  The n-dimensional hypergeometric integrals associated with a hypersphere
arrangement are formulated by the pairing of n-dimensional twisted cohomology
and its dual. Under the condition of general position there are stated some
results which concern an explicit representation of the standard form by a
special (NBC) basis of the twisted cohomology, the variational formula of the
corresponding integral in terms of special invariant 1-forms written by
Cayley-Menger minor determinants. Gauss-Manin connection is also formulated and
is explicitly presented in two simplest cases.
