Sandown, New Hampshire, Meeting House, 1773

UPDATE, July 31, 2025  It is probably best to read this later! 

I substantially revised this post on April 18, 2014.  

11 years later I am rewriting it again. I think now that perhaps the frame and the exterior were conceived independently, then mashed together! 


Timothy Palmer is listed as the master builder of this meeting house, built in 1773. 12 years later he built the Rocky Hill Meeting House in Amesbury, MA., which I wrote about here:  http://www.jgrarchitect.com/2014/02/rocky-hill-meeting-house-amesbury-ma.html

I was curious to find out if the geometric language used to design the Rocky Hill Meeting House could be seen here as well.
I knew of the Sandown Meeting House but had never seen it.
Luckily HABS drawings of the Meeting House are on-line. This photograph is part of that record. I borrowed it through wikimedia. A detailed history with photographs can be found at http://www.colonialmeetinghouses.com/mh_sandown.shtml.


I thought I'd just see what Timothy Palmer built, and how he evolved as a master-builder - simple.
Instead I found a larger fascinating history.
 But first: the geometry of the Sandown Meeting House.

Start with the simple geometry, the square.
Here is the front elevation - 2 squares side by side. I've crossed the one on the left side with both diagonals, but only drawn one diagonal for the square on the right side. The squares determine the size of the front and the structural dimensions: they include the sill and the top plate


The window placement is also simple:
On the right side I have divided the square - see 'a-a-a-a' - in half vertically and then drawn the diagonals for those rectangles. The intersections are at the edges of the windows - see 'c'.  The windows themselves are 2 squares. See the diagonals in the window upper left corner.
Then I've rotated the square to show how the line determines the location and width of the entrance - see 'b-b-b-b'.

 

I have not yet figured out why the door is off-set. Maybe the space needed for the stairs to the balcony threw things off.
Note how the symmetry of the windows is so strong and the triangular pediment such an 'eye catcher' that one has to pay attention to see that the door really isn't centered! 




Where did Palmer begin his design? The church committee overseeing construction would have told him approximately how big to make the building. How did he determine his layout?

I think he began with the pulpit.
Here, as in the Rocky Hill Meeting House the pulpit with its sounding board is the centerpiece of the church. Not only is it ornate and dramatic, it surrounds, protects and presents the preacher and the Bible. The book would be laid out, open, on the lectern. And the lectern is precisely at the crossing of the squares.   (Here I think I need to add a picture of the pulpit.)

 One square begins on the right of the pulpit and extends to the left; the other begins on the left and extends to the right.

I have blacked in the columns as the design locates them. Here the lower edge of the squares runs through the columns which support the balcony. The center the squares locates the columns in the open space  - both, however, in only one direction.
The left and right sides of the squares are the locations of the posts on the north and south walls and the roof trusses above. See red lines on either side of the main aisle. 





The length of the diagonal of the square is also the width of the meeting house itself.  I have used that diagonal to draw a square inside the frame of the meeting house. It extends outside the building at the entrance and the pulpit. Where it crossed the outside walls is the line which determines the posts on each side of the central aisle. See the green square set as a diamond and its left and right green triangles.
The final columns are those on either side of the east and west entrances. The triangles noted in green also mark off the 2 squares on either side of the central aisle. When those squares are subdivided, the subsequent intersections determine the columns - see the small squares and their diagonals on either side of the left (west) door.

 The West Elevation - Interior shows Palmer again using the crossed squares. The diagonals are also the position of mortises in the roof trusses. The extension of either interior diagonal  lands on the top of the brace.






Timothy Palmer did not use circles with 6 points (the daisy wheel). He did use the square 'flat' and 'rotated', and its 8 points to design the entrance. I just needed to determine his basic length: the radius of the circle.


The first dimension I saw was the distance between the center of one pilaster and the other - the horizontal line in the middle of the circle. I deliberately white washed the extensions of that line to show the circle divided into 8 segments and the distance between the pilasters.
Then I realized that that length is also the height of the columns from the pedestal to the capital. Hmmm....
That length is also the radius of the circle that encloses the entry from the peak of the pediment to the bottom of the door.
The width of the pediment is determined by the circle's upper spokes. The height of the pedestals is set by the lower spokes. Perhaps Timothy Palmer's own history accounts for this.
He was apprenticed to Daniel Spofford, an architect and millwright in Newburyport, MA. Some records say he also learned shipbuilding  from Ambrose Spofford. He seems to have been responsible, at age 23, for building this meeting house. Perhaps he also built the pulpit.
His other responsibility was to span the open interior space of the church. He would have know what was necessary to frame a boat hull - which is in some ways an upside down roof.

