As the basis for “father” words, √AT and its extended form √ATAR date all the way back to Tolkien’s earliest ideas. The root itself did not explicitly appear in the Qenya or Gnomish Lexicons of the 1910s, but forms like ᴱQ. atar, G. †ador “father” indicate its presence (QL/33; GL/17). The root ᴹ√ATA “father” did appear in The Etymologies of the 1930s with derivatives ᴹQ. atar, N. adar (Ety/ATA) and the base √AT(AR) “father” was mentioned again in late 1960s notes on Eldarin Hands, Fingers and Numerals (VT48/19). In this late period, the Elvish words for “father” remained Q. atar and S. adar (PM/324).
Primitive elvish
ara
preposition and adverb. beyond, further than
rā/ara
root. noble, high, royal
at(ar)
root. father
atar
noun. father
ay(ar)
root. sea
as
root. beside
As discussed in the entry for √AR, for a considerable time in Tolkien’s life the basis for the word “and” was the root √AR with the sense “beside”, so that Q. A ar B “A and B” originally had the sense “A beside B”. However, at some point during the writing of the Lord of the Rings he decided that the Sindarin word for “and” was a, making √AR no longer suitable for its etymology.
From this point forward Tolkien toyed with two possible roots for “beside; and”, either √AD and √AS, with another option √ÑAR considered and rejected in 1957 (PE17/169). It seems Tolkien vacillated between the √AD and √AS, so an exact timeline is hard to nail down. Their primary difference would be in the prevocalic form of Sindarin “and”: either edhil adh edain [ada > aða] or edhil ah edain [asa > aha] for “elves and men”. The most detailed breakdown of these two possibilities appeared in Tolkien’s notes on words in The Lord of the Rings, probably written in the late 1950s (PE17/41). In these notes he kept flipping back and forth between ancient asa and ada, though ultimately settling on ada.
However, ah appeared in the title of the document Athrabeth Finrod ah Andreth “The Debate of Finrod and Andreth” most likely written in 1959 (MR/329), and in a 1968 note Tolkien said the primitive form was as with S. ah “and” before vowels and a before consonants (VT43/30). So either Tolkien reversed himself again and adopted √AS, or he continued to vacillate. For purposes of Neo-Eldarin, I think it is best to assume the root was √AS.
One result of the change of √AR >> √AS/√AD is that the Sindarin prefix ar- could no longer mean “beside” as it did in Noldorin. Indeed, in notes on The Rivers and Beacon-hills of Gondor written in 1967-69 he said “Arnen originally was intended to mean ‘beside the water’, sc. Anduin, but ar- in this sense is Quenya, not Sindarin” (VT43/17). This leaves us with no good word for “beside” in Sindarin; at one point I coined a neologism sa for this purpose, but it is a real stretch.
As a final note, these 1950s and 1960s roots were not the first time Tolkien used √AS for something like “beside”. All the way back in the 1910s, Tolkien had the root √AS(A) in both the Quenya and Gnomish Lexicons (QL/33; GL/48) with derived forms like ᴱQ. ar “to, against, next, on (wall)” (QL/33), G. hath- “close to, by, beside, touching” (GL/48), and [maybe] G. art “beside, alongside of” (GL/20), though the last form may be unconnected given the unlikeliness of s > r in Gnomish.
tā/taʒ
root. high, high, [ᴹ√] lofty; noble
This root and ones like it were used for “high” things for much of Tolkien’s life. It first appeared as unglossed ᴱ√TAHA in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. tā “high; high above, high up”, ᴱQ. tahōra or tayóra “lofty”, and ᴱQ. tāri “queen”; it had a variant form ᴱ√TAʕA where the ʕ might be a malformed Y (QL/87). The corresponding forms in the contemporaneous Gnomish Lexicon were G. dâ “high” and G. dara “lofty” (GL/29), indicating the true form of the root was ᴱ√DAHA, since initial voiced stops were unvoiced (d- > t-) in Early Qenya (PE12/17). Primitive forms like ᴱ✶dagá > ᴱN. dâ/ᴱQ. tá “high” in Early Noldorin Word-lists of the 1920s indicates the root continued to begin with D for the following decade (PE13/141, 161).
