They seemed to be carved out of huge blocks of stone, immovable, and yet they were aware: some dreadful spirit of evil vigilance abode in them.
Though if an enemy were so rash as to try to enter that land secretly, then it was also a last unsleeping guard against any that might pass the vigilance of Morgul and of Shelob.
The plain to their right was dim and smoky, and they could see there neither camps nor troops moving; but all that region was under the vigilance of the forts of Carach Angren.
He sprang past them; but even as he did so, thrusting the phial back into his bosom, he was aware, as plainly as if a bar of steel had snapped to behind him, that their vigilance was renewed.
But as with Narchost and Carchost, the Towers of the Teeth, so here too the vigilance had failed, and treachery had yielded up the Tower to the Lord of the Ringwraiths, and now for long years it had been held by evil things.
In the dimness of its dreary day few things even in that land of vigilance could have espied them, save from close at hand.
There are no more uses of "vigilant" in the book.
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We need to remain vigilant when interacting with websites we don’t know.