  In our [Higher-order preconnections in synthetic differential geometry of jet
bundles, Beitr\"{a}ge zur Algebra und Geometrie, 45 (2004), 677-696] we have
established the affine bundle theorem in the synthetic approach to jet bundles
in terms of infinitesimal spaces D&#8319;'s. In our succeeding [Synthetic
differential geometry of higher-order total differentials, to appear in Cahiers
de Topologie et G\'{e}om\'{e}trie Diff\'{e}rentielle Cat\'{e}goriques] we have
introduced another synthetic approach to jet bundles in terms of infinitesimal
spaces D_{n}'s, and have compared it with the former approach both in the
general microlinear setting and in the finite-dimensional setting. However our
comparison in the finite-dimensional setting was incomplete, for our use of
dimension counting techniques has tacitly assumed that jet bundles in terms of
D&#8319;'s and D_{n}'s are vector bundles, which is not the case unless the
given bundle is already a vector bundle. The principal objective in this paper
is to establish the affine bundle theorem in our second synthetic approach to
jet bundles and then to compare not merely the jet bundles based on both
approaches but the affine bundles constructed as a whole both in the general
microlinear setting and in the finite-dimensional setting. This completes our
comparsion between the two approaches in the finite-dimensional setting.
