Why does the Captain allow Leggatt to stay and then hide him in "The Secret Sharer"?
In "The Screct Sharer," the captain senses an inexplicable connection to the man floating alongside his ship: "The self-possession of that man had somehow induced a corresponding state in myself....A mysterious communication was established already between us two...."The captain feels that Leggatt is his "double...other self," a reflection of his own being in appearance and size. When Leggatt explains why he swam to the ship, the captain declares, " I saw it all...as though I were myself inside that other sleeping suit."
Worried that the chief mate will come back on deck and see a "confabulation" of the captain with his "own gray ghost," the captain/narrator hides Leggatt in his L-shaped quarters, for it would be extremely difficult for him to explain his harboring of a murderer, let alone one with whom he feels such communion. Like Leggatt, the captain himself is a stranger on his ship, having been appointed without knowledge of the crew or ship, so he feels that it would take "very little to make [him] a suspect person in the eyes of the ship's company." (Leggatt is later described by the captain of the other ship as "not the sort" for that ship.)
Leggatt, too, senses the affinity, "as if you had expected me" he tells the captain. Later, after Leggatt is hidden for a time, the captain feels that he is the "secret sharer" of his life and cannot, therefore, reveal him.