According to "The Program of a Competition for the Selection of an Architect and the Procuring of a General Plan for the Union Theological Seminary in the City of New York," the building was to contain areas for general purposes of instruction and for administration, with easy access from the library.
When describing the completed Administration Building, Daniel Johnson Fleming wrote:
A distinct aesthetic impression is made upon anyone stepping into the Henry Sloane Coffin Administration Building at 120th St. and Broadway. The impressive polygonal foyer is called the Memorial Entrance Hall because of the commemorative bronze tablets upon its walls. A wide marble staircase (an exceedingly difficult problem for the architect) ascends around four high Gothic pillars which carry the fan-vaulted ceiling to the entrance of the Library. It is well worthwhile to scorn the elevator in order to get the whole effect of this Hall.