The Chair
What Chair? I suppose it must be "The Chair she sat in, like a burnished throne." How much explanation is appropriate here? I don't think the quotation is quite as universally recognizable as "April is the cruellest month" or (thanks to Iain M. Banks) "Consider Phlebas". And I'm sure we are not intended to produce a literary essay on the start of the second section of The Waste Land"; in any case Empson's analysis of the verbal complexities of the poetry is comprehensive.
We could consider if there are parallels between Enobarbus and Tiresias. Enobarbus shifts from being the enthusiastic follower of Antony, whose central speech is the analogous description of Cleopatra ("the barge she sat in..."), to abandoning Antony before the end. Tiresias, the blind trans-sexual seer, is, Eliot informs us, "the most important personage in the poem", and that "what Tiresias sees is the substance of the poem". It is, at least, a complex way of telling us that things are going to get worse before they finally fall apart. (It may be comforting that in Little Gidding, Eliot shaped an optimistic view.)
One oddity about the "game of chess" that provides the title to the section, is that Eliot's note refers to the chess game in Middleton's Women beware Women (an extensive scene where the game is reflected in the plot). But the Waste Land also alludes to The Tempest in which Ferdinand and Miranda are discovered playing at chess.
So, is the speaker Tiresias, or Eliot's compound male protagonist, in which Ferdinand is specifically included? The passage is a splendid description, but it is a description of artifice - "strange synthetic perfumes" - "troubled, confused, and drowned the sense". Miranda is, however, a type of naivety.
The speaker could be Eliot himself, which ought to be the simplest choice. But since virtually every poem up to the Waste Land, and much of the Waste Land itself, is written in the voice of a fictional persona, it is not an obvious conclusion. Perhaps we should start by asking who is the subject of the passage. We see a woman who in some way parallels Cleopatra, engaged in leisurely preparations before a mirror. Is this Gertrude, painting herself an inch thick? Although Eliot's Prufrock persona was not Prince Hamlet, nor was meant to be, we do know that Eliot's marriage was not happy.
Another look at Enobarbus, at his speeches before the gushing description of Cleopatra, reveals him to be indifferent, even hostile, to women. He suggests to Antony that the death of Fulvia, Antony's earlier wife, simply presents him with an opportunity to pursue other women. Can that indifference be taken to imply that Eliot's speaker is some subconscious part of Ferdinand (who is "not wholly distinct" from less attractive voices) viewing a future time when Miranda is not wholly distinct from Cleopatra)?
Despite the attractive verse, the implied attitudes are as negative as any in The Waste Land. And the Chair she sat in corresponds to that of the poet, which may in this case be the seat of the scornful.
But in all this I could be mistaken, and it may be that the title actually refers to the largest fence in the Grand National.