In "Ulysses," by Alfred, Lord Tennyson, how does the line "There is the port; the vessel puffs her sail" (and onward) relate to discovery? 

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huntress eNotes educator| Certified Educator

You refer, I take it, to the entire last stanza of the poem. In order to understand how this stanza relates to discovery, you need to understand the context of the poem and the beliefs of the Greeks. 

Odysseus (Ulysses here) fought with Achilles (a half-god) at the siege of Troy, and had ten years of adventures on his way home to Ithaca from the war. While his goal was to get back home to his wife and son and kingdom in Ithaca, he enjoyed the challenges presented to him along his journey. For example, he was warned that no man had ever heard the legendary Sirens sing and live to tell the tale, so he commanded his men to block their ears with wax, tie him to the mast, and row past the sirens so that he could hear. He loved his homeland, but was addicted to adventure and discovery. 

The Greeks believed that if they sailed far enough, they could reach The Happy Isles where their friends and heroes lived in infinite summer, their version of heaven. 

In this poem, Ulysses has returned home and discovered that he is unhappy, unfulfilled: "Match'd with an aged wife, I mete and dole / Unequal laws unto a savage race, / That hoard, and sleep, and feed, and know not me." He's already comparing his life of adventure to the boredom that home life is for him. All these people know--these people who've never left their place of birth--is saving up food and provisions for the winter, eating, and sleeping. They have no way of understanding him, so he has few friends and no one he can talk with except the men who might also set sail with him, to leave and have adventures until they die. 

So in the stanza you refer to, Ulysses turns to the men who've sailed and discovered with him. He's suggesting that old age shouldn't stop them from still discovering new worlds, living the life they love. They aren't stranded here in domesticity: 

Death closes all: but something ere the end,
Some work of noble note, may yet be done,
Not unbecoming men that strove with Gods.
Death, in other words, will end everything, but there's still so much we can do before we die. We may do so many noble deeds, deeds that are worthy of men who fought gods and fought with gods. 
He knows, perhaps, that his men are torn. Perhaps they aren't as enthused as he to leave their homes and families and to again sail into the sunset. This is a motivational speech. He says: "
Come, my friends, / 
'T is not too late to seek a newer world." He wants more adventure. (He's a bit of an adrenaline junkie by now, I think.) He's also driven by curiosity and knowledge. He wants to learn all he can before he dies (a lesson to us all). 
He encourages his men by listing what they may yet live to see and learn before they die: 
It may be that the gulfs will wash us down:
It may be we shall touch the Happy Isles,
And see the great Achilles, whom we knew.
In other words, yes...we may capsize or be washed overboard and drown. Or...we may glimpse heaven and again have the chance to see and perhaps speak with Achilles, a legendary fighter and a friend. We don't know what we'll find, but life lies in discovery.
They are, he says, getting old, and not capable of the great feats they one were. They are "Made weak by time and fate, but strong in will / To strive, to seek, to find, and not to yield." He wants them to join him in his lifelong question for discovery--"to seek, to find"--regardless of the obstacles ahead, and never to yield (to an easy, sedentary, unfulfilling life, or to their own advancing years, where they grow weaker in body but not in spirit).