In The Etymologies of the 1930s Tolkien gave this root as ᴹ√TĀ/TAƷ “high, lofty; noble” with derivatives like ᴹQ. tára “lofty, high”, ᴹQ. tári “queen” and N. taen “height, summit of high mountain” (Ety/TĀ). In Definitive Linguistic Notes (DLN) from 1959 Tolkien gave the root as √TAG or Tā- “high”, and in notes from around 1967 Tolkien gave √TAƷ as the explanation of the initial element of Q. Taniquetil and contrasted it with √TĂR “stand” (PE17/186). In 1970 green-ink revisions to the Outline of Phonology (OP2), Tolkien wrote a marginal note giving √TAƷ > TĀ “high”, but this note was rejected with a statement “transfer to Gen. Structure. No [ʒ] existed in Eldarin” (PE19/72-73 note #22).
This last rejection seems to be part of Tolkien’s general vacillation on the nature and phonetic evolution of velar spirants in Primitive Elvish in 1968-70. For purposes of Neo-Eldarin, I would assume the root form was √TAH or √TAƷ > √TĀ as the basis for “high” words, much like √MAH or √MAƷ > ✶mā was the basis for “hand” words.
khin
root. child
A root appearing in Notes on Names (NN) from 1957 with the gloss “child” (PE17/157), and again in the Quendi and Eldar essay of 1959-60 with the same gloss (WJ/403). It was the basis for the words Q. hína and S. hên “child”, which were probably inspired by the Adûnaic patronymic suffix -hin that Tolkien introduced in the 1940s as part of Êruhin “Child of God” (SD/358), originally an Adûnaic word but later on used in Sindarin (Let/345; MR/330). This root might be a later iteration of the early root ᴱ√HILI from the Qenya Lexicon of the 1910s whose derivatives had to do with children (QL/40). As evidence of this, the Adûnaic word was first given as Eruhil (SD/341).
as(a)
preposition. and
abta-
verb. refuse, deny, say no
an
preposition. to
kalinā
adjective. bright
lā̆
preposition/adverb. beyond
tāra
adjective. high
áse
noun. sunlight
dē
preposition. with
kalat
noun. light
khīnā
noun. child
san-
pronoun. that
An invertible root meaning “noble”, itself an extension of √AR (PE17/147). Given its widespread use, Tolkien did not define this root until quite late. Its first clear mention was in Notes on Names (NN) and Quenya Notes (QN), both from 1957. In NN, Tolkien introduced invertible √ARA/RĀ to give an explanation of the element rod in names like S. Rodon “Vala” and S. Finrod, where Tolkien said:
> S raud “tall, high, lofty, eminent”. √ARA, RĀ. Cf. Q aran “king”. Q arta “high” < árată. S raud < form (a)rā́tă (PE17/118).
Earlier in The Etymologies of the 1930s, the second element of N. Finrod was N. rhaud “metal” (Ety/RAUTĀ), whereas ᴹQ. haran/N. aran “king” was derived from ᴹ√ƷAR “have, hold” (Ety/ƷAR). As for the later root √ARA/RĀ, Tolkien gave a lengthier explanation in QN:
> √AR. ARI-, ARA/RĀ, ARAT/ARAN. Original sense probably seen in adverb/preposition ✱ara/ar/ra, beyond, further than. The stems ARI/ARAN/ARAT mean “good, excellent, noble” - differing from √MAN in stating that any one specimen is “good of its kind”, excels, without necessarily implying that others are bad or marred. Hence ari-, good as prefix, ar/ara/aran as prefixes of excellence especially in royal names, aran king. Q arta noble, arato a “noble”, ráta- excel, surpass. S aran, arod (arāta); or raud excellent, noble, eminent (PE17/147).
Thus all these roots, including the extensions √ARAN and √ARAT, were elaborations on the sense “beyond” from base root √AR. The simple root √AR itself had a lengthy conceptual history; see that entry for details. As for ARA/RĀ, the connection between these forms and nobility seems to be firmly established by the late 1950s and afterwards, with primitive element Ara- “noble” mentioned in The Shibboleth of Fëanor from 1968 (PM/344, 363 note #43), and numerous other mentions of derived forms in documents from this period.