On January 1, Conseil wishes Aronnax a happy birthday. The new year gets them acting all philosophical; see, they're not exactly sure what a "Happy New Year" would be, really. For Ned, it'd be escape. For Aronnax—and Conseil, since he wants whatever his master wants—it'd be more exploration.
Aronnax keeps himself busy studying, as usual, and a couple of days later, the Nautilus enters the dangerous Torres Strait (between Australia and New Guinea).
As luck would have it, the Nautilus gets stuck on a reef.
Ned gets even more pessimistic. He doesn't think Nemo will be able to get the sub off the rocks, but Nemo assures everyone that they'll be up and running soon.
Seeing as they're already stuck on land, Ned and Conseil convince Aronnax to ask Nemo to let them go ashore.
Surprisingly, Nemo is cool with it. So, the three intrepid adventurers head off to the island in the dinghy, carrying axes and guns.