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We show that M-theory compactified on a compact Joyce 8-manifold of$Spin(7)$-holonomy, which yields an effective theory in $D = 3$ with $\N$ = 1supersymmetry, admits at some special points in it moduli space a descriptionin terms of type IIA theory on an orientifold of compact Joyce 7-manifold of$G_2$-holonomy. We find the evidence in favour of this duality by computing themassless spectra on both M-thory side and type IIA side. For the latter, wecompute the massless spectra by going to the orbifold limit of the Joyce7-manifold.Comment: 26 pages, 2 eps figures, Latex file, two references and one footnote  added, corrected some typo

Type IIA Orientifold Limit of M-Theory on Compact Joyce 8-Manifold of Spin(7)-Holonomy