The second person singular in the Lord of the Rings

In Appendix F to The Lord of the Rings, Tolkien says:

The Common Speech, as the language of the Hobbits and their narratives, has inevitably been turned into modern English. In the process the difference between the varieties observable in the use of the Westron has been lessened. Some attempt has been made to represent these varieties by variations in the kind of English used; but the divergence between the pronunciation and idiom of the Shire and the Westron tongue in the mouths of the Elves or of the high men of Gondor was greater than has been shown in this book. Hobbits indeed spoke for the most part a rustic dialect, whereas in Gondor and Rohan a more antique language was used, more formal and more terse.

One point in the divergence may here be noted, since, though often important, it has proved impossible to represent. The Westron tongue made in the pronouns of the second person (and often also in those of the third) a distinction, independent of number, between "familiar" and "deferential" forms. It was, however, one of the peculiarities of Shire-usage that the deferential forms had gone out of colloquial use. They lingered only among the villagers, especially of the West-farthing, who used them as endearments. This was one of the things referred to when people of Gondor spoke of the strangeness of Hobbit-speech. Peregrin Took, for instance, in his first few days at Minas Tirith used the familiar form to people of all ranks, including the Lord Denethor himself. This may have amused the aged Steward, but it must have astonished his servants. No doubt this free use of the familiar forms helped to spread the popular rumour that Peregrin was a person of very high rank in his own country.

In one or two places an attempt has been made to hint at these distinctions by an inconsistent use of thou. Since this pronoun is now unusual and archaic it is employed mainly to represent the use of ceremonious language; but a change from you to thou/thee is sometimes meant to show, there being no other means of doing this, a significant change from the deferential, or between men and women normal, forms to the familiar.

I believe that this table displays all the uses of thou, thee (including the dialectal form 'ee), thy, and thine in the text of The Lord of the Rings:

 I. 2    Ted Sandyman talking to Sam: dialectal
 I. 3    The Gaffer talking to a Nazgul: dialectal
 I. 3    Elvish song to Elbereth: poetic
 I.12   Troll Song: dialectal
 II. 8   translation of Namarie: poetic
 III. 4  Ent/Entwife song: poetic, intimacy
 I. 5    Galadriel to Aragorn (via Gandalf): poetic
 III. 5 Galadriel to Legolas (via Gandalf) : poetic
 III. 5 Galadriel to Gimli (via Gandalf): ceremony
 III. 6 Eowyn to Theoden, bearing wine: ceremony
 IV. 3 Gaffer to Sam (in memory): dialectal
 IV. 5 Faramir apostrophizing dead Boromir : ceremony
 V. 2  Arwen to Aragorn (via Halbarad): ceremony
 V. 2  Isildur to the King of the Dead (told by Aragorn): contempt
 V. 2  Eowyn to Aragorn: intimacy
 V. 6  Witch-king to Eowyn : contempt
 V. 7  Denethor (in madness) to Gandalf : contempt
 V. 10 Mouth of Sauron to Aragorn and Gandalf: contempt
 VI. 5 Aragorn to Faramir: ceremony
 VI. 6 Aragorn to Eowyn: intimacy
 VI.8  Sam to Mr. Cotton: dialectal

Note that except for the characters in the Troll Song, who are dialect speakers, there is not one instance of two people in conversation addressing one another with "thou".