T.S. Eliot's "mythical method" refers to a technique of modernist writing in which the present is constantly juxtaposed with allusions to elements out of myth and the literature of previous ages. He apparently first coined the term in his review of Joyce's Ulysses, indicating that Joyce had used this method of writing in place of what would conventionally be considered "narrative." Probably the most famous illustration of mythical method in Eliot's own work is "The Waste Land." The whole poem sometimes seems a patchwork of quotations and references which represent the distant past, our roots, and are transformed into a parallel with modern life to illustrate both similarities and differences. The very opening of "The Waste Land" confronts us with a striking paraphrase of Chaucer:
April is the cruelest month, breeding
Lilacs out of the dead land, mixing
Memory and desire, stirring
Dull roots with spring rain.
The Prologue of The Canterbury Tales begins:
Whan that Aprille with his shoures soote
The droghte of March had perced to the roote
And bathed every veyne in swich licour
Of which vertu engendred is the flour;
Eliot takes Chaucer's description of the positive quality of spring and inverts it into a symbol of death and pessimism. Pound's technique employs allusions to the past and to past literature, but in a different way, since his personal style is quite distinct from Eliot's. In the first few stanzas of "Hugh Selwyn Moberley" we see a veritable blitz of quotes, names out of myth, names of past authors, and a direct statement that the speaker feels himself out of sync with the time in which he is living:
For three years, out of key with his time,
He strove to resuscitate the dead art
Of poetry; to maintain "the sublime"
In the old sense.
Pound then gives us a quote from The Odyssey, which some editions show in Greek and others transliterate into Roman script, along with a reference to Penelope, but stating that his (Moberley's) "true Penelope was Flaubert." So we're immediately seeing allusions to myth, quotations from an epic poem in the original language, and a reference to a (relatively) recent author, Flaubert.
Though Pound is clearly employing the mythical method not only in these stanzas but throughout "Hugh Selwyn Moberley" as a whole, his verse does not sound like that of Eliot. In general Eliot's tone is quietly contemplative in expressing his negativism and parallels with the past (to the detriment of the present.) Pound's verse has a manic, angry quality, and in my view is even more difficult to understand than Eliot's. I also tend to think that Eliot's poetry, except for the foreign quotations, is accessible even if one is not necessarily familiar with the texts to which he is alluding. For example:
A crowd flowed over London bridge, so many.
I had not thought death had undone so many.
One does not have to know that this is a paraphrase from Dante's Inferno to understand the point that London, in the modern age, seems to the speaker a city of the dead. Pound's verse is more esoteric, but he often uses a more conventional formal structure, with regular meter and rhyme (though Eliot sometimes does also). Part III of "Hugh Selwyn Moberley" begins:
Turned from the "eau-forte
To the straight head
"His true Penelope
And his tool
Here Pound is quoting his own poetry (the line about Penelope and Flaubert), so the mythical method has become self-referential within the same poem. Arguably, more intense study is required of the reader to understand Pound than even his modernist contemporaries, including his close friend Eliot.