No doubt the thought that was uppermost in a thousand of those vigilant minds, even as it was uppermost in mine, was the riddle—how much they understood of us.
It was the only warship in sight, but far away to the right over the smooth surface of the sea—for that day there was a dead calm—lay a serpent of black smoke to mark the next ironclads of the Channel Fleet, which hovered in an extended line, steam up and ready for action, across the Thames estuary during the course of the Martian conquest, vigilant and yet powerless to prevent it.
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.