"Shibboleth" is a rare word defined as a custom, principle, or belief distinguishing a particular class or group of people, esp. a long-standing one regarded as outmoded or no longer important.
The chapter that follows is "The Problem of Ros".
This chapter covers the titular essay by J.R.R. Tolkien which explains the shift from the monograph (letter) þ (as in English 'thing') to s in the spoken 'Exilic' Elven dialect of Quenya, and how this phonological change became connected to broader circumstances. Also included, however, are lengthy 'excursuses' from this essay regarding Elven 'mother-names', the parentage of Gil-galad, the westward migration of the Edain, and the names of various prominent Ñoldor. There is additionally a portion of the main body of the chapter that tells of Galadriel.
The premise of the discussion in this chapter is the 'anomolous' use of s: Tolkien reasons that since in Sindarin (the vernacular tongue of the Noldor after their exile) þ was common, the change þ > s must have become widespread before the Noldor left Valinor. And on the basis of the presence of þ in Vanyarin and Telerin, and its retention in written Exilic Quenya the Noldor must have been able to produce this sound. It is thus concluded that the shift from þ to s was "conscious and deliberate".
With that established, Tolkien explains the adoption of this linguistic change by the majority of Ñoldor and its historical context within the Middle-earth canon. Originally, he explains, the lingual change was criticised by loremasters "who pointed out that the damage this merging would do in confusing stems and their derivatives that had been distinct in sound and sense had not yet been sufficiently considered". Chief among these 'reactionaries' was Fëanor, who opposed the shift from þ to s because of his attachment to the þ sound, which was due to its presence in the mother-name of his mother Míriel, Þerindë (Quenya for 'Needlewoman'). Following the death of Míriel and the antagonism this led to between Fëanor and Finwë's children by Indis, this formerly scholarly debate became, surprisingly, politicised. The use of þ by Fëanor and his followers became entrenched, and he saw the growing adoption of s by the Ñoldor, and especially now by Finwë and Indis themselves, as a deliberate insult to his mother and a plot by the Valar to weaken his influence amongst the Ñoldor. In this way Fëanor made þ > s a political shibboleth; he would name himself the 'Son of the Þerindë', and he once said to his children, "We speak as is right, and as King Finwë himself did before he was led astray. We are his heirs by right and the elder house. Let them sá-sí, if they can speak no better."
Note on the text
The text comprising this chapter was drawn from a single unfinished typescript of Tolkien's, that included handwritten notes, composed sometime after 1968. According to Christopher Tolkien, it would be typical of his father's latest work on the Middle-earth mythology in that the production of new material resulted largely from discursive attempts to explain anomalies and unanswered questions in his earlier work, usually concerning philology, which often resulted in a wide variety of subjects being addressed. 
|Foreign Language||Translated name|
|Arabic||شيبولت من فيانور|
|Dutch||De Sjibbolet van Fëanor|
|Esperanto||La Ŝiboleto de Fëanor|
|French||Le Schibboleth de Fëanor|
|German||Die Schibboleth von Fëanor|
|Greek||Ο Σύνθημα γνώρισμα του Φέανορ|
|Hebrew||שיבולת של פיינור|
|Irish Gaelic||An Teagasc seanchaite de Fëanor|
|Italian||Il Shibboleth di Fëanor|
|Kyrgyz Cyrillic||Фэанорын шибболет|
|Polish||Szybolet z Fëanor|
|Portuguese||A Xibolete do Fëanor|
|Romanian||Șibolet de Fëanor|
|Spanish||La Shibboleth de Fëanor|
|Ukrainian Cyrillic||Шібболет Феанора|