  It is nowadays a quite diffuse idea that variations of polarisation in
condensed matter theory are related to a "Berry phase". The derivation of the
latter geometric phase is correct $\it{only if}$ the restrictive periodic
gauge\cite{KS-V} is used for its derivation, aside giving rise to a "quantum of
polarisation" that is of difficult theoretical interpretation. Its derivation
has not been demonstrated in the general case of an external homogeneous
electric field interacting with the electronic field. In the present paper we
give a brief derivation of the polarisation differences in a general manner
than in\cite{KS-V} allowing for a general boundary conditions freedom showing
that is possible to define it even in the presence of an external electric
field interacting with the electronic field and writing equations in a way
directly implementable in modern first principles codes.