At the Rocky Hill Meetinghouse he used other geometry: a circle with 6 spokes or petals: a daisy wheel, a much more complex double square, and the 3-4-5 triangle.
In 1792 he quit building churches and became a bridgewright. He built many bridges including 4 across the Merrimack River, and the Market Street Bridge in Philadelphia. For more information see Frank Griggs' excellent well illustrated article:  http://www.ce.memphis.edu/3121/stuff/general/timothy_palmer.html

Rocky Hill Meeting House, Amesbury, MA. - 1785

Beware! This post is subject to serious revision. I've learned a lot about Practical Geometry and framing since I wrote this. It will be updated. I suggest you read something else.  1/10/26

 

The Rocky Hill Meeting House was built in 1785 by the people of the West Parish of Salisbury. It was placed on ledge at the top of Rocky Hill on the road to Portsmouth, NH. By 1886 it  belonged to the West Parish Society who, in 1942, gave it to SPNEA, now known as Historic New England. The church is now open occasionally for gatherings and concerts.
Here is the link for the meeting house: http://www.historicnewengland.org/historic-properties/homes/rocky-hill-meeting-house

In the summer of 2013, Historic New England offered a tour of the building led by their staff. A happy group assembled, delighted to look carefully at the building with knowledgeable guides. We were able to sit in the pews, speak from the pulpit, explore the balcony and climb the ladder into the attic to see and touch the trusses that clear span the sanctuary: 48'-9" outside to outside. We visitors came with many specific interests which led to excellent wide ranging discussions.

The drawings were available through HABS, so I, of course, began to consider how the meeting house had been designed.

Here is how I think the building was planned, the dimensions and spacing determined.

The committee knew about how big the building would be, that it would have a balcony and be set on ledge with no crawl space. The first dimensions would have been two  3-4-5 triangles, shown here, with the long sides ('a' and 'b') the location of the interior columns to support the balcony.

For simplicity I have shown the balcony plan here. Remember that all diagrams can be enlarged by clicking on them.

2 squares were laid out, based on the sides.  Here I have labeled the diagonals 'a' and 'b'. and drawn one square with solid lines, the other with dashed. 

These overlapping squares determined the floor plan.



s.
I have drawn the multitude of diagonals that grow from those 2 interlocking squares. The side doors were centered, easily. The pulpit itself, is centered on the space, with the lectern - where the Bible sat - at the center of its square.
Most of the columns fall on the crossing of diagonals. I think where some do not it is because of logistics.
The columns which should be directly in line with the side doors would have made an awkward view and passage for someone entering there. The aisle would have needed to detour around the column - visually and physically unappealing.

Similarly the columns near the back of the church, if placed on the crossings would have created box pews almost too small to be useful. This I know from personal experience, having sat in similar box pews.

The entry 'porch' is also almost a square, a continuation of the pattern. It is about a foot too long. Again, I think the stair- which is quite steep with very tight landings - did not fit so the porch was extended.

  The section is the daisy wheel - circle geometry. Here the 4 side petals determine bottom side of the bottom plate, the top side of top plate (bottom chord of the roof truss), and the bottom of the ridge. The roof trusses were built to sit above the daisy wheel.
The roof pitch is determined by the daisy wheel.

I have noted the top and bottom plates with a  star: *. (No, it's not an asterisk - no footnotes!) 

 The attic trusses are divided in thirds. The center of the determining circle is starred (*). It is the midpoint of the length of the daisy petal. It is also the top of the bottom chord of the roof truss. The radius of the circle I have marked in a thick red line. I did not draw the whole circle - you can project it. 
Note that the central tie beam falls on the radius of the circle.

The front elevation follows the Golden Section layout that seems to have been popular at the time which I drawn in several previous posts.

Here drawn in red, are 2 squares with their diagonals (The Golden Section) crossing in the center.

It could also be 2 squares whose surrounding circles meet in the center, but it's not quite as neat.

Note how the eaves of the porch bump into the windows. The porch is squeezed in... Maybe it was something the house-wright didn't think about very much until he had to build it. I think he is saved by the strength of the proportions - the eye doesn't catch it. I looked twice when I stood at the window in the balcony and saw the eave right there in front of the sash. If nothing else it is an invitation to rot.

