This root first appeared in The Etymologies of the 1930s as ᴹ√PER “divide in middle, halve” with derivatives like ᴹQ. perya- “halve” and N. perin “half” (Ety/PER). It reappeared in notes from around 1959-60 as √PER “half” (PE17/171, 173). In Tolkien’s earliest writings, the sense “half” was assigned to the root ᴱ√LEHE or ᴱ√LEFE² instead (QL/52; GL/53).
root. half, half; [ᴹ√] divide in middle, halve