Next, when I cast mine eyes and see That brave vibration each way free; O how that glittering taketh me!
This poem's all Julia, all the time. The second stanza deals with—you guessed it—this lady and her threads.
The speaker tells us that when he looks ("cast mine eyes") at the vibration, the glittering moves ("taketh") him.
Of course we can't be sure what he's talking about when he says "vibration," but our best guess is that he's referring to the way her clothes shake and shimmer as she moves.
Mine here is just another, old fashioned way of saying my, and free means being able to move in any direction.
Taketh me means something like moves me or captivates me, like when we say, "the teacher was very taken with you." That means you've really got the teacher's attention.
So, to paraphrase, our speaker is saying that when he looks at Julia, and sees how her clothes shimmer as she moves, he's totally mesmerized. She's so very pretty.
Note how the speaker describes Julia's clothes in three different and strange ways: as a liquid, as a vibration, and as a glittering. These clothes seem much more than your average garments. They almost have a life of their own.
What's the deal with this speaker and Julia's outfit? Why's he so obsessed?
Oh, and before we forget: this stanza follows the same all-too fascinating rhyming pattern of the first stanza, making the entire poem's rhyme scheme, AAA BBB.