\cite{Push,AP} (see also
\cite{Singapore,Nauka,DSc})
we consider a lattice with
primitive vectors ${\bf a}_\alpha,\,\, \alpha = 1,2,3$ and introduce discrete
coordinates $N^\alpha$ as the number of steps (each being equal to ${\bf
a}_\alpha$) in the lattice from the origin to a given point. In this notation
the differential coordinates $\,d {\bf r \,}$ which are considered as
physically
infinitesimal (i.e. large compared to the lattice constants but small compared
to any macroscopic distance of interest) can be written in the form:
$$
d{\bf r} = {\bf a}_\alpha d N^\alpha + {\bf {\dot u}} d t
$$
or
$$
d N^\alpha = {\bf a}^\alpha  d{\bf r} - {\bf a}^\alpha {\dot {\bf u}}dt
$$
where ${\bf a}^\alpha$ are the reciprocal lattice vectors which satisfy the
relations
\begin{equation}
{\bf a}_\alpha {\bf a}^\beta = \delta^\beta_\alpha, \qquad
a_{\alpha i} a_k^\alpha = \delta_{ik}.
\ee                   %7

   It is seen from the above equations that
\begin{equation}
{\bf a^\alpha} = \nabla N^\alpha, \qquad
{\bf a_\alpha} = \f{\p {\bf r}}{\p N^\alpha}, \qquad
{\dot {\bf u}} = - {\bf a}_\alpha {\dot N}^\alpha .
\ee             %8
    The time-evolution equations for the vectors $\ba_\alf$ and $\ba^\alf$
can be deduced from plain geometrical considerations (Appendix 1) and written
as follows \cite{Push}:
\begin{equation}
\dot{\bf a}_{\alpha} + 