As regarded its origin there were various explanations, all of which must necessarily have been conjectural.
As the light drew nearer, he beheld, within its illuminated circle, his brother clergyman—or, to speak more accurately, his professional father, as well as highly valued friend—the Reverend Mr. Wilson, who, as Mr. Dimmesdale now conjectured, had been praying at the bedside of some dying man.
There are no more uses of "conjecture" in the book.
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She dismissed it as mere conjecture.
It is important to distinguish between conjecture and fact.