√MI/IMI “in, within, [ᴹ√] inside”
This invertible root had the basic sense “in(side)” for all of Tolkien’s life. It first appeared as ᴱ√IMI² “in, into” and ᴱ√MĪ² in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. imi “in, inside” and ᴱQ. mitta- “enter” (QL/42, 61). Deleted Gnomish forms like G. bi “in” and G. bin “into” might be derived from a strengthened form of the root *ᴱ√MBI (GL/21) but Tolkien said the undeleted prefix bi- or G. ba had a Qenya cognate ve (GL/20), so I think these were based on some other (abandoned) root.
Both ᴹ√MI “inside” and its inversion ᴹ√IMI “in” appeared in The Etymologies of the 1930s (Ety/MI; EtyAC/IMI), though the only derivative of the inversion was ᴹ√IMBE “dell, deep vale” (EtyAC/IMI, IMBE). The root or its inversion appeared a number of times in Tolkien’s later writings as well, up into the 1960s (PE17/41, 92; VT47/11, 30).
This root appeared in a late etymology of the name S. Maeglin (“Sharp Glance”) as √MIK “pierce”, along with several other derivatives including the word Q. hendumaika “sharp-eye[d]” (WJ/337). In earlier versions of the tales, the name was given as G. Meglin, but this form of the name was not given a derivation until the 1930s, when N. meglin appeared in The Etymologies as an adjectival form of N. megli “bear” (Ety/LIS). The form of this name became Maeglin in Silmarillion drafts from the 1950s and 60s (WJ/122 note §119), though when Tolkien devised its new derivation isn’t clear. The (unglossed) Quenya word Q. maica appeared in the second version Tengwesta Qenderinwa (TQ2) from around 1950, and it may be related to √MIK “pierce”, but without a translation it is hard to be sure.
√MILIK “*greed, lust”
The unglossed root ᴹ√MIL-IK appeared in The Etymologies of the 1930s, where its shorter form served as the basis for words like ᴹQ. maile/N. moel “lust” and its longer form for ᴹQ. milka/N. melch “greedy” as well as the name ᴹQ. Melko (Ety/MIL-IK), though in later writings Q. Melkor was derived from √MBELEK (PE17/115). As for √MILIK, it reappeared in Common Eldarin: Noun Structure of the early 1950s serving as the basis for S. maelig “wealth, abundance” (PE21/80), apparently in the same general semantic space as 1930s N. melch “greedy” but with a less negative connotation.
√MIN “one, first of a series; [ᴹ√] stand alone, stick out”
This and similar roots were used for Elvish words for “one” for most of Tolkien’s life, though generally in competition with √ER. The root first appeared as unglossed ᴱ√MĪ¹ in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. mir “one” and ᴱQ. minqe “eleven”; the parenthetical comment (mi’i) indicated it originally had some other now-lost consonant, though Tolkien marked this comment with a “?” (QL/61). It also had derivatives in the contemporaneous Gnomish Lexicon such as G. min “one single” (GL/57).
The Qenya Lexicon of the 1910s had a distinct root ᴱ√MINI² from which “tower” words were derived, such as ᴱQ. mindon/G. mindon (QL/61; GL/57). In The Etymologies of the 1930s these roots were merged together into a single root ᴹ√MINI “stand alone, stick out”, whose derivatives included both ᴹQ. min/N. min “one” as well as ᴹQ. mindo and N. mindon/minnas “tower” (Ety/MIN).
In Tolkien’s later writings √MIN was mostly mentioned in the context of Elvish numbering systems, and given glosses like “one” or “first of a series” (VT42/24; VT47/16-17), but in notes written in 1967-69 Tolkien indicated it was still the basis for “tower” words, most likely from the sense “prominent” (VT42/24). In this later notes Tolkien was careful to distinguish √MIN “one” used in counting vs. √ER “one” used for individual things: √MIN was for the first of a series of things, whereas √ER was for a single thing that was unique, alone or in isolation. The distinct senses of these two roots dates back at least as far as The Etymologies of the 1930s (Ety/ER, MIN).
