For you they call, the swaying mass, their eager faces turning; (12)
It’s important to consider whether the crowd is really cheering for the captain himself, or for the success of the mission. (Or maybe this ship is filled with discount sneakers.) Clearly, the speaker is encouraging us to see the captain as the focal point for the crowd's admiration.
Here Captain! dear father! (13)
With these apostrophes, the speaker encourages enthusiastic admiration from the more than just the people on the shore. It's as though the entire country should spring to life in applauding the captain.