The underlined gerund that functions as the object of a preposition is the one part of the following sentence: The valley later became a center of mining for borax.
Gerunds are words formed with verbs but act as nouns. As they function as nouns, they are subjects, subject complements, direct objects, indirect objects, and objects of prepositions. In this case, the gerund "mining" functions as the object of the preposition "of".