Letting sparks fly freely from the train would increase the value of the railroad by decreasing costs, but decrease the value of the farmland (the farmer might choose to leave the area by the track clear, or plant less flammable crops, change the use to something else entirely, like mining, or vacate the property altogether). Restricting the sparks from the railroad would raise costs and decrease the value of the right of way, but increase the value of the farmland, since it could be put to its most efficient use.

Under a system of land value taxation, rather than requiring the owner of the railroad to negotiate with every farmer on his route, or requiring the state to figure out who should be given what property right to start with, the state would attempt to maximize the net tax revenue (total tax revenue minus transaction costs), which would tend to maximize the overall land value. If the farmer paid a land value tax for his farm, and the railroad paid an LVT for the right of way, it would be in the interest of the state to maximize the value of both, because that would maximize the tax collected.

(Full disclosure: my economic interests tend to be a bit eclectic. :) )

I did see an interesting discussion from a while back that dealt with some of this:
http://www.cooperativeindividualism.org/coase_landtheory.html
but I was wondering what other insights might be brought to bear.

This post was mentioned on Twitter by StevenLandsburg: Happy 99th Birthday, Ronald Coase: http://www.thebigquestions.com/2009/12/29/happy-99th-birthday-ronald-coase/…

*waits for Steven_Landsburg to pay me to go away or otherwise recognize the superficiality of his Coasean analysis*

*provides link elaborating this point*

Snorri, I think Xan points to the answer on who formalized the insight (and points to why formalization was problematic … in the sense of saying almost the opposite of what he had meant to say).