We consider the idea of replacing the gravitational constantGby a function depending on the surrounding medium and whose variation would be noticeable on the galactic scale. Such a function in newtonian dynamics allows one to explain the flat region of the rotation velocity curves of many galaxies, without the dark matter hypothesis. This study is done within a unified field theory of the Kaluza-Klein type where we give an interpretation of gravitation which includes general relativity. ©1999 American Institute of Physics.