After the death of Kapteyn in 1922 he finished his PhD thesis in 1924 with Pieter Johannes van Rhijn 'On a Thermo-Electric Method of Measuring Photographic Magnitudes'.
Schilt's astronomical work included the invention of the Schilt photometer, a device which measures the light output (apparent magnitude) of stars on photographic plates, and, indirectly, their distances.
He worked on the motions of star streams in the Milky Way Galaxy, and was director of the Yale-Columbia Southern Station in Johannesburg and Canberra, as well as Director of the Rutherford Observatory at Columbia.
Schilt was noted at Columbia for walking into his classes the first day after the launch of Sputnik 1 and commenting "Well, gentlemen, it is not every day we have something new in the sky to talk about", following which he devoted the entire class to proving that Sputnik had been deliberately launched into an orbit designed to make it invisible from the United States for as long as possible (six weeks).
13,500 items of his papers are contained in the Rare Book and Manuscript Library of Columbia University.