√RŌ/ORO “up(wards); rise (up), go high, mount; [ᴹ√] high, [ᴱ√] steepness, rising”
This invertible root had a long history in Tolkien’s writings. Its earliest iteration was in a pair of roots in Qenya Lexicon of the 1910s: ᴱ√OŘO [OÐO] with derivatives having to do with the “dawn”, and ᴱ√ORO “steepness, rising” with which it was much confused (QL/70). The latter had derivatives like ᴱQ. orme “summit, crest, hilltop” and ᴱQ. orto- “raise” (QL/70), and Tolkien mentioned an inverted variant ᴱ√RŌ or ᴱ√ROHO with derivatives like ᴱQ. róna- “arise, rise, ascend” (QL/80). The contemporaneous Gnomish Lexicon also gave it as in an invertible root ᴱ√rō-, oro with derivatives like G. oros “rising” and G. ront “high, steep” (GL/63, 66).
The root reappeared in The Etymologies of the 1930s as ᴹ√ORO “up, rise, high” and ᴹ√RŌ “rise” (Ety/ORO, RŌ). The root was mentioned very frequently in his writings from the 1930s, 40s, 50s and 60s, generally glossed “rise” or “up(wards)”. Thus the root was very well established in Tolkien’s mind.
ᴹ√ROK “run on foot, *horse”
This root was the basis for Elvish “horse” words starting in the 1930s. It first appeared as unglossed ᴹ√ROK in The Etymologies of the 1930s with the derivatives ᴹQ. rokko/N. roch “horse” (Ety/ROK). The root was given the gloss “run on foot” in a page of roots from the Quenya Verbal System of the 1940s, but that page was rejected. Primitive ✶rokkō “horse” was mentioned regularly in Tolkien’s later writing (Let/282; PE21; WJ/407), though in one place he clarified that it was more specifically a “swift horse for riding” (Let/382).
√ROM “horn noise; [ᴹ√] loud noise”
This root and ones like it were connected to horns and loud noises for much of Tolkien’s life. The earliest iteration of the root was unglossed ᴱ√RAMA in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. rama- “shout, sound loud, bray, blare” and ᴱQ. ran (ram-) “noise” (QL/78-79). G. rum “noise” and similar words from the contemporaneous Gnomish Lexicon may be derived from a variant of this root (GL/66). The root appeared as ᴹ√ROM “loud noise, horn blast” in The Etymologies of the 1930s with derivatives like ᴹQ. róma/N. †rhû “loud sound, trumpet-sound” and ᴹQ. romba/N. †rhom “horn, trumpet” (Ety/ROM); it also had an augmented variant ᴹ√OROM (Ety/ORÓM).
The root √ROM was mentioned several times in Tolkien’s later writings with glosses like “horn noise” (PE17/138), “noise of horn” (PE17/153), and “used of the sound of trumpets and horns” (WJ/400). Starting in the 1930s, the name Q. Oromë was derived from this root, as opposed to the 1910s where ᴱQ. Orome was initially connected to the root ᴱ√OŘO having to do with “dawn” (QL/70-71).
√RON¹ “arch over, roof in”; ᴹ√ROD “roof, cave”
This root first appeared as ᴹ√ROD “roof, cave” in The Etymologies of the 1930s with derivatives like N. rosta- “to hollow out, excavate” and ᴹQ. rondo/N. rhonn “cave”, having instead the sense “domed roof” in Ilk. rond which served as the basis for (at the time Ilkorin) name Ilk. Elrond = “vault of heaven” (Ety/ROD; EtyAC/ROD). In the Quendi and Eldar essay from 1959-60, Tolkien instead had the second element of this name as S. rond “a vaulted or arched roof as seen from below (and usually not visible from outside); a (large) hall or chamber so roofed” as a derivative of *rono “arch over, roof in” (WJ/414).
Neo-Eldarin: For purposes of Neo-Eldarin, I think it best to assume this root was √ROD, because some of its early forms (rosta-) can be derived from this root but not later RON(D)-.