I was curious to see if the window placement might follow the layout of the overlapping squares used in the floor plan. At least on this elevation it seems as if it does. I have only drawn the left side. The center of the square on the left of the entry determines the left side of the center window. The square with its right side in the center of the porch  - and center of the meeting house facade - lands at the left side of the farthest window.
The right side matches.

The master builders for the Rocky Hill Meeting House were Timothy Palmer and Ambrose Spofford. Palmer is also listed as the master builder for the Sandown, NH, Meeting House, built  in 1773. He is thought to have built that pulpit which is quite similar to the one here.
I am curious to see how that meeting house frame compares to this.

Old First Church Geometry, Interior Elevations - Part 2

The first post on the Old First Church geometry using the daisy wheel, showed how the geometry of the daisy wheel was used to layout the interior view facing east (north/south cross section)  of the church.

The daisy wheel was also used to layout the longitudinal (east/west section) shown here.
(The red circle with its 6 petals is the 'daisy wheel'."
Just as in the first section the top of the circle is the roof of the church. The left and right sides of the circle mark the ends of the sanctuary. The part of the church to the left is the 'porch' or narthex and also the base for the tower.

The balcony on the second floor extends into the tower frame. It is to the left in the photograph. The left hand column is the column at the left side of the daisy wheel above.

The height of the sanctuary - not including the dome - is set by the 4 side petals of the daisy wheel.

The bottom of the circle may have originally been the floor of the basement. The foundation and piers for the columns have been repaired and rebuilt, so it is not possible to be sure where the base of the church really was when the construction began.

The square (4 sides) and its circle  - not the daisy wheel (6 sides in its circle) - determine the wall proportions. The elevation divides neatly into 2 squares.

(See the red x'ed squares that meet at windows centered under the dome.) 
The circles which surround the squares and are generated from a radius made up of half the square's diagonal cross at those centered windows, creating a  'vesica piscis'.  

(Or fish's bladder - the pointy oval, boat shape where the circles overlap.)

On outside of each circle, also the edges of the vesica piscis are the columns.
That spacing is the interval for the columns. It is like the circles that determine the glass pattern in the arched tops of the windows, a pattern that can run either way, or that comes from each side and meets here.

(See my post titled "Geometry of the Old First Church, Bennington, VT" for diagrams of the windows.)

I think a carpenter would have used his dividers to transfer the column and windows spacing instead of drawing all the intersecting circles. To make the pattern clear I show here all the vesicas and part of the circles. I find it complex to read. It wasn't easy to draw.
On the left end I have laid out in green the vesica centered on the column instead of surrounding the window, just to show that the pattern can start with either the window placement or the column placement.

Finally when the 2 squares and their circles are moved so that the edge of the right circle defines the location of the east wall of the sanctuary, the edge of the left circle defines the west wall.

Here I have outlined the sanctuary space in black - showing how the balcony extends over the narthex, but not quite to the front of the tower. The squares and their circles in my first diagram above are simply moved over.

I have written 7 posts on the Old First Church.  Except for the post on the VAS, they are all about the geometry used to design the church.

The French Andrews House Geometry - Part 2 of 2

The geometry of the floor plan of the French Andrews house focused on the fireplace and chimney mass. Two squares determined the space and the surrounding post and beam frame.  (See Part 1)
Did the framer used the same pattern on the elevations.
He did.
The red squares in the center of the front elevation show this. Starting from the stone foundation, the width of the firebox is also the height to the 2nd floor - the location of the 2nd floor beam. The square above determines the attic floor - the placement of beam at the eaves. The top of the third box is at the height of the ridge pole.
Both sides of the front elevation are squares with one longer side determined by the radius of the circle which fits around the square.  For clarity I have only drawn the square with its diagonals on the west side and I have only drawn the arc in question, 1/4 of the circle.    

 The east and west elevations are identical except that the location of the 1st floor door shown here is the location of a window on the east side.
Again the square is the determining geometry. I could have overlaid my red squares in several different patterns which all worked. I chose this one because it shows how the arc hits the center of the window, the center of the original house, and the edge of the square is also the edge of the door frame.
The north side of the west elevation is a duplicate, reversed, of the one shown. Again I didn't draw it so that the pattern would be easier to read.

 This is a geometry for framing. The squares lay out beam and post locations, not necessarily walls and room sizes.

I wondered how the lean-to was laid out, especially since it was added later and its floor plan used the 3-4-5 triangle, not squares, so that the wing would line up squarely with the existing house.
The lean-to elevation is also laid out with squares, but these begin not from the foundation, but from the first floor - which makes sense  - it was a given.

