farther (Adjective) — More distant in especially space or time. ex. "they live in the farther house"
farther (Adjective) — More distant in especially degree. ex. "farther from the truth"
farther (Adverb) — To or at a greater extent or degree or a more advanced stage ('further' is used more often than 'farther' in this abstract sense). ex. "the application of the law was extended farther" ex. "he is going no farther in his studies"
farther (Adverb) — To or at a greater distance in time or space ('farther' is used more frequently than 'further' in this physical sense). ex. "farther north" ex. "moved farther away" ex. "farther down the corridor" ex. "the practice may go back still farther to the Druids"