The Geometry of Gunston Hall's North Porch

This post is about exploring Practical Geometry, getting lost, and finding the simple answer. I have used my working  drawings to show the process. Faint lines show where I erased possibility that didn't work.

 

Gunston Hall was the home of George Mason, a Virginia planter, with a big family, lots of land, and many enslaved people. He was one of the delegates to the Constitutional Convention in Philadelphia is 1787.

He was also a mason: he advised George Washington about mortar mixes. 

When he had his house built, in 1754, he made the formal dining room and parlor (on the right side of the house in this picture) larger than the family parlor and chamber (on the left side of the picture).  

 

That meant that the house was not symmetrical around the door.  (To see this look at the spacing between the windows on the left and right sides.) The lack of balance might have distracted those arriving to either the north or the south entrance. However the small door and windows at the entrance were probably more jarring.

William Buckland, a young architect just come from England, solved the problem. The porches he designed are so inviting they make the asymmetry is almost invisible. More importantly they enveloped the existing entries.

In  2014, I wrote about the house here: https://www.jgrarchitect.com/2014/05/gunston-hall-ason-neck-virginia.html

The geometry I suggested for the north porch never quite fit. I tried other solutions.  Nothing was much better. I could see the geometry of Buckland's design but I couldn't draw it. 

Here is the HABS drawing of the north porch.

 

 

 

 Here is my attempt to understand what geometry had guided the proportions of the design.

It's neat. It seems to work until you consider that the intersections of the lines do not tell the carpenters how to layout the porch, where the parts should go. The diagram is interesting, but gives no useful information.

Here is a later exploration when I still wanted the diagram to describe the porch design.

Perhaps my initial square was too large, not based on the right width or height?

Would a  circle within its square work?

How about a daisy wheel ?  or an octagon?

The pencil lines, the red and blue inked lines are finally just confusing.

7 years later I changed the question. Not, "What geometry did Buckland use?" Rather, "What was he given?" 

I knew this. I'm an architect who works with existing houses. My first questions about a house are, "What's here? What are the existing conditions?" 

The HABS drawing of the Hall show the north wall, a door with a fanlight and small side windows, a baseboard, a chair rail and an expanse of upper wall with some crown molding.  This is what existed, and seen from the outside,  just too little.

I realized that the main problem was not the lack of symmetry, it was the dinky entrance. The door and lovely fanlight are dwarfed by the expanse of brick, the windows are minuscule. 

Refer to my first picture of the house (above) to see how little the windows are compared to the windows on either side.  

Buckland couldn't change this; he had to work with what was there. 

 

What were the existing dimensions?
One was the height from the sill of the door to the eaves of the roof. Buckland could add inches by adding a step down, but he couldn't easily go higher.

The second dimension was the width. His width couldn't be so large that it drew attention to the uneven spacing of the left and right windows. And: the porch needed to be centered on the door,to  enhance it and its fanlight. The side windows had to be integral to the design.

He used the given height for his width. He drew a square and added the diagonals and the mid-lines. horizontal and vertical.

He added his Lines - upper center of the square to left and right corners.

The square was divided into thirds where the Lines crossed the diagonals. Placing the columns within the 1/3 of the width gave more importance to the door while keeping the rhythm, as well as keeping the steps wide and gracious, the porch airy and open. If the columns had been set on - not beside -  the 1/3 lines the design would have been static, staid.

The points where the Lines crossed the diagonals also marked the edge of the frieze (also called the architrave).

The mid-lines divided the square into 4 smaller squares. When  diagonals were added to the upper squares, where the Lines crossed the diagonals located the height of the frieze, the beginning of the gable, the roof. In the lower squares the Line crossed the diagonals at the top of the hand rail.

I have drawn these  Lines only the right side. The layout is hard to read  when all the Lines are added. On a framing floor. all the Lines would be marked and used to layout the frame.

The arch draws our attention. The half-round shape makes the porch open and welcoming. It frames the main door and its fanlight - inviting you to the house.

Its diameter is 1/3 the width of the porch. It is part of the whole.

 I've drawn it with its cascading circles because it's fun. I also wanted to note how the circle can be a tool for laying out a plan.