√RON² “solid, tangible, firm”; ᴹ√RUD “*piece of wood”
A root in Quenya Notes (QN) from 1957 glossed “solid, tangible, firm” with derivative Q. ronda “solid, firm” (PE17/183). It had a couple variants: √GRON > S. grond “solid, tangible, firm”, also the name of Melkor’s hammer, as well as √SRON > Q. hrón/S. rhû “matter” and Q. hrondo/S. rhond “body”. The root √SRON appeared again with the gloss “flesh, substance, matter” in etymological notes associated with the essay Of Death and the Severance of Fëa and Hrondo from the late 1950s, along with both Q. hrón “matter” and Q. hrondo “physical body” (MR/231 note #26). However, in the title of this essay hrondo was revised to Q. hroa (MR/217), elsewhere derived from primitive ✶srawā (MR/350); see the entry on √SRAW for further discussion (MR/330).
Regarding S. grond: in The Etymologies of the 1930s this word was derived instead from the unglossed root ᴹ√RUD, which had derivatives ᴹQ. runda “rough piece of wood” and ON. runda > N. grond “club” (Ety/RUD); it also had strengthened variant ᴹ√G-RUD (EtyAC/G-RUD).
Neo-Eldarin: Despite the change of Q. hrondo >> Q. hroa, I think √SRON might be retained in the more limited sense “matter” rather than “flesh”, along with related root √(G)RON “solid” from 1957. As for ᴹ√RUD, it might also be retained, with S. grond “solid; club” being a blending of ᴹ√RUD and √(G)RON.
√ROS “spindrift, spray; [ᴹ√] distil, drip”
This root appeared in The Etymologies of the 1930s as ᴹ√ROS¹ “distil, drip” with derivatives like ᴹQ. rosse “fine rain, dew” and N. rhoss “rain”, the latter an element in N. Celebros “Silver-rain” (Ety/ROS¹). In later versions of The Silmarillion, the name S. Celebros was translated “Foam-silver” (WJ/151), indicating a shift in meaning, though the element still meant “rain” in other later names like S. Silivros “Sparkling Rain” (MR/155) and S. Dimrost “Rainy Stair” (S/220).
Tolkien discussed this root at length in a 1968 essay labeled The Problem of Ros (PM/367-371). He indicated that by this point, the intended meaning of the root √ROS was “spindrift, spray”, but he felt this meaning was problematic due to its conflict in Sindarin with S. ross “red haired” and the similarity of the root to Latin “rōs” = “dew” (PM/368). He then launched into a lengthy discussion formulating a new theory whereby the element -ros was actually Beorian to explain its use in various Beleriandic names, only to remember at the last minute that he had also used the element in Third Age place name S. Cair Andros “Ship of Long Foam”, rendering his alternate theories unviable (PM/371). Presumably at this point the original meaning of the root was restored.
√ROT “delve underground, dig, excavate, tunnel, [ᴹ√] bore; [ᴱ√] hollow; [√]cave”
The earliest iteration of this root was ᴱ√ROTO “hollow” from the Qenya Lexicon of the 1910s, with derivatives like ᴱQ. rotl “cave, hollow” and ᴱQ. rotse “pipe, tube” (QL/80). The primitive root ᴱ√roto also appeared in the contemporaneous Gnomish Lexicon with derivatives like G. rod “tube, stem” and G. †roth “cave, grot” (GL/65). The root reappeared as ᴹ√ROT “bore, tunnel” as a late addition to The Etymologies of the 1930s that Christopher Tolkien omitted from the published version of The Lost Road; it had with derivatives ᴹQ. rotto/N. (g)roth “cave, tunnel” (EtyAC/ROT), and was also an element in the name N. Nogrod (EtyAC/NAUK).
The root appeared as √ROT “cave” in notes on Words, Phrases and Passages in the Lord of the Rings from the late 1950s or early 1960s (PE17/49), as *groto “dig, excavate, tunnel” in the Quendi and Eldar essay of 1959-60 (WJ/414), as unglossed (g)roto in other notes associated with that document (VT39/9) and as rot, s-rot “delve underground, excavate, tunnel” in notes associated with The Shibboleth of Fëanor from 1968 (PM/365 note #56). Thus in later writings the root √ROT had variants √GROT and √SROT.
Neo-Eldarin: For purposes of Neo-Eldarin I would ignore the gloss “cave” which seems to be a loose translation, and stick with the meaning “excavate, tunnel, bore” for the root √ROT; I’d also retain the meaning “hollow” from the 1910s to allow salvaging similar early words from the Qenya and Gnomish Lexicon.