The roof pitch surprised me because it is so obvious: the diagonal through 2 squares. Given the pattern already established it came naturally and is steep enough when shingled with wood shakes to keep out the rain.

Sometimes when I see these patterns emerge I shake my head and look at myself askance, "Of course! What else would have worked so easily?"

 On the second floor plan are dotted lines indicating the exposed beams overhead. Using my calipers I scaled them and found they made a square. They are not the dimensions of the 'chambers' - they mark the outer edges for the placement of the posts and beams.
Next, drawing the arc based on the length of the square I marked where the arc crosses the diagonal - the Golden Section. All the windows in the south elevation (except the one above the front door, see Part 1) are placed by the Golden Section. The windows are not centered by the Golden Section as they would be a few decades later. Instead the line marks the side of the window. It tells the carpenter where to start to frame the window opening.

Enjoy how the stair hall space within the beams is also a square, although the hall itself is slightly wider as the walls have been placed on the other edge of the beams.

The French- Andrews House geometry, Topsfield, MA - Part 1 of 2

updated 1/ 2019: the geometry is not the Golden Section. It is the square and its diagonal which I have found in many later houses.


When I was thinking about the original salt box shape of the Locke Tavern, I looked at other early Georgian saltboxes I knew for a comparison.
I thought I would find a similar geometry that would reinforce what I had already seen. Instead I found another way to use squares and the circles that fit around them to organize a frame.

This house I have only seen from a distance. However, measured drawings for it are available on HABS. And
a website for the French Family includes many pictures and a time line.

http://www.loc.gov/pictures/item/ma1015.sheet.00002a/resource/
 www.frenchfamilyassoc.com/FFA/ARCHITECTURE/Topsfield.htm

The French Family site says the house dates to 1675. The HABS drawings, done for SPNEA ( now Historic New England) in 1933, say 1710. Abbot Lowell Cummings says 1718. In any case it predates the Locke Tavern, and it was built in the same neighborhood.
Here is what I can see about its construction by looking at its geometry.

 Notes on the drawings for the second floor say at the wall between the lean-to and the upstairs bedrooms: "rear wall old weathered clapboards... balance of wall is shingled". This means the lean-to was added; the exterior siding left in place. I have seen this in other early houses. It is not unusual.

It does mean that the front of the house, the chimney, the hall and the chamber were built first.

The geometry for the main house is the square and its diagonal. The entry and chimney block consisting of 2 squares (red x's in the center) The corners would be the location of posts and bearing for the summer beams - the beams which are in the center of the rooms.
The size of the rooms is determined by the extended square and its diagonal (dotted red line showing the square and the diagonal).

The front door is not centered. For a while I thought this might mean one side of the house was built before the other. But then I realized that for the door to swing fully open it had to be off-centered, and that I had seen this layout in other early small houses.
You can see in the elevation that the hall window above the front door is also not quite centered - but carefully placed to minimize the asymmetry so that it would not apparent at first glance.
Here I have to stop and appreciate the builder who understood how far off from the center of the door and then, from the spot equidistant between the 2nd floor windows he could position the window where it would least call attention to the discrepancy. A fine mind there, one which speaks to me today. He succeeded.
Now in January 2019, I am wondering if he framed the wings after the chimney block was determined, as the Parson Capen House seems to have been. This would mean the window geometry came first, the door location last.  

The lean-to dimensions were determined by the 3-4-5 triangle (the green triangle on the plan).
This made the framing square to the house - the joists, purlins and sheathing would fit neatly, the house would be tight.
From the drawings we can tell that the width of the house was already 45'-6". The depth of the house became 34'-6".
45.5' divided by 4 is 11.375'.
34.5' divided by 3 is 11.5' .
Was the master carpenter 4+" off? Maybe. But I do not know from what place he began his dimensions - the foundation? the outside of the frame? the outside of the sheathing?
Perhaps the house shifted in 200+ years between its construction and  its measuring, or was re-sheathed. And the measurements might be 4" off.

The Locke Tavern, once a saltbox - Part 4 of 4

During the recent updating of the plumbing  for the Locke Tavern  the floor between the first and second stories behind the center chimney was removed.
I took this photograph standing on the first floor looking up at the exposed second floor wall between the old bathroom and the northwest bedroom while the carpenters worked around me. They were very pleased to share what they had uncovered. Here is what we saw:
* Modern plumbing running next to the chimney stack to the left as we expected.
* A diagonal beam with stud framing below and above that do not match up - ie: the beam was there before the framing.
* A door opening into the nw bedroom  - the white angle on the right.