Palladio used a circle as his unit of measure: he called it a 'module',  a 'diameter'. His diameter was usually the column in his drawing. Although it's possible that the circle here was also the unit of measure, I think it more likely that it was one of the elements Buckland knew how to use, one that would enhance and unify the porch with the house, especially as its diameter came from the basic geometry of the porch.    

For an introduction to the Rule of Thirds see: https://www.jgrarchitect.com/2020/08/lesson-6-rule-of-thirds-part-1_21.html 

 

An after thought: George Mason used the geometry of the 3/4/5 triangle to layout Gunston Hall, including the dimensions of  his windows. If William Buckland had used the geometry of the square and its circle, its proportions would not have complimented the Hall.

 

Practical Geometry, Drawing the Diagrams #2, the 3/4/5 Triangle

Here's the second diagram I taught at the 2016 PTN Workshops.

I did not lay it out as I have done here. Today I think this diagram would have been a good handout.I could have drawn it; the participants could have followed along and had a cheat sheet to take home.

4/18/2017: this diagram is awkward. I will redraw and simplify.

Using the  3/4/5 triangle for construction

 3/4 5 triangles always have a 90* angle where the side with 3 units meets the side with 4 units.

Draw a line and mark off your unit.



Lay out lines of 3 units, 4 units and 5 units.
On my diagram:  A-B = 3 units
                            A-C = 4 units
                            B-D = 5 units

Swing an arc from either end of A-B; one arc with a 4 unit radius, one arc with a 5 unit radius,
Where the arcs cross is E.





Draw lines from A to B  to E to A.
This is a 3/4/5 triangle. The corner at A is 90*

For fun I have laid out another triangle beginning with 5 units, use 3 and 4 units for the radii of the arcs. It is another 3/4/5 triangle with a 90* corner.

We used Gunston Hall, built of brick by George Mason from 1755 to 1759, as an example. Mason  was a real mason; he gave George Washington advice about mortar recipes. He would have used the 3/4/5 triangle when he built walls or, as a Master Mason, instructed others. The triangle was/is one way to keep brick square and true.
It would have been ordinary for him to use 3/4/5 geometry to design his house.

The base of the brick work at Gunston Hall is 4 units. The height of the brick work of the end wall at Gunston Hall measures 3 units. The diagonal is 5 units.

The floor plan is also laid put using the 3/4/5 triangle. See my post for more information and drawings:  http://www.jgrarchitect.com/2014/05/gunston-hall-ason-neck-virginia.html

I asked the participants at the PTN session to divide the width of the Gunston Hall side elevation into 4 equal parts. I wanted them to draw the geometry for themselves, to see it come to life.

Again a handout with step by step instructions would have been helpful.   

Not everyone knew how to divide a line into parts; but those who did showed those who didn't. It was a excellent group.

One of the first figures in the pattern books on Practical Geometry is the division of a line by a perpendicular. Here is  Figure 5, Plate II, of  Asher Benjamin's The American Builder's Companion, first edition published 1806.











 Asher Benjamin's Figure 3, Plate II,  shows a
simply drawn 3/4/5 triangle expressed with units 6/8/10
with short arc lines at c, the top, to show the use of a compass to make a circle with the radius determined.

His description assumes a familiarity with the language of geometry and compasses.

"To make a perpendicular with a 10 foot rod. Let b a be 6 feet; take eight feet in your compasses; from b make the arch c, with the distance ten feet from a; make the intersection at c, and draw the perpendicular, c b. "

Gunston Hall, Mason Neck, Virginia

updated 5/14/2014

Gunston Hall was built from 1755 to 1759 by George Mason as a home for his family on Mason Neck, Virginia.

Gunston Hall in February, 2014,  photograph by Justin Wilcox, through Wikipedia.
The drawings are from the HABS collection.

Gunston Hall, Return to Splender, the 50 page booklet published by the Board of Regents in 1991, came to me from a friend who knew I would like the pictures, the excellent recounting of the history of the house and its restorations, and the HABS drawings. She was right.

The booklet relates how George Mason began the building himself and then had his brother find and send  William Buckland from England to help him finish the work.

I was intrigued by the fact that George Mason, a very well educated man, realized that he needed help. I wondered if I could see why by looking at the drawings. He knew enough about construction to begin. What happened? Would the expertise William Buckland brought to the work be visible?



