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Farther vs. further
Farther and further both mean at a greater distance, and they are used interchangeably in this sense. In the United States, though, farther is more often used to refer to physical distances, and further more often refers to figurative and nonphysical distances. For example, we might say that one mountain is farther away than another, while we might say the price of a stock (a nonphysical thing) fell further today than yesterday. This is not a rule, however, and further is often used for physical distances. The distinction does not exist in the U.K. and elsewhere in the (British) Commonwealth of Nations, where further is preferred for all senses of the word and farther is rare.
Further has senses it does not share with farther. It works as an adjective meaning additional—e.g., “I have no further questions.” It works as an adverb meaning additionally—e.g., “He said he did not spend the money, and stated further that he had never even received it.” And it works as a verb meaning to advance (something)—e.g., “This website is meant to further understanding of 21st-century English.” Farther is not commonly used these ways.
The physical/nonphysical distinction in the U.S. extends to the superlatives farthest and furthest. Furthermore is an adverbial extension offurther and often bears replacement with the shorter word. The rare furthermost is sometimes used to mean farthest or furthest, and it likewise bears replacement with the shorter words.
Grammarist.com
