  Given a vector bundle, its (stable) order is the smallest positive integer n
such that the n-fold self-Whitney sum is (stably) trivial. So far, the order
and the stable order of the canonical vector bun- dle over configuration spaces
of Euclidean spaces have been studied by F.R. Cohen, R.L. Cohen, N.J. Kuhn and
J.L. Neisendorfer [5], F.R. Cohen, M.E. Mahowald and R.J. Milgram [7], and S.W.
Yang [17]. Moreover, the order and the stable order of the canonical vec- tor
bundle over configuration spaces of closed orientable Riemann surfaces with
genus greater than or equal to one have been studied by F.R. Cohen, R.L. Cohen,
B. Mann and R.J. Milgram [6]. In this paper, we mainly study the order and the
stable order of the canonical vector bundle over configuration spaces of
disjoint unions of spheres.
