The passage was not provided. However, from the dictionary meaning of the word, we can deduce what ardently means in that context. Ardently means enthusiastically or eagerly.
The dictionary meaning of a word can help us deduce its meaning in a context. The word ardently is an adverb which describes the manner of action or desire.
In this context, it refers to the eagerness or enthusiasm that Mrs. Saville's brother had to reach an unexplored land.
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