Thursday, November 21, 2019

God with His Compass

Just a little fun with a medieval illuminated manuscript which includes a compass:

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

It's called 'God Measuring the World'.

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

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. He pays close attention on His first day as he begins to create the World. He sees that it is good.
If He were dividing the firmament from the depths His compass width would be smaller.

In case you don't know this story:

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.

Note:  I'm not yet comfortable with the Beatty-Cramer House, Part 2, which is mostly written. This is a diversion while I cogitate.

Saturday, November 9, 2019

Beatty-Cramer House and its daisy wheel

An Introduction

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. 



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.

I found that the plan was determined by the 'eye', the 3 petals of a daisy wheel.

The 2 squares can be seen as 2 half circles. They could have been laid out with twine and pins.

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.

The bents for both rooms were laid out from the Rule of Thirds applied to 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.

With this information the carpenter could 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:

Sunday, October 27, 2019

Portraits of Master Builders with Their Compasses, Part 2

My previous post had portraits of men who designed and built - Master Builders - with their compasses. 
Here are a few more.
Before 1800, in the States especially, the word 'architect' referred to master carpenters and masons, not a specialized group of people who had not trained in actual hands-on construction.
For more clarification look up the word 'architect' in the OED - the Oxford English Dictionary - which gives origins, sources, and historic uses of words. Its first definition of 'architect' is 'master builder'.

Men who drew and designed buildings, machines, and equipment used compasses. They often had other jobs too - painters, builders, tool makers, teachers, surveyors, erstwhile inventors.They are well-rounded, experienced craftsmen.

Here is James Watt, a famous Scottish inventor with his compass. He vastly improved the efficiency of the steam engine, working on the refinements from about 1765 to 1790. While he refined the parts of the steam engine, he made mathematical instruments and was a land surveyor. 
The Britannica has an excellent biography on him. 

This sculpture is in the  National Museum of Scotland in Edinburgh.
For more pictures and information about James Watt  see my blog post:

By the mid-1800's men who drew buildings were beginning to call themselves 'Architects', no longer 'Master Builders'.
Asher Benjamin and others designers are said to have joined together as 'architects' teaching in Boston in the 1840's.*
New York architects created the American Institute of Architects in 1857.
MIT, founded in 1868, was the first school to train architects. The department was, and is, called  Course IV. William Ware, mentioned below, was its first Director.
The street directories in Lawrence Massachusetts,  1845-1880, show men who first advertise themselves as carpenters, later listing themselves as builders, and then as architects.

John Haviland called himself an architect. He apprenticed to an architect in England, then sought to become an engineer in Russia, before migrating to the States in 1816. Here he is, with his compass.

For information about the portrait see the blog post listed above for James Watt.

Edward Shaw published his pattern book in 1854. He referred to himself as an architect.

His book discusses design and relationships between parts. It also includes detailed information for carpenters, masons, plasterers.  
I wrote about this illustration and the tools shown here in this blog post:

Le Pere Soubise is the legendary founder and saint of the Campagnons Passants Charpentiers de Devoir.

There is more about le Pere Soubise and his compass here:  

An engraving of Giacoma Barozzi da Vignola (1507-1573) with his compass.
Vignola trained under Serlio, then worked in France for Francis I at the same time Serlio was there. He wrote Canon of the Five Orders of Architecture in 1562. It was widely available, reprinted, and translated into many languages. This image is from the edition translated by John Leeke into English in 1669, now available through Dover Publications.  

And why did they need compasses? The compass was a tool of layout - for design, for setting proportions. A ruler could then be used to measure those proportions. 
*I had the citation about 10 years ago, but cannot find it now. Perhaps it could not be substantiated.
I apologize for the type size changes. If I understood what causes them I would fix them.

Sunday, October 20, 2019

Portraits of Master Builders with Compasses, Part I

This past year I have given 8 presentations on Practical Geometry, the last 3 at the International Preservation Trades Workshop (IPTW) in Stirling, Scotland. My workshop begins with a power point introduction about how geometry was used in construction. Then we practice using compasses, straightedges, pencils, and twine (chalk lines, anyone?) to layout and design frames and buildings. 
The portraits here of master builders holding a compass, the symbol of their profession,  are part of those presentations.

Sebastiano Serlio, 1475-1554, master builder and author of    'On Architectura'
 posthumous portrait by Bastolomeo Passerotti c. 1575, 
now in the Martin von Wagner Museum,  University of Wurtzburg.

