What does the Capatin/Narrator in Conrad's "The Secret Sharer" mean when he says this?
"They had simply to be equal to their tasks; but I wondered how far I should turn out faithful to that ideal conception of one's own personality every man sets up for himself secretly."
This important quote relates explicitly to the way in which the Captain, who is also the narrator of this brilliant short story, is struggling to define himself and also is desperately eager to prove himself as a Captain and as a leader. Consider the way in which the Captain appears to be overwhelmed by the many duties that come with his role. In the quote you have identified, the Captain draws a comparison between himself and his sailors, who have to be "equal to their tasks" and no more, and himself, and in particular to the "ideal conception" that he has of who he is and the set of expectations he has placed on himself. Of course, the story, and in particular the friendship that the Captain strikes up with Leggatt, who functions as a double of the Captain, explores how the Captain manages to come to terms with his natural aggressiveness and how he manages to cope with the expectations he places on himself and the reality of who he is.