Neither Batty nor Swan!

This is a photo of the mouldings in my house, which look so much like the ones used in the Robert E. Lee house, in Arlington VA. I thought it would be an easy matter to matching this moulding pattern to an illustration in a pattern book - I assumed that I'd simply look in the books that the American builders (joiners) were using in about 1800, find the right page, and there it would be.

Nope.

The door casings here at the farm and at Lee's house have a simple 1/4 circle curve, as part of a sequence of square edges, beads and flat sections (although not in that order!). But the mouldings in Batty Langley's 'The Builder's Director or Bench-Mate', 1751, and in Abraham Swan's 'The British Architect', 1758, both published in London, are more complicated. Both show reverse curves: Cimarecta, which first curves in before it curves out, and Ogee, which starts the other way, convex before it is concave. But the American casings use 1/4 round or a Scotia, which is a 1/4 round that curves in, not out.

However, Asher Benjamin, in his book 'The Country Builder's Assistant,' published in 1795 while he still was practicing in various towns on the Connecticut River, show an 'architrave' similar to the ones I know. So, was Benjamin inventing? If he was copying, who was his inspiration? Was his book well enough distributed that carpenters 500 miles away from each other would have seen it? Is this an example of different 'styles' (preferring one shape over another), or is a reverse curve moulding harder to make? Or is this something about the tools - the planes, the knives or blades which were available to the builders?