The crescent moons on the harnesses of the horses suggests that they may be associated with Selene, the Goddess of the Moon. See, for example, the crescent on the horse on the so-called Endymion Sarcophagus at the Palazzo Doria Pamphilj, no. 161 in G. Koch, Römische Sarkophage. For a related fragment preserving a quadriga formerly in the James and Marilynn Alsdorf Collection, see no. 11 in R.W. Shaw, The Horse as Motif: 1200 B.C.-1966 A.D.