The diagonal beam is the beam for the original roof over the back wing .
On the top edge of the beam you can see where the purlins were let in. Over that would have been laid the sheathing and then wood roof shingles.


The Locke Tavern once had a lean-to back wing. The space was served by a third fireplace set against the chimney block.
This house shape is referred to as a 'salt box'.
Sometimes these wings were added later, the new roof laid over the existing one, often at a slightly different angle. I have not yet seen how these 2 roofs join.



For readers who don't know about the  form: Here is a picture of a saltbox c. 1715: the John Kimball House in Ipswich Mass. The name was applied to this way of  extending a house much later, in the 1890's. It comes from the shape of a kitchen salt box of that period. Another name for this roof configuration is a "cat slide". 
I chose this house as an example because Kimballs also lived in Andover, Mass. The picture comes from the HABS archives.


This means the northwest wing was extended and a second floor added over the lean-to when the house was enlarged and updated around 1790.

How was the size of the lean-to determined? I think the master carpenter used  the geometry of the square and the Golden Section just as he did for the main house.
 In the diagram the lean-to is outlined in black (a). The square and its diagonal extended (the Golden Section)  determine both the left and right sides (b).
The center section (c) is more problematic. I wish I had been able to photograph and  measure it on site when it was open. The drawings I am using are of the house before it was opened up. Clearly the framing extends on each side of the chimney block with the kitchen fireplace set in between. There are posts in the outside wall and posts on each side of the chimney, at the back corners of the front rooms. Maybe the shape is a rectangle that has sides determined by the 3-4-5 triangle. But I don't know precisely.

It would have been so easy if the basic floor plan were a 3-4-5 triangle! But it isn't. The house measures 36 ft x 28 ft.

Luykas Van Alen House, 1737, Kinderhook, NY, Part 4 of 4

In January and February, 2012, I wrote about the geometry of the Luykas Van Alen House.
The daisy wheel of circle geometry fit the plan and elevations - mostly. The right hand side didn't work. Or rather, I didn't see a consistent geometry.
To see the earlier posts, search using 'Van Alen'. 

Since then I have toured the house twice.

Once arriving early, I had a private  tour with a knowledgeable docent. After the tour she handed me a 2" thick report on the house and left me happily engaged as she gave the next tour.

The house has been measured at least 2 more times since the HABS  documentation in 1934, and the field notes of Gerald Watland and MC Hopping in 1958. Each time the chimney configuration  on the north end of the house - the right end in the drawings - is slightly different. Recently the exterior chimney visible in the field notes has been removed along with the English fireplace.
The drawing here is from Watland and Hopping's field notes reproduced in John Steven's Dutch Vernacular Architecture in North  America, 1640-1830.
Note that it shows a traditional Dutch fireplace whereas the HABS drawing shows the later, remodeled English fireplace.

 Click on the drawings to enlarge them.

So.
Where might the original wall have been?

I have 2 suggestions. Both are shown on the second drawing.
1) The circle geometry - shown in red - used for the first wing (see Part 1) if rotated 90* could have been used to determine the north foundation wall before the firebox was rebuilt.
2) A 3-4-5 triangle - shown in green - might also have been used. It fits quite well.


The family history says the north wing was added or rebuilt to be living space when the son and his family joined the father. If the foundation was already here, as shed space, then the fireplace and flue would have been added to the existing masonry.
If the wing dates from the arrival of the son, the questions are: How did the builder make it square? How did he fix the proportions when the left wing was already there? To use the same circle geometry he would have had to set the radius. He could have done that by locating the center of the circle from the corners of the existing foundation. The length of that wall is the radius.
Or he could have relied on the 3-4-5 triangle to get his corners square.

Once the foundation is in place the next step is the first floor framing.
Here is the geometry:
Shown in red: The circles based on the interior width of the house determine the wall between the hall and the parlor, the north wall and the location of the floor beam in the hall.  The center lines -'a' and 'c' - locate the wall between the left and right wings and the wall at the parlor. The intersections - 'b' and 'd' - locate the hall floor beam and the edge of the exterior wall.
Shown in green: -The parlor needed closer framing. The space, a 3-4-5 rectangle, is divided in 4 parts which determine the beam locations - 'e' .
.

Finally the window placement:

Here the 3-4-5 triangle determines the size of the space, the location of the windows and door, maybe even the depth of the side walls of the English hearth. That may be later. If so not a valid dimension. Here the red lines show the 3-4-5 triangles, the green: a right triangle (half a square). The dotted black line is the center line through the wing.