  Following Newton, Ivory and Arnold, we study the Newtonian potentials of
algebraic hypersurfaces in $R^n$. The ramification of (analytic continuations
of) these potential depends on a monodromy group, which can be considered as a
proper subgroup of the local monodromy group of a complete intersection (acting
on a {\em twisted} vanishing homology group if $n$ is odd). Studying this
monodromy group we prove, in particular, that the attraction force of a
hyperbolic layer of degree $d$ in $R^n$ coincides with appropriate algebraic
vector-functions everywhere outside the attracting surface if $n=2$ or $d=2$,
and is non-algebraic in all domains other than the hyperbolicity domain if the
surface is generic and $d\ge 3$ and $n\ge 3$ and $n+d \ge 8$. (Later, W.
Ebeling has removed the last restriction $d+n \ge 8$).
