I was on the phone with my girlfriend last night, when we had a scintillating conversation about grammar. (It is not entirely clear why she continues to talk to me, given that I find conversations about grammar to be scintillating.) The central part of it revolved around her having used farther in a sentence and then immediately questioning whether it ought to have been further. Neither of us had the slightest idea, despite the facts that she’s well-spoken/well-read and I went to Catholic school, where English class consisted of learning the same bloody grammar rules over and over again.
Now why could it be that two fairly intelligent people can’t remember a meaning difference between these two words? Some might say it’s because there is no meaning difference between these words. But such people would be dunces. I happen to know that those people would be dunces because I’ve read a lot of grammar books and they all agree that people who can’t differentiate farther and further are, point of fact, dunces. Regrettably, this means that the following people are dunces: the editorial board of the Oxford English Dictionary, John Milton [cited in OED], Charles Dickens [in Martin Chuzzlewit], and John Bunyan [in Pilgrim's Progress].
They’ve all confused farther and further. Here’s the deal, according to today’s spokesperson for prescriptivism, Tim at Mother Tongue Annoyances: farther is to be used in situations involving distance or length, and further is to be used in situations involving time or amount. In other words, farther refers to literal distance, and further refers to metaphorical distance.
Let’s consider this opinion. First off, are there situations where only one or the other is acceptable? It would seem not. The OED cites examples of farther used metaphorically (1) and of further used non-metaphorically (2):
(1) Then we need argue no farther. [Edgeworth 1802]
(2) It was not thought safe for the ships to proceed further in the darkness. [Macaulay 1855]
And citations for such usage extend back over 700 years. So it’s looking like the two are pretty interchangeable. Specifically, there doesn’t see to be a generalized distinction between further as strictly metaphorical. And in case you were worried that in the past they were the same but since have separated in meaning, you’d be misguided. Google Books returns 11 hits for walked further before 1800 to 19 hits for walked farther before 1800. That’s an insignificant difference between the two, so there’s no evidence of the metaphorical sense prior to 1800. But the same is true recently: Google Books has 654 hits for walked further and 649 hits for walked farther since 1990. So at the least, further has been and continues to be used in non-metaphorical senses, which makes the two look pretty much indistinguishable. That said, there are situations where only further is acceptable to me:
(1) *Farther research is necessary before I agree to buy a third grill.
(2) *I am soliciting farther advice regarding my grilling needs.
These situations use further as an adjective meaning “additional” or “more extensive”, which is a role that farther just can’t take in my idiolect. However, the OED [def'n. B2] disagrees, citing usages such as:
(3) There is one farther objection made by those who have answered this book. [Jonathan Swift 1704]
And if the author of A Modest Proposal is willing to use farther to mean “additional”, I’m not about to disagree. Except I’m going to disagree: this usage seems to be quite rare, especially in modern English; the instances I could find on Google Books were either very old or were scanning errors where further research was misread as farther. So there is one distinction between the farther and further; in some very metaphorical usages, farther is ungrammatical. Such minor distinctions aside, it doesn’t look like farther/further was a strict distinction in the past, and it definitely isn’t now. The OED does claim that in standard English (i.e., Oxonian English), farther is preferred as the comparative form of far and further is preferred when the notion of distance is absent, so you may want to keep that in mind for formal writing purposes. However, for everyday usage, go with whichever sounds better. I know I prefer to use further in most situations (perhaps because I prefer its vowel), while my girlfriend prefers farther. Just don’t go around telling people their choices are wrong. There is no categorical distinction between their usages, only preferences.
Summary: Farther and further are basically the same, and in most situations you can decide between them on the basis of which one sounds more pleasant to you. If you’re striving to follow the conventions of formal English, the OED claims there’s a preference for farther to mean “more distant” and for further when literal distance is not salient, but these are only preferences, not something inalienable. Let your ears decide.