The root ᴱ√MIQI “kiss” appeared in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. miq- “to kiss” and ᴱQ. miqele “kissing” (QL/61). Derivatives also appeared in the contemporaneous Gnomish Lexicon such as G. mib “a little kiss, a peck” and G. mictha- “kiss, bill” (GL/57). The word ᴱQ. miqilitse “little or tender kiss” appeared in the ᴱQ. Nieninque poem from the 1920s (MC/215; PE16/90, 92). Tolkien created a new version of this poem in 1955 and reused many of the same words, including Q. mikwi- “kiss” and Q. miquelis “(soft, sweet) kiss” (PE16/96); the latter also appeared as ᴹQ. miqilis “kiss” in the Declension of Nouns from the early 1930s (PE21/33). These later examples support the ongoing validity of this root, perhaps as *√MIKW.
√MIR “precious; esteem, value”
The first appearance of this root was as ᴱ√MIRI “smile”, along with variant ᴱ√MṚT͡YṚ and derivatives like ᴱQ. mire “smile” and ᴱQ. mirmile “ripple of laughter” (QL/61). However, in The Etymologies of the 1930s unglossed ᴹ√MIR had derivatives like ᴹQ. míre/N. mîr “jewel, precious thing, treasure” (Ety/MIR), senses these words retained thereafter. The root √MIR appeared several times in Tolkien’s later writings with glosses like “esteem, value” (PE17/37) or “precious” (PE17/165).
ᴹ√MIS¹ “go free, stray, wander”
An unglossed root in The Etymologies of the 1930s glossed “go free, stray, wander”, with derivatives like ᴹQ. mista-/N. mista- “stray (about)”, ᴹQ. mirima “free” and N. mist “error, wandering” (Ety/MIS). It was originally just glossed “free” (EtyAC/MIS).
An unglossed root in The Etymologies of the 1930s with no derivatives of its own but two extended roots ᴹ√MISIK and ᴹ√MISID; probably the sense of the base root was “*wet” (EtyAC/MIZD). It was also Tolkien’s intent that this ᴹ√MIS² be the basis for ᴹ√MITH “*grey, mist” by way of blending with ᴹ√KHITH “mist, fog” (EtyAC/MITH). Extended ᴹ√MISIK or ᴹ√MISK had derivatives ᴹQ. miksa/N. mesg “wet” (Ety/MISK) and extended ᴹ√MISID or ᴹ√MIZD had various different meanings in derived languages: ᴹQ. miste “fine rain” vs. N. mîdh “dew” vs. Dor. mîd “moisture” (Ety/MIZD). The root ᴹ√MIZDI also appeared in both the first and second versions of Tengwesta Qenderinwa from the 1930s (TQ1: PE18/43) and around 1950 (TQ2: PE18/93).
Tolkien introduced the root ᴹ√MITH in The Etymologies of the 1930s as a blending of ᴹ√MIS² “*wet” and ᴹ√KHITH “mist, fog”, with the derivative N. mith “white fog, wet mist” as in N. Mithrim “*Mist Lake” (Ety/MITH, RINGI; EtyAC/MITH). As a later addition to this entry Tolkien wrote the adjective N. mith “grey”, and that was the more common use of this word in Tolkien’s later writings. In a 1955 letter to David Masson Tolkien specified that “usage suggests that MIÞ- is paler and whiter, a luminous grey” (PE17/72).
A root in The Etymologies of the 1930s glossed “whine”, with derivatives like ᴹQ. maiwe/N. maew “gull” and ᴹQ. miule “whining, mewing” (Ety/MIW). Tolkien’s continued use of Q. maiwë (MC/222) and S. maew (PE17/97) for “gull” indicates the ongoing validity of this root. The word ᴱQ. māwe “gull” appeared under the root ᴱ√MAWA “?cry, bleat” (the “?” is Tolkien’s) in the Qenya Lexicon of the 1910s, along with other derivatives like ᴱQ. maule “crying, weeping” and ᴱQ. moa “sheep” (QL/60), making this early root a likely precursor to ᴹ√MIW.