A verb for “to strive, ✱try” based on the root √RIK in notes from the 1960s (PE17/167). As suggested by Christopher Gilson, this appears to be a draft of Tolkien’s attempt to define the phrase “try harder” in Quenya (ultimately á ricë amrícië). This Sindarin verb has a number of difficult-to-interpret forms. The base verb was given as {reitha >>} raitha, cognate to Q. rihta and thus probably derived from ✶riktā-. However the expected result of primitive ✶riktā- would be S. rítha- or ritha- because of how spirants vocalized and became vowels, so that [ikt] > [ixθ] > [īθ] > [iθ]; compare [N.] critha- “reap” < ᴹ✶k’rikta- (Ety/KIRIK).
Indeed, Tolkien gave several inflicted forms of this verb, all showing ritha-: rithant, rithas, rithessin, rithanen, apparently various transitive and intransitive past forms. Perhaps the uninflected verb form {reitha >>} raitha indicates some kind of a-affection occurring only in the uninflected verb form: [-ikta] > [-ixθa] > [-exθa] > [-eiθa], but if so the expected result would be the deleted {reitha} and not raitha, since [[s|[ei] > [ai] only in final syllables]] in Sindarin.
Neo-Sindarin: Given the rather tenuous nature of this verb, various Neo-Sindarin alternatives have been proposed, including ᴺS. rítha- by Elaran and ᴺS. rig- by myself [Paul Strack] as a direct cognate of Q. ric- “try”. However, I have gradually become more comfortable using S. ritha- as given by Tolkien, since I retain the use of some similarly derived Noldorin verbs such as [N.] critha- “reap” and ᴺS. ritha- “jerk, twitch, snatch” [from N. rhitha-].
This root first appeared as unglossed ᴹ√RIG in The Etymologies of the 1930s with derivatives like ᴹQ. ríe/N. rhî “crown” and ᴹQ. rína/N. rhîn “crowned” (Ety/RIG). The root was then altered to ᴹ√RIƷ (EtyAC/RĪ). A similar root √RIK with derivation ✶riknā >> Q. rína (all unglossed) appeared in the first layer of composition for the Outline of Phonology from the early 1950s, but this section was revised in green ink around 1970 and the root did not appear in the revisions (PE19/85-86 and note #79).
The root √RIG appeared a number of times in Tolkien’s writings from the 1950s and 60s, variously glossed “wreath, garland, crown” (PE17/59), “twine” (PE17/182), and “twine, wreathe” (PM/347), but √RIƷ “wind about, wreathe” also appeared in notes on the names of Galadriel and Celeborn from 1968 (NM/349, 353). Thus it seems Tolkien vacillated between √RIG and √RIƷ with a brief aside to √RIK in the early 1950s.