ᴱ√KAŊA “weave, twine”
A root appearing in the Qenya Lexicon of the 1910s as ᴱ√KANGA “weave” with various derivatives of similar meaning (QL/45), but the actual root probably had medial Ŋ as with ᴱ√KAŊA “twine” appearing later in that same document (QL/98). There are a number of probably-related forms in the contemporaneous Gnomish Lexicon starting with either cang- or cing-, such as G. cang “tangled”, G. cingra “plaited”, and G. cing(win) “spider” (GL/25-26). There are no signs of this root in Tolkien’s later writing, but I think it is worth positing a Neo-Eldarin root ᴺ√KANGA “tangle” to salvage various Gnomish words having to do with tangles and confusion.
This root was established as the basis for “four” very early, though the earliest known Elvish word for “four” was actually ᴱQ. nelde from the Qenya Lexicon of the 1910s (QL/65), which became “three” later on (PE14/49). In the Gnomish Lexicon written soon after, the Gnomish word for “four” was G. cant (GL/25), and by the Early Qenya Grammar of the 1920s, the Qenya word likewise became ᴱQ. kanta “four” (PE14/49, 82). The Quenya word kept this form thereafter, and the Noldorin form became N. canad in The Etymologies of the 1930s, where the root ᴹ√KANAT “four” explicitly appeared for the first time (Ety/KÁNAT). The words and root for “four” remained the same thereafter (VT42/24-26; VT47/15-16; VT48/10), with occassional minor (and transient) variations such as √KENET (VT47/41).
ᴹ√KAP “leap, [ᴱ√] spring”
This root appeared in The Etymologies of the 1930s glossed “leap” (Ety/KAP), and was simply a later iteration of ᴱ√KAPA “leap, spring” from the Qenya Lexicon of the 1910s (QL/45). The root appeared in various other places in the 1920s (PE14/66), 30s (PE19/42) and 40s (PE22/102), always with the same meaning. The root itself did not appear in Tolkien’s later writing, but his continued use of derivatives like S. cabed “leap” (S/224) and S. cáfru “*flea” < ✶kamprū (PE17/131) indicate its continued validity.
√KAR “do, make, build, [ᴹ√] construct”
Tolkien introduced the root √KAR with the sense “do, make” very early, and it retained this form and meaning for his entire life. It appeared as ᴱ√KARA “do, make” in the Qenya Lexicon of the 1910s (QL/45), as ᴹ√KAR “make, build, construct” in The Etymologies of the 1930s (Ety/KAR), and in numerous other places in various notes, including a last known appearance in verbal notes from 1969 as √KAR “do” (PE22/155). Though its exact set of derivatives varied over time, the root itself was extremely stable in Tolkien’s mind.
√KARAK “[ᴹ√] sharp fang, spike, tooth”
Christopher Tolkien gave this root as carak- in the Silmarillion appendices as the basis for Q. carca/S. carch “fang” along with various related words (SA/carak). Its origin dates all the way back to the earliest version of the language: its first iteration was (unglossed) ᴱ√KṚKṚ in the Qenya Lexicon of the 1910s, already the basis for ᴱQ. karka/G. carc “fang” (QL/48; GL/25), though its other derivatives were more variable in form due to the vagaries of the phonetic developments of syllabic ṛ in Early Qenya and Gnomish. After Tolkien dropped syllabic consonants from the vowel system of primitive Elvish, the root became ᴹ√KARAK “sharp fang, spike, tooth” in The Etymologies of the 1930s (Ety/KARAK). The frequent appearance of its derivatives in later writings indicate its continued validity.
This root appeared in The Etymologies of the 1930s glossed “red” (Ety/KARÁN), a later iteration of ᴱ√KṚNṚ of the Qenya Lexicon of the 1910s of the same meaning, but with syllabic ṛ (QL/48). Its main Quenya derivatives, Q. carnë, retained the same form throughout Tolkien’s life, but its Gnomish forms G. carn(in) “scarlet” and G. crintha “rosy, pink” (GL/25, 27) became N. caran “red” in the 1930s, and retained that form thereafter.
√KARAP “*talk, speech”
The root √KARAP appeared with various forms and meanings throughout Tolkien’s life. Perhaps the earliest iteration was ᴱ√KᴬRPᴬR [KṚPṚ] “pluck” from the Qenya Lexicon of the 1910s (QL/45), with derivatives in the contemporaneous Gnomish Lexicon as well such as G. carp “bundle, bunch” and G. crib- “gather, pluck” (GL/25, 27). The verb form ᴱ✶kṛp- > ᴱQ. karpe “pluck” reappeared in the Early Qenya grammar of the 1920s (PE14/58).
The root ᴹ√KARPA appeared unglossed in the first version of Tengwesta Qenderinwa (TQ1) as an example of a KALTA-stem root, but whether it was related to earlier √KṚPṚ is unclear. Possibly also related is N. carab “hat”, appearing in N. Amon Carab an earlier name of S. Amon Rûdh.
Finally, the root √KARAP appeared in notes probably dating to the early 1960s, serving as the basis for various “speech” words such as Q. carpa-/S. carfa- “talk, speak, use tongue”, but that root was probably replaced by √PAKAT (PE17/126). Given the muddled history of this root, I would mostly avoid its use for purposes of Neo-Eldarin.
