Agricultural production functions

Different types of agriculture have different manpower needs---at least they did in the early 19^th century. For a farm of any given size, less workers are required for livestock than for arable. Arable requires a lot of labour for sowing, weeding, harvesting, threshing and all the rest of it. So we might expect to see the number of workers per farmer increasing with an increasing share of arable. Now, here is the interesting thing. The ratio between arable and livestock changed with proximity to London, at least it did from the perspective of the southwest of England. The closer the farm was to London, the more arable. Cornwall, Devon , Dorset and Somerset were heavily into livestock.

So, how about we plot the ratio between arable and livestock against distance from London AND the ratio between number of labourers to farmers?  I have used lowess smoothing to get a single trend line from a mass of points. I have to say that I was really deeply surprised by the closeness of the two lines. And the best thing is that the data sources were entirely independent. The farmer to labourer ratio came from the 1851 Census records, and the arable to pasture ratio came from the 1836 Tithe Commission Files. The 'kink' at around 200km from London is the beginning of the heavily pastoral country, eastern part of Somerset.