dominated by peaks in the restricted field strength, at least
some of which are located close to structures in the colour field consistent
with with theoretical expectations for the monopoles. We show that the string
tension extracted from the monopole contribution to the restricted field is
close to that of the entire original field; again suggesting that confinement
can at least partially be explained in terms of these monopoles.
