√KE/EKE “may (be); have chance, opportunity or permission; it is open”
This root appeared in various notes from the late 1960s as the basis for the particle of uncertainty Q. cé. This particle meant “if” or “maybe” in various contexts, but in notes from 1969 √KE was given the sense “may (be)” and paired with √KWI “suppose”, which was the basis for qui “if” (PE22/158). This can be compared to another paradigm also from 1969 associated with the Ambidexters Sentence where cé meant “if” and it seems the root √keye (with derived verb cíta-) meant “suppose” (VT49/19). Of the two paradigms, I think √KE “maybe”/√KWI “if, suppose” is more useful for the purposes of Neo-Eldarin, but it seems Tolkien’s own thoughts on the subject were in flux.
In notes written in 1967, Tolkien gave what was apparently an inverted form of this root, √ek “it is open”, from which the impersonal Quenya verb ec- “may, can” in the sense “have the opportunity to” is derived (VT49/20). This inverted form is almost certainly related to √KE, as suggested by Patrick Wynne.
√KEL “flow (down or away), run (of water or rivers), go away, [ᴹ√] run away especially downwards or at end; [ᴱ√] ooze, trickle”
√KEL was established as the root for “flow” very early in Tolkien’s Elvish languages, also with the variant vocalic extension √KELU. ᴱ√KELE appeared in the Qenya Lexicon of the 1910s glossed “flow, run” and also “ooze, trickle”, though the latter sense did not appear in later writing (QL/46). It also had a variant ᴱ√KELU elsewhere compared to ᴱ√QEL+U of similar meaning (QL/75). It had derivatives in both Qenya and Gnomish such as ᴱQ. kelu- “flow”, G. celu- “trickle” and ᴱQ. kelu(me)/G. celu “stream” (QL/75; GL/25).
The root ᴹ√KEL reappeared in The Etymologies of the 1930s where it seems to have an added connotation of “flow downwards”, given its gloss “go, run (especially of water), flow away downhill” (Ety/KEL). This more specific meaning to the root appeared in later writings, with glosses such as 1930s “flow, flow away, run (of rivers)” (PE18/58), 1940s “run away especially downwards or at end” (PE22/114), 1950s “go away, flow away or flow down (of water)” (PE18/103), and 1960s “flow (down)” (PE17/157). The u-extension ✶kelu with the (continuative?) sense “flow, well up” remained common throughout all these periods as well (PE18/86; PE22/98, 133, 135).
Starting with the The Etymologies of the 1930s, Tolkien compared this root with etymological variants √KWEL “fade (away), die away, grow faint” and √KYEL “come to an end, cease, run out” (Ety/KWEL, KYEL; PE18/58, 103), and indeed Tolkien used it as one his basic examples of such etymological variations:
There existed in Quenderin 1. √KEL “flow, flow away, run (of rivers)”. Of this simple base, since the initial variation is possible, while the sundóma is the same 2. √KJEL “cease, come to an end”, and 3. √KWEL “fade, die away, grow faint” may be regarded as differentiated variants (second version of Tengwesta Qenderinwa, TQ2, circa 1950, PE18/103).
A similar note appeared in the first version of Tengwesta Qenderinwa (TQ1) from the 1930s (PE18/58). Likewise ✶kelu was one of his main examples of variant vocalic extensions:
This “variant extension” always had the form i or u. It appears in many cases where its original function is no longer discoverable, if indeed that was more than to serve as a euphonic connecting link to affixes. But the added element [u] often appears as a differentiator as in kel¹-u beside kel², and some old verbs have a fixed u as the end of their base (TQ2, PE18/86).
In the Quendi and Eldar essay of 1959-60, it seems that √KYEL “end” was replaced by √TEL “close, end, come to an end” (WJ/411) as indicated by the replacement of 1930s ᴹQ. tyelma “ending” (LR/72) by later Q. telma “conclusion” (WJ/411). In a 1967 note the etymological variant √KYEL seems to have been assigned a new meaning “go down slowly”, which served as the basis for Q. tyellë “grade, a step in a stairway or ladder” (PE17/157).
To summarize, the base root √KEL meant “flow (down)” for pretty much all of Tolkien’s life, usually used with a variant vocalic extension √KELU, and starting in the 1930s it had etymological variants √KWEL and √KYEL, with √KWEL always meaning “fade (away), die” and √KYEL meaning “cease, end” from the 1930s to 40s, but changing to “go down slowly” sometime between the 1950 and 1967 (but probably before the 1st edition of LotR), with “end” being reassigned to √TEL by 1960. See the entry on √TEL for further discussion of those developments.
