À la Dante, Eliot must have been intrigued by the mystic 3.
"Here is the man with three staves"
London Bridge is falling down falling down falling down
Poi s’ascose nel foco che gli affina
Quando fiam ceu chelidon—O swallow swallow
Le Prince d’Aquitaine à la tour abolie
These fragments I have shored against my ruins
Why then Ile fit you. Hieronymo’s mad againe.
Datta. Dayadhvam. Damyata.
Shantih shantih shantih
Then at dawn we came down to a temperate valley,
Wet, below the snow line, smelling of vegetation;
With a running stream and a water mill beating the darkness,
And three trees on the low sky,
And an old white horse galloped away in the meadow.
In Hindu belief, the mystic 3 represents "Om", an emblem of cosmic spirit which in its formless aspect is the cosmic space which is all-pervasive -- there is nothing that is not subsumed in it. And now a piece of sheer whimsy. Eliot ends TWL with the Upanishadic incantation of "Shantih", leaving an all-too-conspicuous space before it. This could be deliberate, tacitly assuming an "Om" there -- so that those who know will know.
BTW, Eliot's use of 3, somehow, always reminds me of Coleridge's vision of a poet in "Kubla Khan":
"Weave a circle round him thrice,
And close your eyes with holy dread,
For he on honey-dew hath fed
And drunk the milk of Paradise."
According to Grover Smith, Eliot admitted to being temperamentally a romantic, and only 'in tendency' a classicist.
He abhorred the gap, writes Smith, between the actual and the ideal.