George Mason knew about what kind of  plan would fit his family and their life. He knew how to build with stone and brick, how to set a foundation, cap a window, taper a gable, frame a roof. He knew enough geometry to use 3-4-5 triangles and their permutations.

Remember that the diagrams can be enlarged by clicking on them.

The plan  is 4 triangles, or 2 rectangles with 2 sides 3 units long, 2 sides 4 units long. On the right side he has divided the rectangle in half to make his two formal rooms. He has laid out the diagonals of both smaller rectangles. Where they cross he has placed the wall at the edge of the hall.

Note that the rectangles do not meet at the center of the main doors, but to the right side.

The left side of the house was the family dining room and the Masons' own room which Ann Mason also used as office as she managed much of the plantation.

Here a hall separates the rooms.To determine the width George Mason divided the rectangle in half lengthwise and then added the diagonals. The center point is the location of the inside of the wall to the hall. Where the  diagonals cross to the other side of the brick wall, the corridor walls begin. Note that the stair width is also determined by another division of the rectangle and its subsequent diagonals.

On the right side the inside space is divided - it would be smaller than the outside space - into thirds to place the fireplaces in the center of the rooms. I think it is possible that this is one of the changes Buckland made.
Understanding that wall thickness can throw off symmetry comes from experience. Buckland had training as a finish carpenter (a joiner), but he was young, just 22. Mason was 30; he knew brick and mortar, not perhaps not the finer points of symmetry. Proving this supposition would only be possible if the chimney stack was opened and taken apart - not very likely! So this is truly conjecture on my part.



The end elevations continue to use the 3-4-5 triangle for its proportions.
The door is centered. The top of the brick walls is the top of the rectangle.  The gable repeats the triangles. The bricks end on the upper edge. The shape is square and sound, made possible by the 3-4-5 90* triangle which is always true.
I have noted with a strong dot on the upper diagonals how the window height and location are also determined by the diagonal intersections.

Note that the depths of the porches are also 3-4-5 triangles -  drawn in green.

So then to the main elevations, one facing the water, the other the road.

 We already know that the left and right sides of the house are not equal as George Mason wanted larger formal rooms on the right side.

 Here is where I think he got himself in trouble: the left side is truly not as long as the right - see the dotted red line. Look carefully and the dormers: they are balanced but not symmetrical, nor evenly spaced.

 Perhaps Buckland stepped in here, adding the windows on either side of the front door.
What he really did was divert the eye - he added the Gothic porch to the river front: inviting, decorative. with half circles and Gothic curves. We are drawn to the porch and ignore the symmetry.

March 18, 2023: I wrote this almost 9 years ago.  I now know a lot more about Practical Geometry. Please also see my most recent  post about the porch: 

https://www.jgrarchitect.com/2021/07/the-geometry-of-gunston-halls-north.html

I will not delete the following discussion of the porch design. I want a potential geometer to see that as we recover a lost skill we make assumptions and therefore mistakes. That's ok. It's part of the work..

 

Here and in the house his knowledge of Palladio and what was fashionable in England is obvious. William Buckland knew the classic vocabulary. The booklet shows how plain the walls were without his embellishments. His  use of geometry was also much more sophisticated than George Mason's.

The road front porch which we see today came later, after the Revolution. As roads and bridges improved visitors arrived by carriage, as well as by boat.
The center arch within the pediment, flanked by openings marked by classic columns and lintels, comes right out of Palladio's Books.
And it creates an inviting porch. It is scaled to people - we would like to standing there, hand on the railing, welcoming a guest coming down the drive.
 This layout that we now call  'Palladian' was already widely used in Virginia churches where it was referred to a 'Venetian Window'.

I have drawn the first square - set on the diagonal -  that comes from the height. From that comes the outside dimensions, the outside square, and the square turned 45*. The lines regulate the roof pitch, the floor, the line for the lintels. No doubt he adjusted the size of the square to fit the space.


Then the squares are divided in half and the diagonals added. Now the placement and the width of the columns is determined.

I add this diagram to show how the semi-circular arch in the pediment unfolds down the center of the porch to mark the top of the columns, height of the railing and lands on the first step above the foundation.