It will probably seem to the reader, however, that the Doctor’s vigilance was by no means excessive, and that these two young people had an open field.
He was not in the least in a state of tension or of vigilance with regard to Catherine’s prospects he was even on his guard against the ridicule that might attach itself to the spectacle of a house thrown into agitation by its daughter and heiress receiving attentions unprecedented in its annals.
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.