The electric quadrupole moment of a dipolar molecule depends upon the molecular origin from which it is measured. An electro-optical method has been successfully used for measuring the quadrupole moments of non-dipolar molecules, and the question arises: when the same method is applied to a dipolar substance what is the molecular origin to which the measured quadrupole moment should be referred? It is shown that this origin is not the centre of mass, but another point which may be called the ‘effective quadrupole centre’, the position of which depends in general on the wavelength of the light. Dipolar molecules experience a force in the field gradient and this enhances the contribution to the refractive index anisotropy from molecules which are out of line with the detector but in the light beam. This contribution is proportional to the dipole moment and is origin-dependent; it vanishes if the effective quadrupole centre is chosen as the origin. It is concluded that the electro-optical experiment should give identical quadrupoles for isotopically distinct species, and that the results for dipolar molecules may show an apparent dependence on the frequency of the light. The effects of distortion of the molecule by the field gradient are also considered.