  Unlike Newtonian dynamics which is linear and obeys the strong equivalence
principle, in any nonlinear gravitation such as Milgromian dynamics (MOND), the
strong version of the equivalence principle is violated and the gravitational
dynamics of a system is influenced by the external gravitational field in which
it is embedded. This so called External Field Effect (EFE) is one of the
important implications of MOND and provides a special context to test
Milgromian dynamics. Here, we study the rotation curves (RCs) of 18 spiral
galaxies and find that their shapes constrain the EFE. We show that the EFE can
successfully remedy the overestimation of rotation velocities in 80\% of the
sample galaxies in Milgromian dynamics fits by decreasing the velocity in the
outer part of the RCs. We compare the implied external field with the
gravitational field for non-negligible nearby sources of each individual galaxy
and find that in many cases it is compatible with the EFE within the
uncertainties. We therefore argue that in the framework of Milgromian dynamics,
one can constrain the gravitational field induced from the environment of
galaxies using their RCs. We finally show that taking into account the EFE
yields more realistic values for the stellar mass-to-light ratio in terms of
stellar population synthesis than the ones implied without the EFE.
