The Vail House, c. 1805, Bennington, Vermont

 

The Vail House was deconstructed this past summer for repair and reconstruction in another town.


 

It was once one of the most stylish houses in Bennington, its architraves and columns more complex than most local houses, its fanlight and surround unique to this part of Vermont. 
Similar details exist on a few houses across the border in New York.

The Victorian updating can be seen here - the double windows on the first floor, right, and the porch with curly brackets   Well executed at the time and then let go.
  I measured and photographed it about 4 years ago. I wish I had documented it more carefully. I have no image of the front of the house!

On September 16, I will include its  geometry as part of my presentation  'Practical Geometry' for the Bennington Historical Society lecture series at the Bennington Museum.

The family wanted a broad front hall with space for a sweeping staircase. This was the new style. The framer's answer was to  add 1/3 of the width to each side. The red square in the center shows how this worked. It was divided into 3 equal parts using the Rule of Thirds.
The house was to be 3 parts  deep and 5 parts wide. 


As you can see the division into 3 is not quite where the posts and beams are.
While the size was set by an addition of proportional lengths, the rooms were set by a different application of the Rule of Thirds . I call it 'Crosses Squares' .
 Each side is a square, the Rule of Thirds applied to each side makes the front rooms square, the back rooms long and skinny, The posts and beams are set where the walls will be. 
Usually the front hall will be the width of the extra third. Here you can see that it is wider.  Or perhaps the house is wider... slide those 
squares on each side towards each other about a 12" and the  crosses squares would mesh.

The floor plan is traditional for this part of Vermont: 2 square front rooms, a long skinny space in the back divided into smaller rooms, the plan of a salt box. I wrote about this in an earlier post:  http://www.jgrarchitect.com/2016/06/the-persistence-of-saltbox-floor-plan.htm





 This is the west elevation. The shutters are a later addition.

Here is the Practical Geometry: a square in the middle, with the left and right sides 1/4 of the whole. The Lines locate the windows' size and placement. The sash themselves are squares, which is in keeping with the layout. The  decorative architrave's height is determined by the half of the square.

As I did not measure the exterior extensively I have not tried to layout the geometry of the corner boards or the frieze.
The photographs show that I have not accurately located the quarter circle vents in the eaves.  They are farther apart than I drew them, The proper location is probably on the 1/4 line of the square.
I think the roof pitch matches the Lines which divide the square into quarters - or the dash dot line I use to call out the left quarter of the house. This would be a logical choice:  a natural choice, using proportions the framer already is working with and also complementing the design of the house.  

Practical Geometry - what our ancestors called this geometry

Practical Geometry.
It's what our ancestors called these diagrams I draw.


 Here is Peter Nicholson who wrote about Practical Geometry. His writings make clear that geometry was once an expected and necessary part of construction, used both by the designer and the artisan.

His first book, The Carpenter's New Guide, published in London in 1792.

He begins with a Preface, some of which I quoted in an earlier post: http://www.jgrarchitect.com/2016/08/practical-geometry-as-described-by_16.html


Page 2 is copied here.

The use of geometry in construction was so accepted that Peter Nicholson waits until his third paragraph before he shares that geometry is useful in mathematics and science too.



By the time of his death in 1844, Nicholson had published 27 books in London, New York City, and Philadelphia.  More than 10 years later his books were still in print.

This portrait is in his updated book The New and Improved Practical Builder, published in 1837.

This time he writes a whole paragraph explaining Practical Geometry. Has he been asked to be more thorough? Have the new uses of geometry in science changed the perception of what geometry is? Have men become carpenters by necessity - especially in the New World - rather than by apprenticeship, and thus desire to educate themselves?




Here is the Introductory Chapter. 

The second paragraph describes the 2 branches of Geometry: Theoretical and Practical.
Now  the Theory of  Geometry is carefully described, including a reference to Euclid, but it is still one of the 2 branches of Geometry.
The other branch, Practical Geometry,
 allows "the architect to regulate his designs and the artisan to construct his lines".



Later, on page vii, he writes, "There is no mechanical profession that does not derive considerable advantage from it."


first portrait: by James Green, 1816, now in the National Portrait Gallery, London
second portrait: the frontispiece of The New and Improved Practical Builder. Don't miss his compass.

