As two fluid particles separate in time, the entire spectrum of eddy motions is being sampled from the smallest to the largest scales. In large-scale geophysical systems for which the Earth rotation is important, it has been conjectured that the relative diffusivity should vary respectively as D-2 and D-4/3 for distances respectively smaller and larger than a well-defined forcing scale of the order of the internal Rossby radius (with D the r.m.s. separation distance). Particle paths data from a mid-latitude float experiment in the central part of the North Atlantic appear to support these statements partly: two particles initially separated by a few km within two distinct clusters west and east of the mid-Atlantic ridge, statistically dispersed following a Richardson regime (D-2 similar to t(3) asymptotically) for r.m.s. separation distances between 40 and 300 km, in agreement with a D-4/3 law. At early times, and for smaller separation distances, an exponential growth, in agreement with a D-2 law, was briefly observed but only for the eastern cluster (with an e-folding time around 6 days). After a few months or separation distances greater than 300km, the relative dispersion slowed down naturally to the Taylor absolute dispersion regime.