A root Tolkien introduced in a late note of unclear date to provide a new explanation for the name of Galadriel and Gil-Galad (PE17/59-60). The second element of N. Gil-galad was originally N. calad “light” (Ety/GIL, KAL), and the name of N. Galadriel was originally associated with trees (TI/246, 249); Galadriel was so spelled (rather than Galadhriel) because in Lord of the Rings drafts Tolkien often represented [ð] as d: compare N. Caradras with S. Caradhras. In notes on the words and phrases in The Lord of the Rings, Tolkien revisited Galadriel’s name, deciding that it, like Gil-Galad, was connected to light, from the root √KAL (PE17/50). But this was also unsuitable, since Galadriel began with a g and could not have undergone soft mutation like the name of Gil-Galad.
The introduction of the root ÑGAL “gleem, sheen” resolved this problem, as ✶Ñ(g)alatā-rigelle would become Galadriel in Sindarin, but the intermediate nasal would be lost in ✱Gil-(ñ)galatā (PE17/59-60). Tolkien mentioned this new etymology in a few other places, with slightly different glosses for the root such as √Ŋ(G)AL “shine clear” (PE17/169), √ÑAL “shine, glitter (applied to light reflected from water, metal, glass, gems, etc.)” (NM/353), and √ÑAL “shine by reflection” (PM/347), the last of these from The Shibboleth of Fëanor from 1968, one of the last detailed discussion of the etymologies of these names.
A root variously meaning “blessed, fortunate, prosperous” (PE17/146) and in some circumstances “healthy” and “good (physically)” (PE17/149, 172) or just simply “good” (PE17/146, 150, 153, 158). It was first mentioned in The Etymologies of the 1930s in association with the root ᴹ√ALAM “elm” to which it might be related “since the elm was held blessed and beloved by the Eldar” (Ety/ÁLAM). In Quenya at least its sense was influenced by √GAL “grow, be healthy, flourish” (PE17/146, 153). At one point Tolkien said “this stem was less used in Sindarin, but occurs in a few old forms”, notably S. elia- “to cause to prosper, bless” and S. alw [alu] “wholesome (PE17/146).
The existence of this root is one of reasons that Tolkien decided to abandon la-negation around 1959, saying “AL, LA have too much to do”. Tolkien’s vacillations on the nature of la-negation might therefore have pushed this root in and out of favor, but it is difficult to tell for certain.