The warmer southern farthing of the Shire, with its chief town being Longbottom. This was the region where most of the Shire'spipe-weed production was concentrated.
Notes
1
The only specific mention of the Shire's southern point (and hence the southern borders of the Southfarthing) is in the Prologue to The Lord of the Rings, where we're told that the whole Shire stretched '...fifty [leagues] from the northern moors to the marshes in the south.' There is no specific mention of Sarn Ford here, but there are good reasons for thinking that it marked the boundary. We know, for example, that the Rangers who guarded the borders of the Shire maintained a post there.
Even more telling is the story of the final departure of Merry and Pippin from the Shire, long after the War of the Ring in IV 63. In Appendix B to The Lord of the Rings, we're told that they '...handed over their goods and offices to their sons and rode away over the Sarn Ford, and they were not seen again in the Shire.' It seems very likely from this that Sarn Ford marked the Southfarthing's southern boundary.
2
Detailed maps exist only for the most northerly segment of the Southfarthing (shown by the dashed borders to the north of this map). Beyond that, its extents are uncertain, but the road across Sarn Ford is several times stated to have entered the Shire through the Southfarthing, so it must have covered an area close to that shown.