ᴹ√KEM “soil, earth”
This root was established as the basis for “earth” words early in Tolkien’s writing. It first appeared as ᴱ√KEME “soil” in the Qenya Lexicon of the 1910s, its most notable Qenya derivative being ᴱQ. kemen “soil, earth” (QL/46). The root ᴹ√KEM “soil, earth” reappeared in The Etymologies of the 1930s along with ᴹQ. kén (kem-) or kemen “earth”, as well as various other Quenya and Noldorin derivatives (Ety/KEM). Tolkien’s continued use of Q. cemen and S. ceven for “earth” or “the Earth” in later writings indicates the continued validity of this root.
√KEN “see, perceive, note, [ᴹ√] look at, observe, direct gaze”
Tolkien first introduced this root in The Etymologies of the 1930s as a variant of ᴹ√KHEN “look at, see, observe, direct gaze” along with ᴹ√KYEN (EtyAC/KHEN). In The Etymologies it had no derivatives, but in the Quenya Verbal System it appeared with the gloss “see, perceive” as the basis for the verb ᴹQ. ken- of the same meaning (PE22/103). √KEN “see, perceive” appeared regularly in Tolkien’s writing thereafter (PE17/156, 187; PE22/155; VT41/5).
ᴹ√KEPER “ridge; knob, head, top”
A rejected (Noldorin-only?) root in The Etymologies of the 1930s initially glossed “knob, head, top”, perhaps replacing the also rejected root ᴹ√KOPAR of the same meaning (Ety/KEPER; EtyAC/KEPER, KOPAR). Tolkien changed the gloss of ᴹ√KEPER to “ridge” before he rejected the entry. The most notable derivative of this root was N. ceber in N. Sarn Gebir, whose gloss is unclear but might be “?limestone, -rock”. Despite his rejection of this root, S. Sarn Gebir did appear in The Lord of the Rings (LotR/391) and was in one place translated as “Stone-spikes” (RC/327), so perhaps Tolkien restored the root, though what it might mean is unclear.
A root appearing in the Gnomish Lexicon of the 1910s with variants ᴱ√kerek- and ᴱ√kereχ- and derivatives like G. crech “spittle”, G. crectha- “spit”, G. agrectha- “despise”, and G. agrectharol “despicable” (GL/27). The first of these derivatives reappeared in Early Noldorin of the 1920s as a derivative of ✶kǝ̀rekka along with the Qenya form ᴱQ. rekka (PE13/140). This Qenya form, and the meaning of the Gnomish words from the 1910s, resembles the derivatives of the root ᴱ√RETYE from the Qenya Lexicon of the 1910s such as ᴱQ. retye- “spit” and ᴱQ. retima “despicable” (QL/79). Thus ᴱ√KEREKE may be variant or replacement for ᴱ√RETYE.
In The Etymologies of the 1930s there is a later root ᴹ√PIW “spit” which may have supplanted ᴱ√K(E)REKE, but the derivatives of ᴹ√PIW are only verbal and I think it worth positing the existence of a Neo-Eldarin noun root ᴺ√K(E)REK “spittle” to salvage the Gnomish words, especially those having to do with contempt.
√KETH “enquire of, question, examine something”
This root appeared in 1964 etymological notes as KEÞ [KETH] glossed “enquire of, question, examine something”, with derivatives like Q. ces- “to search, examine (something)”, Q. cesta- “to seek, search for”, and Q. cesya- “to cause interest, (lit.) to cause one to enquire”; the root was initially given as (rejected) KES (PE17/156). Given the root meaning “question”, it is probably related to the earlier verb ᴹQ. kesta- “ask” appearing in Quendian & Common Eldarin Verbal Structure (PE22/97), Quenya Verbal System (PE22/118, 120-122) and Common Eldarin: Verb Structure (PE22/138-139) from the late 1940s and early 1950s.
√KEW “new, fresh; anew, repeated; live of vegetables”
This root appeared as KEWE, KWĒ “live of vegetables” in 1957 Quenya Notes with derivatives Q. quëa “vegetable” and (unglossed) Q. ceula, as well as being an element in Q. laiquë “herb” (PE17/159). The root KEWE reappeared in various notes from the late 1960s with the gloss “new, fresh” and “anew, repeated” where Tolkien connected it to the final element of Q. minquë, which roughly had the ancient sense of “*a new ‘one’ (as in a second round of counting)” (VT48/7-8). In these 1960s notes √KEWE had a variety of derivatives having to do with newness and freshness in Quenya, Sindarin and Telerin.