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He entered the Society of Jesus in Rome 12 November 1814, shortly after the re-establishment of the order, and was professor of humanities successively in the colleges of Terni, Reggio Emilia, Modena and St. Andrew of the Quirinal. After completing his course and making his religious profession (1833) he became professor of rhetoric in the Roman College and held this position until 1842. Meanwhile, he devoted his leisure to study, applying himself through choice to non-Christian antiquities. In 1838 he was made prefect of the Kircher Museum, a position he retained until his death.
He soon gave special attention to Christian antiquities, hoping thus to find a means of restoring Christian art. In 1840 he announced his intention of collecting into one large publication the monuments of Christian architecture, painting, and sculpture. His archæological pursuits recommended him to Gregory XVI as qualified to succeed Settele in the position of Conservatore dei sacri cimiteni di Roma (1842). About this time Marchi made the acquaintance of youthful Giovanni Battista De Rossi, who accepted him as master and thenceforth accompanied him on his visits to the Roman catacombs. These ancient cemeteries had been abandoned but thereafter were more accessible and could be studied on the ground. In 1844 Marchi published the first volume of his "Monumenti", devoted to the construction of the catacombs, especially that of Saint Agnes. He proved the Christian origin of these ancient burial-places and, through his studies, brought about (21 March 1845) the discovery of the crypts of Saints Peter and Hyacinth in the catacomb of St. Hermes.
It was De Rossi who made the great discoveries in the catacombs. He knew better than Marchi how to make use of ancient topographical data and all the resources of learning. Marchi was appointed Consultor of the Congregation of the Index in 1847 and several years later (1854) he took part in the creation of the Lateran Museum of which, with de Fabris, he became director. In July, 1855, his labours were interrupted for the first time by a stroke of apoplexy, to which he succumbed in 1860.
The notes intended for the continuation of the "Monumenti" were lost, but some of them were found by Father Bonavenia and made known at the Second Congress of Christian Archæology at Rome (1900). These recovered documents were destined for the second volume of the "Monumenti", which was to treat of the non-cemeterial Christian architecture of Rome.
- Musei Kircherniani Inscriptiones ethnicæ et christianæ (Milan, 1837);
- L'aes grave del Museo Kircheriano, ovvero le monete primitive dei popoli dell' Italia media in collaboration with P. Tessieni (Rome, 1839);
- Monumenti delle arti cristane primitive nella metropoli del cristianesimo: I. Archittetura della Roma sotteranea cristiana (Rome, 1844).