  In this paper we derive the continuum limit of a multiple-species,
interacting particle system by proving a $\Gamma$-convergence result on the
interaction energy as the number of particles tends to infinity. As the leading
application, we consider $n$ edge dislocations in multiple slip systems. Since
the interaction potential of dislocations has a logarithmic singularity at zero
with a sign that depends on the orientation of the slip systems, the
interaction energy is unbounded from below. To make the minimization problem of
this energy meaningful, we follow the common approach to regularise the
interaction potential over a length-scale $\delta > 0$. The novelty of our
result is that we leave the \emph{type} of regularisation general, and that we
consider the joint limit $n \to \infty$ and $\delta \to 0$. Our result shows
that the limit behaviour of the interaction energy is not affected by the type
of the regularisation used, but that it may depend on how fast the \emph{size}
(i.e., $\delta$) decays as $n \to \infty$.
