Both Uses

vary
in
The Gold-Bug
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Had Kidd concealed his plunder for a time, and afterwards reclaimed it, the rumors would scarcely have reached us in their present unvarying form.†

unvarying = consistent or the same

standard prefix: The prefix "un-" in unvarying means not and reverses the meaning of varying. This is the same pattern you see in words like unhappy, unknown, and unlucky.
In the present case—indeed in all cases of secret writing—the first question regards the language of the cipher; for the principles of solution, so far, especially, as the more simple ciphers are concerned, depend upon, and are varied by, the genius of the particular idiom.†
*

varied = differed; or changed

Definitions:

(1) (vary)
to be different, or to change

Vary is often used to describe small differences or changes--especially about things of the same type. It would be more common to say "The weight of full-grown elephants varies depending upon diet and other factors," than to say "The weight of elephants varies from that of mice."
(2) (meaning too rare to warrant focus)