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The ball rolled further into the alley.Both of the above examples are correct. In fact, the Oxford English Dictionary entry for farther says that it is a variation of the word further. So when talking about physical distances, using either word is fine, but it's best to stick with it once one is chosen.
The ball rolled farther into the alley.
The city council decided the annexation proposal deserved further discussion.In this instance, the word means "beyond or in addition to what has already been done." This definition is unique to further. Using farther not only would be incorrect, it'd sound strange, too:
The city council decided the annexation proposal deserved farther discussion.Further also means "additional." As in the example:
For further information, please visit our Web site.That's the letter of the law in a nutshell. However, the difference between further and farther is one instance where keeping things simple is probably a writer's best bet.
Alicia threw the shot put 10 feet farther than Jane did.Those additional 10 feet that the shot put traveled are a physical distance and can be measured. Therefore, reserving farther for this instance is appropriate.
That could not be further from the truth.If all else fails, just remember, farther can't be spelled without the word "far" and "far" refers to physical distance.
Sources: Oxford Dictionary of Current English.