[2]: 361–371 Oldham's most important contribution to seismology was the first clear identification of the separate arrivals of different groups of waves, as detected by seismograms at distant locations.

[2] In subsequent papers, Oldham compared data from numerous earthquakes, with seismic observations at different distances from the epicentre.

He found a discontinuity in the travel times for the S-waves at about 120° angular distance from the earthquake, suggesting refraction by a dense core with a diameter of about 0.4 that of the earth.

[4][5][1][6] Oldham was not the first to suggest that the earth had a dense core, but he provided the first direct evidence of its existence and size.

[7] In 1903, Oldham resigned from the GSI due to ill-health and returned to the United Kingdom, living in Kew and various parts of Wales.