This root has a lengthy history in Tolkien’s writing. It first appeared as ᴱ√HIL, unglossed but with derivatives having to do with children and offspring (QL/40); in this sense it may have reemerged later as the root √KHIN “child” (PE17/157; WJ/403). In the Gnomish Lexicon of the 1910s, the root appeared as χili with derivatives like G. hiltha “youth”, G. hilwed “adolescent”, G. hilm “posterity”, and G. hilmir “heir” (GL/49); the words for “heir” were also based on √KHIL in Tolkien’s later writing.
The root reappeared in The Etymologies of the 1930s as ᴹ√KHIL “follow”, its most notable derivative being ᴹQ. Hildi “followers, mortal men” as the second (following) race that were the children of Eru (Ety/KHIL). In later writings this name for Men became Q. Hildor “Followers” (S/103). The root √KHIL “follow” continued to appear in Tolkien’s later writings (PE17/18, 101, 157; WJ/387).
In The Etymologies ᴹ√KHIL had no Noldorin derivatives, and in the Quendi and Eldar essay from 1959-60 Tolkien said “the stem ✱KHILI ‘follow’ was not current in Sindarin” (WJ/387). Elsewhere, however, it is clearly evident as the basis for several Sindarin words, such as echil “follower(s)” (WJ/219) and Eluchíl “Thingol’s Heir” (S/188). It was also used with the sense “heir” in the phrase: Q. sinomë maruvan ar Hildinyar tenn’ Ambar-metta “in this place will I abide, and my heirs (hildë 1st-person-possessive plural), unto the ending of the world” (LotR/967), connecting back to its earliest meaning.
This root and its variants were the basis for “mist” words for much of Tolkien’s life. It first appeared as ᴱ√HISI with derivatives like ᴱQ. híse “dusk” and ᴱQ. hiswa “dim, fading” (QL/40), and as an element in ᴱQ. Hisilóme which was glossed “Shadowy Twilights” in the earliest Lost Tales (LT1/112). Thus the early root might have meant “✱dusk, dimness, shadow”. The root was probably also an element in the Gnomish equivalent Hithlum from this period (GL/20), perhaps the result of the sound change whereby [[g|[s] became [θ] before [l]]] in Gnomish.
The sense “haze” and “mist” for ᴱQ. híse first appeared in drafts of the Oilima Markirya poem (PE16/62, 75). In The Etymologies of the 1930s Tolkien gave this root as ᴹ√KHITH with variant ᴹ√KHIS and the gloss “mist, fog”; ᴹ√KHIS was listed first but all the actual derivatives were from ᴹ√KHITH (Ety/KHIS). The root appeared again in Notes on Galadriel’s Song from the late 1950s or early 1960s as √KHIΘ “mist” (NGS, PE17/73).
Tolkien’s continued use of Q. Hísilómë and (Northern) S. Hithlum throughout his life testifies to the enduring nature of this root, though it seems to have shifted in sense from 1910s “✱shadow” to 1930s “mist”, and from s to th.