  We introduce a new approach to analyzing the interaction between classical
and quantum systems that is based on a limiting procedure applied to
multi-particle Schr\"{o}dinger equations. The limit equations obtained by this
procedure, which we refer to as the classical-quantum limit, govern the
interaction between classical and quantum systems, and they possess many
desirable properties that are inherited in the limit from the multi-particle
quantum system. As an application, we use the classical-quantum limit equations
to identify the source of the non-local signalling that is known to occur in
the classical-quantum hybrid scheme of Hall and Reginatto. We also derive the
first order correction to the classical-quantum limit equation to obtain a
fully consistent first order approximation to the Schr\"{o}dinger equation that
should be accurate for modeling the interaction between particles of disparate
mass in the regime where the particles with the larger masses are effectively
classical.