Presentation and Workshop at Hale Village and Farm, 2 PM, June 22.

Yes!
Here's the link: 
https://www.wrhs.org/hfv_adult_workshops_2018/



Here's the announcement:
 

Wondering what these diagrams have to do with historic structures? They are 'Practical Geometry'.

Consider that those buildings we love were often built before we had tape measures. This is what we used. Curious? Find your compass and show up at Hale Village and Farm outside Cleveland on June 22.

I'm giving a lecture with lots of illustrations and a hands-on workshop. No math ability required. I will have compasses to share

I will use the Streetsboro Baptist Church as an example. We can look at it inside and out as it is now in the Hale Village. I'd like to see the framing, of course. Maybe there's a hatch into the  attic.



I will also show the geometry of the brick Jonathan Hale House, begun in 1810.
The house plan and elevations are squares with a straight forward application of the Rule of Thirds determining window and door placement.




The window geometry is a little more subtle; it uses the intersection of the arcs of the sides of 2 squares for the sash size.
A framer - or in this case a mason - would build the house and then turn the finish work over to a joiner whose knowledge of practical geometry would be more sophisticated.
The pane sizes were determined by dividing the width into quarter and the height into thirds,

I will take my daisy wheel. It is incised into a 9' length of sheathing from a 1780 barn built for/by a Quaker farmer in Vermont.
It will help explain how geometry was a practical way to layout and measure parts.  







                If you come to the talk, please introduce yourself.  

Of Course Geometry is Magic!

I am often told that daisy wheels used in Practical Geometry are magic.  Here is my response

Yes, geometry is magic.

The technical word is 'apotropaic': these shapes are protective symbols.





The basic shapes of geometry are perfect. They never change.
So is it any wonder that we think these perfect shapes that we humans can not just imagine but also draw, are paths to the supernatural? Of course we see them as holy, sacred, mystical.






Consider:
A circle of any size always comes back upon itself. Its radius, diameter, and circumference are always in the same ratio to each other. If they aren't  - it's something else, NOT a circle.
 Pi (the ratio between the circle's circumference to its diameter) is real and easy to see. Its arithmetic equivalent is infinite; it has been computed to more than 1 million digits with no end yet. (Google the number, just for fun!)

A triangle with sides 3, 4 and 5 units in length always has a 90*, square corner - seen here on the lower right side.


The square is always made up of 4 sides of equal length with 90' right angles. If any of those definitions is not present, it's not a square.







These shapes are part of each other: Here I've drawn a circle, some of its triangles, the squares that come from it.  These are the simplest forms, combined they can become endlessly varied and complex.





Geometry is science. On the grand scale geometry is the double helix of our DNA, the rotation of the planets.
It is a basic in our natural world, the small scale: the bee's honey comb, the crystals in a geode, the reflection in a mirror, the ripples of a pebble in a pond.
The Golden Section seen in the sun flower and conch shell is the expansion of these basic forms.

Too many of us found only relentless logic in our high school geometry class. We didn't twirl compasses, make daisy wheels, stars, hexagons, pentagons, octagons... using just arcs, points, and lines.
We rarely delighted in learning the magic of this world of patterns, proportions, rhythms that we are part of, that does not need words or numbers. Ionic volutes, daVinci's man, the tile in the Alhambra didn't grace our walls.


Practical Geometry is the use of geometry for construction: the arch of a Roman aqueduct or the cantilever of a suspension bridge, the vaulted ceiling and the rose window of a cathedral, the timber frame of a barn, the placement and size of architectural elements. It was used to build the pyramids, noted in the Bible. It is ancient, now mostly forgotten due to the Industrial Revolution.


















I study and blog about this practical geometry, part of our heritage which we no longer perceive, to help us recover it.
I hope we will learn again to see it and use it.





For more on this c. 1830 house see: http://www.jgrarchitect.com/2014/09/how-to-construct-square.html

For the use of geometry in the past several thousand years see: http://www.jgrarchitect.com/2017/04/the-bible-and-vitruvius-know-about.html

Practical Geometry at MIT

 This is the curtain wall of the Mass Ave entrance at MIT,  the Massachusetts Institute of Technology, Cambridge, Mass.
The picture arrived in my mail box last week.



