The summary of Parts II and III take the four men in the open boat from far out at sea to within sight of land, a feat they celebrate with four dry cigars and three dry matches.
Part II opens with the cook, who is bailing out the boat (an important job), expressing gratitude for the on-shore wind that was driving them landward, saying "where would we be" without it. The captain, still in shock from the foundering of his ship, speaks of the reality of their not having much chance now. This brings a shamed silence down. The others hem and haw for hoping for a chance, yet know the "ethics of their condition" prohibited any expression of hopelessness." This is an important thematic moment in the story because it reveals they are struggling for their lives under the auspice of a governing ethic that they intuitively decline to violate.
A grisly and discomfiting canton flannel sea gull tries to alight on the captain's head and in a great show of control and command of will the cook, the oiler, the correspondent keep to their tasks while the captain slowly and carefully waves the gull away with his open hand thus saving his hair and head. Had they behaved otherwise, they'd have shipped water, strayed from their course, overturned the dingy: "because anything resembling an emphatic gesture would have capsized this freighted boat,...."
The oiler and the correspondent row and row "and also row" until the captain spots the lighthouse. All soon see it like the "point of pin." They see they are on course. To keep the boat going forward without swamping with water, the captain tells the cook: "Bail her, cook."
Part III establishes the "brotherhood of men" that now exists in the dinghy. At the start, the three seamen were in a fraternity of seamen and knew the mysterious ferocity of the sea. The correspondent was a guest on the ship and on the sea after the ship foundered; he did not know the ways of the sea. Yet now--after rowing and rowing and rowing some more with the oiler or after the oiler or while the oiler slept or while the oiler rowed while he slept--the correspondent is accepted as one the initiated followers of the sea, part of a brotherhood, one who suddenly and without warning has learned the mysterious fierceness of the sea that they fight to befriend and to conquer.
The lighthouse grows to the size of a "long black shadow on the sea." They realize the lighthouse marks a refuge house, not a rescue station and understand that "[n]one of those other boats could have got ashore" or there would be rescue boats looking for them--they four are the only survivors.
Finding four dry cigars out of eight in the correspondent's top coat pocket and three dry matches, the men--two of whom had let down their make-shift mast and topcoat sail that had blown them so speedily toward land--lit their cigars and puffed optimistically to happy thoughts of rescue and land.
the four waifs rode in their little boat, and with an assurance of an impending rescue shining in their eyes, puffed at the big cigars and judged well and ill of all men.