Tolkien used a similar set of forms for “(a)cross” for Elvish throughout his life. The earliest of these was the unglossed root ᴱ√TARA⁽⁾ in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. tara- “cross, go athwart, cross rivers” and ᴱQ. tarwe “cross, crucifix” (QL/89). In QL Tolkien gave a Gnomish form tor, but the Gnomish Lexicon itself had derived forms like G. taru “cross; crossing”, G. trantha- “to cross” and G. trath “passage, ford” (GL69, 71). The forms G. adr(a)/ᴱQ. arta “lying athwart; situated on far side” are clearly related (GL/17).
There was another unglossed root in the Qenya Lexicon: {ᴱ√SAŘA >>} ᴱ√SARA with derivatives like ᴱQ. sara- “saw”, ᴱQ. sarat “plank”, and ᴱQ. sarno “table” (QL/82). Gnomish forms G. sard “table” vs. G. thar- “saw (up)” may represent a blending with another root ✱ᴱ√ÞARA (GL/67, 71). However, Tolkien compared G. sard to G. thrad [< ✱s(a)rat-?] (GL/67), whereas G. thrad “a board, shelf” was deleted from underneath G. thar- (GL/71). Perhaps this means there was a conceptual shift of {ᴱ√SARA >>} ✱ᴱ√ÞARA, though G. thrad “plank, board, shelf” was retained undeleted elsewhere in the document (GL/73).
As a later entry to The Etymologies of the 1930s, Tolkien gave the root ᴹ√THAR “across, beyond” serving as the basis for the names N. Thar-gelion (“Land beyond Gelion”) and N. Thar-bad with an unclear gloss, probably “Crossway” (Ety/THAR). The root √ÞAR appeared in a list of Sindarin words associated with Definitive Linguistic Notes (DLN) from 1959, where it served as the basis for words like S. athrad “crossing” and prefix S. athra- in words like S. athrabeth “conversation (interchange of words)” (PE17/14); in this note Tolkien specified that the root √ÞAR was not found in Quenya, but the root does appear to be an element in later Quenya words like 1972 Q. Mondósar “Oxford” (DTS/70).
Note that the root √THAR appeared a few other times in Tolkien’s later writings with a different meaning: ᴹ√THAR “stand” in the Quenya Verbal System (QVS) from 1948 (PE22/126) and √THAR “vigour” (another Sindarin-only root) in an explanation of the name S. Thranduil in a list of roots from 1959 (D59: PE17/187).
Neo-Eldarin: For purposes of Neo-Eldarin, I would assume “across” is the main meaning of this root. However, I would ignore Tolkien’s 1959 statement that the root was not found in Quenya in order to salvage early words from ✱ᴱ√ÞARA, with the verbal sense “saw” = “(cut) across” and from this sense deriving words like “plank” and “table”.
An “older and simpler name” of the Vala Oromë in some linguistic notes for the early 1950s (PE21/82). Its meaning is unclear.