Na-chaered "to a remote distance": na- "to" + *haered "remote distance" (compare the Quenya adjective haira "remote, far"); *haered is lenited to chaered following the prepositional element na-.
palan-diriel "having gazed far": palan- "afar, abroad, far and wide", an element borrowed from Quenya (occurring in palantir, "that which watches from afar"); -diriel lenited form of tiriel "gazing, watching", participle of tir- "watch". It is lenited as the second part of a compound. According to Tolkien, palan-diriel with a long stem-vowel (i) means "having gazed far away" (in the past), while palan-diriel as in Sam's invocation, with a short i, means "gazing away" (now). The distinction is past vs. present. - The stem tir- "watch" is of course the same as in Quenya palantir. Indeed the whole phrase palan-diriel is intended to suggest "having looked into a palantir", since this is a hymn sung by Elves that had been on a "pilgrimage" to the Emyn Beraid to look towards the Blessed Realm using the Seeing Stone there. - One may ask why the final n in palan, when prefixed to tiriel, does not cause nasal-mutation - sc. n + t becoming th, as when the underlying phrase *in tiw "the runes" manifests as i thiw in the Moria gate inscription. Instead of nasal mutation, the t of tiriel undergoes lenition (soft mutation) to become d, producing palan-diriel. Tolkien addresses this question in Letters:427: "palan-tiriel should phonetically > -thiriel...but grammatically before actual forms of verbs, the soft mutation only was normally used in later S[indarin], to avoid the confusion with other verb stems".
Упс.. однако, диакритика... мда.
