A root whose existence is implied in Tolkien’s writings from the 1950s and 60s by various reflexive pronouns such as Q. imni “myself” and S. im “self(same)” (VT47/37). Though the root itself did not appear in Tolkien’s later writings, it seems to have been a long standing idea of his, appearing as ᴱ√IMI “same, alike” in the Qenya Lexicon of the 1910s with derivatives such as ᴱQ. iminqa “exactly alike, identical” and ᴱQ. inye- “imitate, make like” (QL/42). It seems to have had Gnomish derivatives from this period as well, such as G. inco “the same, the identical”, though Tolkien put this form under the root for the definite article: ᴱ√I (GL/50). In any case, √IM as the basis for “sameness” and reflexives seems to have been a well established idea in Tolkien’s languages.
Primitive elvish
imi
root. in
iminye
feminine name. Iminye
mī
preposition. in, within
imin
masculine name. One
mi/imi
root. in, within, [ᴹ√] inside
im Reconstructed
root. same, alike, [ᴱ√] same, alike
min
cardinal. one
ne
root. *in
This invertible root had the basic sense “in(side)” for all of Tolkien’s life. It first appeared as ᴱ√IMI “in, into” and ᴱ√Mβ 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 “in“ 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).