“which feat our charioteer performed with an air not unlike that of Rhesus, had he but been as suitably furnished with chariot and steeds!”
Inferred Fuller names 'Rhesus' as a figure of a dashing charioteer without citing a textual source; the reference draws on Iliad Book 10 and/or Euripides' tragedy Rhesus. Rhesus was a mythological king of Thrace and ally of Troy in the Iliad (Book 10), famous for his magnificent white horses and golden armor.
The allusion is to the classical tradition, principally Homer's Iliad 10.435-514 or the tragedy Rhesus attributed to Euripides.