When I was shown the charts and the diagrams, to add, divide, and measure them; (line 3)
All those charts and figures are like toys compared to the reality that they are supposed to represent: in this case, the stars. To emphasize this point, Whitman doesn't use the word "stars" throughout the first half of the poem, even though we know that's what the astronomer must be lecturing on.
ranged in columns (line 2)
The astronomer tries to organize the outside world within set boundaries. You still wouldn't know by this point that the poem has anything to do with nature.
When I, sitting, (line 4)
Everything in the first half of the poem is meant to contrast with the second half. Whitman the poet loved to walk, and he loved the open road. He wasn't a sitter, no sir. So obviously this situation can't last very long.