Reasoning that it is this alternate vision of Mars to which their foe has fled with the girl, they determine to travel there themselves by means of the symbolic logic formulas originally devised by Chalmers.
Arriving on Barsoom, the Sheas seek out the aid of the royal family of the city-state of Helium, which includes Burroughs' protagonist, the transplanted earthman John Carter.
He regards Carter as something of a blowhard, claiming impossible prowess in battle, and Ulysses Paxton, the other earthman resident on Barsoom, as a rabble-rouser, advocating Terran ideas of equality and freedom unwelcome to the hierarchical, slave-owning Martians.
Thavas consents to aid the couple in return for some professional help from psychologist Shea; having previously had Paxton transplant his brain from his original aged body into a young and virile one, he has had difficulty adjusting to changed societal expectations, not to mention the youthful urges of his new form.
On the other hand, Thavas provides something of a corrective to the jaundiced Kajak's view of Carter, who in his experience is a genuinely charismatic leader who can exact pledges of a defeated foe and make them stick.
Thavas uses his medical skills to save the life of the enchanter to keep Belphebe out of trouble with the law (a sword duel is considered a fair fight by Barsoomians, while a shooting death is murder).
Satisfied, the Sheas depart, though not (immediately) to their home dimension; their pursuit has been costly, and they need to return their rented flier to Zodanga to recover their deposit on it, and resell the purchased thoats they had left there.
Previous venues were generally based on mythology or pre-modern fantastic literature; these were depicted faithfully according to the original sources, and much of the action involved puzzling out and becoming proficient in the magical systems holding sway in them.
In the most notable instance, the Burroughs works Malambroso is found to have read consist of contemporary paperback copies in addition to the editions available earlier in the century, and the Sheas too appear familiar with the later versions.