Immediately I saw the geometry. I knew what geometry the designer used and how it was manipulated.





I was writing posts for this blog and my local blog. None quite came together. Each had parts which require more drawing, thinking, and better choice of words.
Frustrating.
Then the latest MIT mailing to alumni/ae showed up with this picture.
I laughed. I walked beneath that wall of glass and columns for 4 years. In that time I paid a lot of attention to how we used the space it sheltered, how the shape and size of that 'entrance' directed what we did. The curtain wall was not part of my thinking, although the light it allowed into the rotunda was.
The wall's pattern, rhythm, proportions - or even the idea that it was geometry - was not part of my analysis, nor was it ever alluded to by others. 


Here is the pattern.
Upper left : A square and its diagonals.
Upper middle: The circle that comes from using the diagonal of the square as the circle's diameter.
Upper right: The square that fits around the circle.

How the pattern grows:
Top row: Overlap a circle of the same size, so that the perimeter of each circle touches the square inside the other.
Second row: This pattern can grow sideways as well as up and down.
4 squares on the right: Once established leave out the circle, continue the squares, add the diagonal, horizontal, and vertical lines.


The pattern could have started with the circle and the 2 squares fitted around it.
Using the circle as the unit  - the 'module' or 'diameter' in classical terms - is the traditional way to begin a design. (See Palladio through Asher Benjamin.)

From a photograph I cannot judge the diameter of the column.  Does it taper? have entasis? The pilaster in the corner on the right appears to be the same width as the unit I chose: the original square.
If instead the column is the unit, the module,  the circles of the curtain wall might be 3/4 or 2/3 of the module.

I have been told that the main buildings at MIT - dedicated in 1916, designed by William Wells Bosworth -  were designed using geometry. The drawings of those buildings would be well worth studying.

Practical Geometry has become an integral part of how I see buildings.  I was surprised to find that it has become a design tool for me as it was for those who used it for construction.

Meanwhile, this little bit of geometry was just plain fun.

The geometry of a 1870's barn

 This Vermont barn was built in the 1870's . It has been used for storage for the last 20 years.

I prepared a report on its history and structure for its owners so they could consider repair and reconstruction with some real knowledge - not just good memories and/or worry about costs.

The barn was well built by a farmer who knew his land and a framer skilled at his trade.
The frame is regular, much of it still sturdy. Its mortises,  tenons, and pegs are still secure.














Its bents use dropped girts and posts to purlins which support  common rafters, a framing system regularly used in the Hudson Valley watershed, not often seen in this area of Vermont.









While I was not asked about the barn's geometry, as I laid out the plan and the frame I could see the geometry clearly - not complex, quite simple, repetitive, and straightforward.


Here is the 3rd bent and the lower level floor plan.
The bent is one of the 4 timber frames across the barn that are then fastened together with plates and girts. Walls and flooring have been left out.
The plan is mainly the post locations. I have not included the exterior wall girts.  The braces which are visible in the photograph to the right are barely noted.

The floor plan could easily have been laid out using circle geometry.

I have added Laurie Smith's diagram for drawing a square beginning with a circle. It is a very clear description.

For his websites see: http://www.thegeometricaldesignworks.com/

and  http://historicbuildinggeometry.uk/

Here is my drawing of the floor plan with its posts laid out using circles. The first  (top) 2 bays are of equal depth and width.  The dashed green line shows the layout determined by the circles.

The lower bay (between bent 3 and 4) is not as deep. Perhaps the land dropped off too steeply, or the lumber available was not as long. The dotted red line in the lower right rectangle shows how the crossing of the arcs of the square determined the depth of the bay. 

The base of bent 3 is vague on purpose. I don't really know the depth of many of the lower level posts. The land slopes west to east. The floor on the east end has been built up over the years with layers of discarded boards.  The right end has been reconfigured for cows; the left end has a false ceiling.
The main  barn level of the bents is divided into thirds. The  posts are the height of a third of the bay's width - the space they outline is a square. I've drawn it in red. The dropped girts are set at the point where the arcs of the square cross. Also drawn in red.
This is similar to how the lower level east bay's depth was determined.
The posts that support the purlins ( the roof beams ) are centered on the squares below. The height of the ridge is also determined by where the arcs of the loft square cross.






