In this poem, Longfellow compares two forms of action, represented by an arrow and a song. The speaker shoots an arrow into the air and it falls to earth, out of sight. What could it symbolize?
As a weapon, with the capacity to cut and kill, it could represent our destructive emotions and behavior. We say a bad word, we spread a rumor, we lie. Our hatred may fly out of sight, but who’s to say there’s no lasting damage?
In the second stanza, the speaker breathes a song “into the air.” A song suggests something carefree and benign. Formless and free, it is the opposite of the arrow, but its destination is similarly unknown.
Does it represent our efforts to celebrate life rather than to damn it? To look for the good in people rather than to condemn them for their flaws? But if we do someone a good turn, is our virtue ever rewarded?
There may be other ways of looking at the arrow and the song, however. After all, the arrow has positive, even heroic connotations of strength of will, resolve, and purpose. (Robin Hood comes irresistibly to mind.)
If the arrow represents the realm of physical action, then the song may, by way of contrast, represent the realm of poetry and art. Falling to earth, falling on deaf ears, it seems horribly ineffectual. (Anyone who’s ever given a poetry reading knows the feeling well.)