## Monday, November 20, 2023

### The Practical Geometry of the Parson Barnard House: the Bents

This is the second part of my study of the use of geometry in the layout and design of the Parson Barnard House, in North Andover, Massachusetts.

Here's the house. The left section, the 'front', was built in 1715; the saltbox added in 1720. The rear extension to the right came in the 1950's.

The first floor plan shows the 2 back wings. The middle section, labeled kitchen, back hall, and study is the 1720 saltbox addition. The laundry and entry spaces were added 230 years later.

The geometry of the first and second floor plans match. The posts and beams of the second floor match those of the first floor.

The plan shows a step down into the saltbox addition.

The side elevation also shows this step down. The dashed lines locates the floors and the step down.

The layout Lines locate the inside edge of the posts and the inside width between the posts on either corner of the house. Together they outline 3 sides of a rectangle, the layout for the bents of the frame.  The radii of the arcs is the width of the frame. They cross at the placement for the lower side of the beam which supports the attic floor joists. It is the upper beam of the bents that frame the house.

This use of geometry matches the way the parlor width was determined. The thin black Line marks the rectangle which is the inside of the bent.

The rectangle from that layout crossed with its diagonals. Where the Lines cross is the height of the beam which carries the second floor joists.

For reference here is the geometry of the first floor plan with the Hall on the right, a square; the Parlor on the left, a rectangle whose width is laid out by the arcs. This geometry is laid out from the inside edges of the posts.

When the same geometry is used to lay out the bent using the width from the outside of one post to the other as the dimension, the crossing of the arcs is at the upper side of the attic beam.

**Look back at the elevation of the house with the rectangle derived from the interior dimensions. Note that the second floor and attic windows - which appear to be original - are centered on the space. Using the outer dimensions the windows are no longer centered.

Here is the design for the 6 bents for the Parson Barnard House (without the braces). This simple layout requires only basic knowledge of Practical Geometry.

The bottom red line is the sill.

Do the layout differences I've shown here - between the use of the inside and the outside widths - provide evidence that the interior widths were used? Or do they simply mean the drawing is too small, my lines too thick or not perfectly placed, that the attic framing might yield other information for an accurate assessment?

*  https://www.jgrarchitect.com/2023/11/the-practical-geometry-of-parson.html