The root for “head” was established very early in Tolkien’s Elvish languages, appearing in the Qenya Lexicon of the 1910s as ᴱ√KASA “head” (QL/45), though in this period its Qenya derivative was ᴱQ. kar (kas-) because final [s] became [r] in Early Quenya (PE12/26). It had derivatives in the contemporaneous Gnomish Lexicon such as G. cas “head, skull” (GL/25), a word that reappeared in Early Noldorin word lists of the 1920s as ᴱN. cas “skull” (PE13/140).
The root ᴹ√KAS “head” reappeared in The Etymologies of the 1930s, still with the form ᴹQ. kár (kas-) “head” (Ety/KAS), but Tolkien eventually abandoned the Early Qenya phonology and the Quenya form became Q. kas after some vacillation (PE19/103). The root √KAS “head” continued to appear frequently in Tolkien’s later writing (PE17/114; PE21/70; VT42/12).
√KAT “shape, [ᴹ√] make”
The root ᴹ√KAT “shape” appeared in The Etymologies of the 1930s with derivatives ᴹQ. kanta- “to shape”, ᴹQ. kanta² “shaped”, and N. echad- “fashion, shape” (Ety/KAT). All these derivatives reappeared in Tolkien’s later writings, though Q. canta was more typically used as the noun “shape” (PE17/175; PE18/84, 90). The root appeared frequently in both the first and second version of Tengwesta Qenderinwa as an example of a biconsonantal root (TQ1: PE18/34, 46, 62; TQ2: PE18/84-85, 87, 89-90, 95).
This root was primarily used as the basis for the word Q. coa “house”, which first appeared (without the root) in the Quendi and Eldar essay of 1959-60 (WJ/369). The root √KAW “shelter” appeared in various etymological notes from the mid-to-late 1960s (PE17/107-108, 164; VT47/35). The root √KAWA also appeared in the 2nd version of the Tengwesta Qenderinwa written around 1950, but there it was unglossed and had no glossed derivatives, so whether it meant “shelter” in the early 1950s is unclear.
The only published root with form similar to √KAWA prior to 1950 is ᴱ√KAẆA “stoop” from the Qenya Lexicon of the 1910s (QL/45), also appearing as kava- or cava- in the contemporaneous Gnomish Lexicon (GL/25, 27). The Ẇ is Tolkien’s usual representation of derivatives of ancient labialized velar spirants [ɣʷ] or [xʷ] (PE12/15-16). The derivatives of this root included words like ᴱQ. kauko/G. caug “hunchback” and ᴱQ. kawa-/G. cam(m)a- “bow”, so it seems to have no connection to later √KAW other than its similarity in form.
√KAWAK “*caw, croak”
This (hypothetical) onomanopoetic root served as the basis for primitive forms ✶k(a)wāk “crow” from the Quendi and Eldar essay of 1959-60 (WJ/395) and ✶kāwāk “frog” in notes from the late 1960s (VT47/36). These same late 1960s notes also mention onomanopoetic kā “crow” as a homophone of kā “house” (elsewhere derived from √KAW). Thus the root probably meant something like “caw, croak”.
The root √KAWAK is probably a later iteration of the root ᴱ√QAHA or ᴱ√QAQA from the Qenya Lexicon of the 1910s, unglossed but with derivatives likes ᴱQ. qá “duck” and ᴱQ. qaqa- “quack, squawk, cackle” (QL/76). This root is probably also the basis for ᴱQ. qaine “wailing” from the phrase ᴱQ. ve maiwin qaine “like gulls wailing” in the ᴱQ. Oilima Markirya poem written around 1930 (MC/213), and so perhaps actually meaning something more like “squawking”.
For purposes of Neo-Eldarin, I think the 1910s derivatives of ᴱ√QA(QA) could be salvaged as derivatives of √KAWAK > *k(a)wa(k), but I think the 1959-60 Q. quáco “crow” is too close in form to late 1960s quácë “frog”, and I recommend using 1930s ᴹQ. korko for “crow” instead. I suspect √K(A)WAK is a Quenya-only root, since phonetic changes (kwa- > pa-) would have ruined the onomanopoetic nature of the root in Sindarin.
√KAY “lie, [ᴹ√] lie down; [ᴱ√] rest, dwell”
Tolkien used this root for “lie (down)” for most of his life. It appeared as ᴱ√KAYA “lie, rest; dwell” in the Qenya Lexicon of the 1910s (QL/46), but in that document there was another root ᴱ√KAMA¹ “lie down”, with the derivative ᴱQ. kama- “to lie down” (QL/44). There is no sign of ᴱ√KAMA¹ being used this way after the 1910s, and in the 1920s Early Qenya Grammar, the verb for “lie down” was kaita- (PE14/58), which in the Qenya Lexicon of the 1910s had the transitive sense “to place” (QL/44).
The root ᴹ√KAY “lie down” reappeared in The Etymologies of the 1930s (Ety/KAY), and again in the Quenya Verbal System of the 1940s as the basis for the verb ᴹQ. kaita- “to lie (down)” (PE22/126). The root continued to appear in Tolkien’s later writings all the way up through the late 1960s, always with the sense “lie” (PE17/72; PE22/156).