  We prove an integrability criterion and a partial integrability criterion for
homogeneous potentials of degree -1 which are invariant by rotation. We then
apply it to the proof of the meromorphic non-integrability of the n body
problem with Newtonian interaction in the plane on a surface of equation
$(H,C)=(H_0,C_0)$ with $(H_0,C_0) \neq (0,0)$ where C is the angular momentum
and H the energy, in the case where the n masses are equal.
