ᴹ√PIK “*tiny”
Tolkien used a variety of roots for Elvish words for “small”. One early root was ᴱ√PIKI with variants ᴱ√PINI and ᴱ√PĪ from the Qenya Lexicon of the 1910s, unglossed but with derivatives like ᴱQ. pínea “small” and ᴱQ. pinqe “slender, thin” (QL/73). It also had derivatives in the contemporaneous Gnomish Lexicon such as G. pinig “tiny, little” and G. pibin “small berry, haw” (GL/64).
The root reappeared in The Etymologies of the 1930s as unglossed {ᴹ√PEK >>} ᴹ√PIK with derivatives like N. pigen “tiny” and N. peg “small spot, dot” (Ety/PIK; EtyAC/PIK). Further evidence for this root can be seen in later words like Q. piki- or pitya “petty” (WJ/389) and Q. píka- “lessen, dwindle” (MC/223). A variant root √PEY appeared in a list of roots having to do with large and small, with a single derivative Q. pia “little” [< *peya], but it was immediately followed by the forms pikina, pinke, pitya which point back to √PIK (PE/117).
In the Shibboleth of Fëanor from the late 1960s, Tolkien changed pitya to Q. nitya in the name Q. Nityafinwë “Little Finwë” (PM/353, 365 note #59), which may indicate a replacement of √PIK by √NIK, another root used regularly in Tolkien’s later writings for “small”. But I believe √PIK and √NIK may coexist with slightly different meanings: “tiny” vs. “small”; see the entry on √NIK for further discussion.
ᴱ√PILI¹ “rob”
A root in the Qenya Lexicon of the 1910s glossed “rob”, with derivatives like ᴱQ. pili- “steal”, ᴱQ. pilu “thief, robber” and ᴱQ. pilwe “robbery, theft” (QL/74). There are no signs of this root in Tolkien’s later writing, but I think it is worth retaining as the Neo-Eldarin basis for “theft” words. A possible later replacement might be the root √RAPH “seize, grab” from the Outline of Phonology (OP2) from the early 1950s which had the derivative Q. arpo “seizer, thief” (PE19/89), but the verb form Q. raf- was glossed “wave, brandish”, so I don’t think it is suitable for a direct replacement.
ᴹ√PILIN “*arrow”
An unglossed root in The Etymologies of the 1930s with the derivatives ᴹQ. pilin “arrow”; in The Etymologies as recorded by Christopher Tolkien the root was given as ᴹ√PÍLIM (Ety/PÍLIM), but according to Carl Hostetter and Patrick Wynne the root might also be read as ᴹ√PÍLIN (EtyAC/PÍLIM). This root is probably a later iteration of the early root ᴱ√PILI² from the Qenya Lexicon of the 1910s, unglossed and with derivatives like ᴱQ. pilin “feather” and ᴱQ. pilna “arrow” (QL/74); it also had derivatives like G. pilon “arrow, dart” from the contemporaneous Gnomish Lexicon (GL/64). Later “feather” words were based on the root ᴹ√KWES (Ety/KWES; LotR/1122), but ᴹQ. pilin remains the best known Elvish word for “arrow”.
√PIR “close eyes, blink, wink”
A root introduced by Tolkien in Definitive Linguistic Notes (DLN) from 1959 with the gloss “close eyes, blink, wink” to provide a new explanation for the flower name S. alfirin (originally “immortal = not mortal”) after he decided the prefix al- meant “well” rather than “not” (PE17/146). He derived the names Q. pirindë and S. pirin for “a flower that opened and shut quickly with any change of light”. The root ᴱ√PIRI also appeared (unglossed) in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. piri- “spin, turn”, ᴱQ. pirin “thin rod, pin” and ᴱQ. piruke “swirl, twisting, pirouetting” (QL/74).
Neo-Eldarin: For purposes of Neo-Eldarin, I find these earlier meanings of the root to be much more useful, and prefer to use ᴺ√PIR for “spin” rather than “blink”.
ᴹ√PIS “juice”
This root was one of a surprisingly large number of roots Tolkien used for “juice”, appearing unglossed in The Etymologies of the 1930s with derivatives like ᴹQ. pirya/peich “juice, syrup” and N. pichen “juicy” (Ety/PIS). A similar primitive form ᴱ✶pisye appeared in Early Noldorin Word-lists from the 1920s, with derivatives ᴱQ. pihye/ᴱN. hî “sap, juice” (PE13/147). This in turn might have been a later iteration of unglossed root ᴱ√PḶQḶ from the Qenya Lexicon of the 1910s with a single derivative: ᴱQ. pulqe “juice”.
Neo-Eldarin: For purposes of Neo-Eldarin, I would assume this root refers mainly to syrup and tree sap, as opposed to fruit juice which would be derived from ᴹ√SAB.
ᴹ√PITH “spit”
A root appearing in the Quenya Verbal System of the 1940s glossed “spit” with the derived verb ᴹQ. pis- of the same meaning (PE22/103). It may be a later iteration of the early primitive verb ᴱ✶pṣt- “spit”, first mentioned (unglossed) in the The Qenya Phonology of the 1910s and again in Early Quenya Grammar of the 1920s as well as several Early Noldorin Word-lists from this same period (PE13/147, 163). Other earlier roots for spit include ᴱ√RETYE from Qenya Lexicon of the 1910s (QL/79), ᴱ√KEREKE from Gnomish Lexicon of the 1910s (GL/27), and ᴹ√PIW from The Etymologies of the 1930s (Ety/PIW).
Neo-Eldarin: For purposes of Neo-Eldarin, I would stick with the better-known root ᴹ√PIW from The Etymologies of the 1930s for verbs meaning “spit”, as it has derivatives in both Quenya and Noldorin. For nouns meaning “spit”, I personally adapt the early root ᴱ√KEREKE as a Neo-Eldarin root ᴺ√K(E)REK to salvage early Quenya and Gnomish words for spittle; see those entries for details.
ᴹ√PIW “spit”
A root in The Etymologies of the 1930s glossed “spit” with derivatives like ᴹQ. piuta- and N. puia- of the same meaning (Ety/PIW). See the entry ᴹ√PITH for a discussion of other roots of similar meaning.