After the fall of Sauron, Isildur, the son and heir of Elendil, returned to Gondor. There he assumed the Elendilmir [1] as King of Arnor,...
...
Elendur, not yet harmed, sought Isildur. He was rallying the men on the east side where the assault was heaviest, for the Orcs still feared the Elendilmir that he bore on his brow and avoided him.
...
Isildur turned west, and drawing up the Ring that hung in a wallet from a fine chain about his neck, he set it upon his finger with a cry of pain, and was never seen again by any eye upon Middle-earth. But the Elendilmir of the West could not be quenched, and suddenly it blazed forth red and wrathful as a burning star. Men and Orcs gave way in fear; and Isildur, drawing a hood over his head, vanished into the night. [25]
...
There he rose up out of the water: only a mortal man, a small creature lost and abandoned in the wilds of Middle-earth. But to the night-eyed Orcs that lurked there on the watch he loomed up, a monstrous shadow of fear, with a piercing eye like a star.
...
...
In a casket on a high shelf two things were laid. One was a small case of gold, attached to a fine chain; it was empty, and bore no letter or token, but beyond all doubt it had once borne the Ring about Isildur's neck. Next to it lay a treasure without price, long mourned as lost for ever: the Elendilmir itself, the white star of Elvish crystal upon a fillet of mithril [31] that had descended from Silmarien to Elendil, and had been taken by him as the token of royalty in the North Kingdom. [32] Every king and the chieftains that followed them in Arnor had borne the Elendilmir down even to Elessar himself; but though it was a jewel of great beauty, made by Elven-smiths in Imladris for Valandil Isildur's son, it had not the ancientry nor potency of the one that had been lost when Isildur fled into the dark and came back no more. Elessar took it up with reverence, and when he returned to the North and took up again the full kingship of Arnor Arwen bound it upon his brow, and men were silent in amaze to see its splendour. But Elessar did not again imperil it, and wore it only on high days in the North Kingdom. Otherwise, when in kingly raiment he bore the Elendilmir which had descended to him. "And this also is thing of reverence," he said, "and above my worth; forty heads have worn it before." [33]
When men considered this secret hoard more closely, they were dismayed. For it seemed to them that these things, and certainly the Elendilmir, could not have been found, unless they had been upon Isildur's body when he sank; but if that had been in deep water of strong flow they would in time have been swept far away. Therefore Isildur must have fallen not into the deep stream but into shallow water, no more than shoulder-high, Why then, though an Age had passed, were there no traces of his bones? Had Saruman found them, and scorned them burned them with dishonour in one of his furnaces?

(UT, THE DISASTER OF THE GLADDEN FIELDS)

Notes

[1] The Elendilmir is named in a footnote to Appendix A (I, iii) to The Lord of the Rings: " ...in Arnor, whose kings wore no crown, but bore a single white gem, the Elendilmir, Star of Elendil, bound on their brows with a silver fillet." This note gives references to other mentions of the Star of Elendil in the course of the narrative. There were in fact not one but two gems of this name; see p.289.

[25] The meaning, sufficiently remarkable, of this passage appears to be that the light of the Elendilmir was proof against the invisibility conferred by the One Ring when worn, if its light would be visible were the Ring not wore; but when Isildur covered his head with a hood its light was extinguished.

[31] For that metal was found in Númenor. [Author's note.] In "The Line of Elros" (p.232) Tar-Telemmaite, the fifteenth Ruler of Númenor, is said to have been called so (i.e. "silver-handed") because of his love of silver, "and he bade his servants to seek ever for mithril." But Gandalf said that mithril was found in Moria "alone in the world" (The Fellowship of the Ring II 4).

[32] It is told in "Aldarion and Erendis" (p.193) that Erendis caused the diamond which Aldarion brought to her from Middle-earth "to be set as a star in a silver fillet; and at her asking he bound it on her forehead." For this reason she was known as Tar-Elestirnë, the Lady of the Star-brow; "and thus came, it is said, the manner of the Kings and Queens afterward to wear as a star a white jewel upon the brow, and they had no crown" (p. 225, note 18). This tradition cannot be unconnected with that of the Elendilmir, a star-like gem borne on the brow as a token of royalty in Arnor; but the original Elendilmir itself, since it belonged to Silmarien, was in existence in Númenor (whatever its origin may have been) before Aldarion brought Erendis' jewel from Middle-earth, and they cannot be the same.

[33] The actual number was thirty-eight, since the second Elendilmir was made for Valandil (cf. note 26 above). In the Tale of Years in Appendix B to The Lord of the Rings the entry for the year 16 of the Fourth Age (given under Shire Reckoning 1436) states that when King Elessar came to the Brandywine Bridge to greet his friends he gave the Star of the Dúnedain to Master Samwise, while his daughter Elanor was made a maid of honour to Queen Arwen. On the basis of this record Mr. Robert Foster says in The Complete Guide to Middle-earth that "the Star [of Elendil] was worn on the brow of the Kings of the North-kingdom until Elessar gave it to Sam Gamgee in Fourth Age 16." The clear implication of the present passage is that King Elessar retained indefinitely the Elendilmir that was made for Valandil; and it seems to me in any case out of the question that he would have made a gift of it to the Mayor of the Shire, however greatly he esteemed him. The Elendilmir is called by several names: the Star of Elendil, the Star of the North, the Star of the North-kingdom; and the Star of the Dúnedain (occurring only in this entry in the Tale of Years) is assumed to be yet another both in Robert Foster's Guide and in J. E. A. Tyier's Tolkien Companion. I have found no other reference to it; but it seems to me to be almost certain that it was not, and that Master Samwise received some different (and more suitable) distinction.