Ai! Lá polin saca i quettar!
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This root appeared a number of times in Tolkien’s writing over the years, but never with the same meaning. In the Qenya Lexicon of the 1910s, unglossed ᴱ√LUKU appeared with derivatives like ᴱQ. lúke “slime” and ᴱQ. lukso “mud” (QL/56). The Gnomish words G. ûg “mud” and G. ûgrin “muddy” in the contemporaneous Gnomish Lexicon may be related, but if so also indicate a shift in the root to ✱ᴱ√UKU (GL/74).
In The Etymologies of the 1930s the root ᴹ√LUK “magic, enchantment” appeared with derivatives like ᴹQ. lúke “enchantment” and N. lhûth, and the root served as the basis for the name Ilk. Lúthien, translated as “Enchantress” (Ety/LUK). However, in later writings the name S. Lúthien was given a new etymology as a feminization of S. lûth “blossom, inflorescence” (PE17/15).
The root √LUK itself reappeared in notes from around 1968 with the gloss “haul, drag”, serving as the basis for Q. lunka “heavy transport wain (wagon)” (PE17/28; VT43/19). This sense of the root might have an earlier origin, since the verb ᴱQ. luk- “pull” in Early Qenya word lists from the 1920s has a similar meaning (PE16/134).
Another set of possibly related forms are Q. lucassemmar, Q. luciemmar, or Q. luhtammar “✱our debts, our trespasses” from Quenya prayers of the 1950s, as suggested by Wynne, Smith, and Hostetter (VT43/19). These appear to be derived from √LUK, but don’t seem to be connected to any of the attested meanings of this root. In any case, these words for “trespasses” were replaced in later versions of the prayers, becoming Q. rohtammar >> Q. úcaremmar (VT43/19).
Neo-Eldarin: For purposes of Neo-Eldarin, √LUK “haul, drag, ✱pull” is probably the most enduring meaning of this otherwise variable root, but the sense ᴹ√LUK “magic, enchantment” is also very popular, being the basis for some of the better known Elvish words for “magic”. I personally retain both senses, with “magic” by way of analogy for “pulling” on the physical world to affect change. There is a similar analogy to “breath” for the “emission of power (of will or desire)” by analogy with breath fogging a cold surface; see the entry on Q. súlë for discussion. However, this interpretation of √LUK is pure invention on my part to justify retaining the 1930s words for magic.