Further

[William Hupy]

This is another "F" word ripe with controversy. Some contend that only "farther" should be used to describe distance and that further should be utilized to describe something that exists to a greater extent so that the two are not synonymous. Anyone game to set the record straight?

[Perry Lassiter]

That's been my understanding too. I generally preserve that distinction in writing, but not necessarily in speaking. I have reqd articles maintaining it made no real difference.

[Slava]

It seems both are correct in many places, but not all:

Although some usage guides insist that only farther should be used for physical distance ( We walked farther than we planned), farther and further have been used interchangeably throughout much of their histories. However, only further is used in the adverbial sense “moreover” ( Further, you hurt my feelings) and in the adjectival senses “more extended” ( no further comment) and “additional” ( Further bulletins came in).
The expression all the farther (or further) in place of as far as occurs chiefly in informal speech: This is all the farther the train goes.

I've never heard or heard of this last usage.

[Perry Lassiter]

I've heard all the farther (further?), but in relation to ideas or arguments, not trains, roads, nor vehicles.

[Slava]

I would say "furthermore" for ideas and arguments.