Thursday, November 21, 2019

God with His Compass


This is referred to as 'God Measuring the World'.

 I think the title could be 'God Creating the World'.

The image is c. 1250. It is the frontispiece of German Bible. The person who drew this was most likely a monk.

Here's what I see:
God is holding the world in His left hand. His right hand holds His compass, ready to be turned in an arc. He has set His feet to steady Himself in a door frame.  His right foot is outside the frame; His toes catching the sill. 

His brass compass is long - 24"? It has a well wrought hinge which might have a nut on the right side and a handle long enough for easy grasping.  Its wing has generous length, allowing God to adjust His dimension.
The accuracy of the depiction of the compass and the posture of God tell me that the illustrator knew personally how a mason or carpenter used a compass. It was a portrait of God. The model could have been a friend or himself.


Earth appears to be a flat disk, a plate, with the darkness upon the deep, the light divided from the darkness, and the earth without form - just as described in Genesis. 

God has put one compass point into the center of the world. He has set His width to a pleasing radius. He is drawing a circle, the first step in compass layout; or perhaps He has just finished drawing the circle: He has just laid out the World.  He pays close attention on His first day as He creates the World. He sees that it is good.
If He were dividing the firmament from the depths  - measuring - His compass width would be smaller.

In case you don't know this part of the Bible:

The  Bible (using 17th c. English, the King James Version of the Bible,  not the Latin this monk probably knew):
"In the beginning God created the heaven and the earth.
And the earth was without form, and void; and darkness was upon the face of the deep. and the spirit of God moved upon the face of the waters.
And God said let there be light. And there was light.
And God saw the light, that it was good; and God divided the light from the darkness.
And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.
And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.
  Genesis, Chapter 1.1-6.

The sun and the moon are not created until the fourth day in verse 16.

See also Proverbs, Chapter 8. 22-29.


Saturday, November 9, 2019

Beatty-Cramer House and its daisy wheel, Part 1 of 2



An Introduction 
I wrote this too quickly. I am now revising it. Proceed thoughtfully - and check back to see if my words make more sense. I can see the geometry faster than I can explain it.



This house in Maryland was about to be burned down because its owner had no use for it. It looked to be a c.1850 farm house that might have also been an inn.



A local historian asked to look at it. 
He had seen the frame and the brick nogging (infill between the posts used for insulation) where the siding was missing on the end. Both looked to be Dutch, not English; the spacing appropriate for a Dutch jambless fireplace. The post below the window had been cut to make room for the window.
What had it been when it was built?

                                                                                                        
Inside he found another house, 1-1/2  stories: the main room on the north end with beams 4 ft apart supporting the 2nd floor.
The original kitchen to the south end had been down half a story. It opened out on grade to the well house  a little farther down the slope.

This 'inner house' is the Beatty House, built in the early 1730's by the family of Susannah Beatty who moved here from Ulster County, NY.  The property is now owned by Frederick County Landmarks Foundation.
The Beatty House is 20 ft. x-.40ft., story and a half with a lower kitchen, and an H-bent timber frame, an Anglo-Dutch style found most often in New York. 
The well house, just south of the main house, had a well below and a smoke house above. The Foundation has restored it.



In the 1850's, new owners, the  Cramers, dramatically remodeled. 
The windows were relocated; the old openings blocked. 
The half story split of the wings was eliminated; the 2nd floor gained full head room. 

All of this was done by building a new structure around the original  house. 

The photographs shows the original 2nd floor half story with the new house wall behind it. The views are to the northeast corner and the southeast corner. The end of the plate - where it was cut off  for a window - is visible in the northwest view. I've added a close up view below.

The southeast view shows the new windows cut into the original frame. Also note the original nogging in all the photographs. 



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On the second floor the plate, which had been carved to be the fascia and soffit for the roof overhang, was left in place. The new house was simply framed outside of it. 









As shown above, much of the history of the house is visible in the frame. Here is the mortise for a missing beam.

There are remainders like this all over the house. The original frame can be read, and the later renovations too. The attic over the raised south end - the c. 1850 kitchen and bedroom wing - was framed with reused rafters: many with scribe marks but not in order.  



The Geometry


These 2 diagrams are on  a stud on the second floor.
The daisy wheel is about 3.5 inches across.
The 'eye' - which is  1/3 or 3 petals of the daisy wheel is about the same size.

Could I discover how/if these diagrams governed the layout?

The Foundation had measured drawings of the Beatty House - the original house. They gave me a set.
I began to look.
Of course the builder considered the land, the size of the house, what rooms were needed, how situated. He knew how he would frame, where the windows and hearth were to be located. Much of this would have been tradition.
The siting was specific to this location: the wall facing the road and the width of the house were known before the actual staking of the Lines.




This is framing layout for the bents to support the second floor.
East is to the right.

The east room is a square. The west room is less than a square. The framing is shown for the jambless fireplace in the south room, that for the north room is missing. The ends of the tie beams are still there in the exterior east wall.


I found that the plan could be determined by the 'eye', the 3 petals of a daisy wheel.
Here is an introduction to how the diagrams can be used.


 The eye is 3 petals of the daisy wheel. The length of one petal is the distance between the petal tips. It gives the builder his first dimension from which all the others come. Here it is the width of the house:  C-D in the floor plan below.


I first thought the house was laid out as described below.
Today I think probably not.
Still this is a clear clear description of how a house could be laid out with a given dimension, a Line (twine), and pegs. 

The 2 squares can be seen as 2 half circles. 
The front wall is A-B;  initially it is a Line of unknown length.  The width of the house (C-D) is the radius. It is set where the builder thinks the wall between the 2 rooms should be.  With C as the center of the circle swing an arc from A to B. 
Then with D as the center of a new circle, swing an arc from E to F.
G marks the intersection of both arcs.
The line perpendicular to A-B and D-C-E  at G, parallel to C-D  is the inside edge of the south wall of the south room.




Rethinking
G is located on the inside of the west wall. This made me reconsider. I've seen many barns and buildings whose dimensions begin from that first Line. The builder set his first wall location - the red line between the petals on the left side - and then did his layout from the inside face of the sill.
He could swing arcs - noted with black arrows - the width of the house,  the first dimension. Where they cross the center of the daisy wheel  becomes the length of the west rooms. a straight line there is easy to draw: it has 3 points - the petal points and the center of the wheel. 





He continues laying out his frame from the middle wall. Here he extends the parallel Lines that are the .south and north  walls, uses the arcs of his Line, C-D above, to lay out a square and the east end of the house plan.

The builder used both the daisy wheel and the eye for his floor plan.  
The west side of the house is not square so a circle does not fit.
The bents for both rooms are easily laid out by the Rule of Thirds, begun at the inside of the sills. See the red rectangles laid out on the inside of the sills.
The narrower west room placed the bents symmetrically: 2 on the west sides, 2 on the east sides of the Lines.
The east room placed the bents on the east side of the Lines. This gave a little extra room for the jambless fireplace.
See the red spots on the sides of the bents.



The supporting side beams for the jambless fireplace were located at the quarter points of the exterior wall.  See the dashed red lines that are right beside the beam locations.
The builder could also simply marked the inside width of the west wall on his Line, folded the Line in half and then in half again. He would then have the quarter points.  
The carpenter could then set his marks for mortises in the sills and tenons in his posts and beams. The height of his bents is not yet determined.


The elevations and the daisy wheel will be in another post.
For an introduction to the Rule of Thirds see: https://www.jgrarchitect.com/2016/10/practical-geometry-drawing-diagrams.html