The sentence in question is:
Brookfield was but one of many feeding streams.
What purpose does the word but serve here?
It's a matter of emphasis, or drawing the reader's attention to a particular aspect of the sentence.
One definition of "but" is synonymous with "only", and using "only" here draws the reader's attention to the fact that the subject of the sentence (the stream in Brookfield) is not unique.
"Brookfield was one of many feeding streams." - simple statement of fact.
"Brookfield was but one of many feeding streams." - emphasises the existence of other feeding streams, and makes the reader think about the others: in fact, the other streams could be argued to become the primary subject of the sentence: the reader might expect the speaker to go on to say something else about the other streams.
In this case, but is used to mean merely/just/only.
Brookfield was only one of many feeding streams.
See: http://www.thefreedictionary.com/but "adv. 1"