Jason Kottke posts a Richard Feynman video in which he explains that question, after he tells us why trains can go with solid axles and no differential.
What I now want to know is when was the method invented? And why didn't Conestoga wagons need a differential (I assume because the wheels could slip?)
[Updated: turns out the conical shape also contributes to the sway of a railway car. See this wikipedia article on "hunting oscillation" ,which is a generic name for the phenomena. And this article goes into more detail than the Feynman video. It also briefly mentions an alternative to the coned wheel--canting the track. Not quite clear on how that works--a canted racetrack presumably uses gravity to counterbalance centrifugal forces. Is that the effect of a canted rail track, or does it also reduce the difference in distance traveled by outside and inside wheels? Still nothing on when coned wheels were invented.]