Yes, the semicolon is used correctly in the given sentence. A semicolon is used to connect two independent clauses (complete sentences) that are closely related in meaning. In this case, the first independent clause is "After this discourse the friends became unsympathetic towards him," and the second independent clause is "pelting Job with accusations of sin." The semicolon is appropriate because both clauses are related to the same topic and flow logically one after the other.