Lastly the location of the lower girt which becomes the plate for the wing is determined by the Rule of Thirds.



Such basic practical geometry tools! They are  those described by Serlio, Palladio, and Asher Benjamin - circles, arcs, lines - applied in very simple ways with impressive results.


Well thought out, straightforward without fancy flourish, the space and the frame speak to me. But I am simply the one who documented this, sharing the power, the grace, that I found.

The barn, after 150 years, is no longer essential. It is very possible that it may not survive until a new purpose discovers it.

.

How Practical Geometry is practical

This is a sequel to my previous post: http://www.jgrarchitect.com/2017/11/the-tuckahoe-cabin-geometry.html

Do I think the carpenter who laid out the small simple cabin at Tuckahoe actually drew the arcs on the  ground? or on the floor  - once he had squared the foundation and set the sills?

No, I think he knew the geometry. Someone had already taught him what I drew.
I think he swung the arcs but marked only the foot or so where he  knew the crossings would be. He knew that he wanted to locate the center of each wall, and  - by basic geometric rules - he needed 2 points to draw a line perpendicular or parallel to the wall in question.






Here is a lithograph of le Pere Soubise, patron saint of the Campagnons, French carpenters who have finished their apprenticeships and begin traveling from town to town, from job to job to learn new skills. (In English an Apprentice becomes a Journeyman at this stage of his training because he 'journeys'. When he has gained enough experience he is then eligible to become a Master.)

le Pere Soubin is probably mythical. But the date of his portrait is known: 1882. Click on the print to read the attribution. 
In 1882 a portrait of an important man included the tool of his trade: le Pere Soubise holds a compass.






I have enlarged that part of the image. He holds his hand in  a way that he would if he were using the compass to measure a distance based on the drawing held in his other arm. Or as he would to  mark joist pocket locations on a beam, stepping off from one to the next.

Today a carpenter marks stud spacing with a tape measure that has multiples of 16" highlighted in red. The carpenter doesn't count 16" each time, he uses the tape's marking as a shorthand.
Similarly the framer in 1860 did not need to swing the arc from one point to the next, he used the compass to keep his spacing consistent.




As I was writing this a timber framer who did a lot of repair of old barns mentioned that he often found common rafters laid out at 39.5". 
I laughed and told him he had given me a challenge: Why 39.5"?

Here's the arithmetic: Many of the barns were about 40 ft long. 40 ft = 480" . 12 x 39.5 " =  474", 6" shorter than the barn's length. 3" each end for the end rafters.
However, that begins with the solution. It doesn't address how the framer found his answer.


Here's the  geometry.
The framer knows he will use  3" wide rafters on each end of his 40 ft long  barn, so he will have 474" in between for his rafters.
He wants to figure out what distance will work so he can tell the men working with him where to set the rafters and cut the pockets in the plate. The plate is sitting right there in his framing yard -  which might be the floor of the barn he is building.

He could make a scale drawing on a board and scale up to the plate using his compass, like this:

Or he could stretch his line the length of the plate between his end rafters. Then fold the line in half and and then half again. Now he had the length of the plate divided into 4 equal Parts. ( #1 , # 2)
 He thinks 12 rafters should do it. That means 3 rafters for each Part. But what's the spacing? On the framing floor he draws out a square using the Part as the side.  The handy Rule of Thirds quickly divides the square into 3 equal rectangles and the Part into 3 equal lengths. (#3)
4 parts x 3 divisions = 12 rafters. Good to go.
He doesn't care that the length of each is 39.5". He cares that he has divided his plate evenly. (#4)




Note that the framer does not add, subtract, multiply or divide. He could show this system to someone who spoke a different language. Neither would need know how to read words or compute. They would need to be able to think logically and reason visually.  Geometry is a language in itself.



By the 1860's  - the time of the Pere Soubise portrait - both France and England had standardized dimensions (meters in France, feet and yards in England). Tape measures existed  but were not widely used. Wooden folding rules were popular after the Civil War,  but carpenters still understood and used compasses for layout and design. 

I have met young timber framers who journey as Compagnons.
 For more information about the French Compagonnage historically and today:
http://www.historicalcarpentry.com/compagnonnage.html
And note the compass leaning against a beam in the first engraving.