I wrote an introduction to Serlio here:

 Andrea Palladio,  1508-1580
architect and author of The 4 Books of Architecture, 1570

The engraving and the painting it came from may have been made 100 years after Palladio died.

James Gibbs, born in Scotland, died in England: 1682 - 1754. Architect of St. Martin's in the Field church, 1722. author of the Book of Architecture. 1728. This book of engravings of his buildings is known to have been in the Colonies. It influenced a great many designs.

Portrait in the Scottish National Portrait Gallery

William Buckland - 1734-1774
indentured to  George Mason of Gunston Hall, 1755 

Master Builder in Virginia and Maryland

Note his compass on the table below his hand 

I write about him here:

Peter Nicholson  - 1765 -1844  
Author of texts for master builders, architects and engineers, and mathematicians beginning in 1793 , extending through the 1840's. His books were in print many years after he died and went through many editions both in London and in the States. Asher Benjamin and Owen Biddle credit him in their pattern books. Minard Lefever says (here I paraphrase):  "Refer to Nicholson . He's the master!"

For more on Peter Nicholson see:

Much of what I taught this year is not yet on this blog.  It should be, so this is a beginning.

Thursday, October 10, 2019

The Compass in Construction

Compasses are regularly portrayed in construction images, and are also regularly ignored.

In October, 2018, the Preservation Trades Network (PTN) met at the National Park Service Historic Preservation Training Center in Frederick, Maryland, for its annual workshops.

I gave 2 presentations on the use of compasses in historic layout and design. More than 30 participants practiced their geometry - with enthusiasm. They asked good questions.

PTN workshops were held in the shops, the yard and storage bays, and an office of the Training Center. Around us were the HPTC logos.
They all included a trowel, a plane, and a compass.

As posted here: 
top: on a brochure
middle: real tools mounted on a board hung on a wall
bottom: an image posted on a bulletin board

I asked the staff who came to my presentation what they knew about using a compass. They told me: not very much.

The image of  a compass is there, along with a trowel for plaster, masonry, and stone work and plane for wood working. The compass as an equally important tool for layout and design. The understanding of how and why to use one has been lost.

 In September, 2019,  PTN joined with Historic Environment Scotland to hold the International Preservation Trades Workshops (IPTW) at the Engine Shed, Stirling Scotland. I gave 3 presentations with slides and hands-on practice drawing layouts and elevations without numbers,  using only a compass, a straight edge, and a pencil.

Our final evening we dined in the Banquet Hall of Stirling Castle, historic home of Scottish kings, including Mary, Queen of Scots, and James VI who became James I of the United Kingdom.  (No, the roof trusses were not this pink! just what my camera saw!)

 Before dinner we toured the castle which is set high above the land and the river.

It is beautifully cared for; the rooms used by the royal family furnished with fascinating furniture and tapestries depicting the time when Mary Queen of Scots and James VI lived there. The signage is excellent: clear, colorful,  with historically accurate graphics and information.

 Even jokes were in period dress: These plaques were beside the  restroom doors; a medieval beast which might be a griffin was watching from the newel post.

This poster was in the courtyard. I liked the images:  the tools in use, the appropriate clothing, and surroundings. visually interesting and easy to understand.

The text explains the work. Except for that compass the master mason holds under his arm.  It is perhaps 24 inches long, with brass fittings and an armature to set the span. This is a serious instrument.
No explanation is given for its use.

I think people simply don't understand how a compass was used. No one  asks how the project was organized, how it was planned and set down so that all the craftsmen  could reference what was to be built.

How did they share their understanding of the scope and detail? The master craftsman laid out the design of the work.
He used his compass to accurately draw and explain his plan to  the other workmen.
 I looked on the internet for the proper name of the 'armature' on a compass used in construction. 'Hinge' is sometimes used but that refers to the part where the legs join.  In the 1920's the 'arm' had become a bar with an adjusting screw; the compass called a 'spring bow".  
Because there is so little written about compasses used in construction I may need to revise this post as I learn more. 

Bow compasses

Page 614, Audels Carpenters and Builders Guide #2, Theo. Audel & Co., Publishers, NY, NY, 1923

Tuesday, September 24, 2019

John Haviland and James Watt with their compasses

Portraits of master carpenters and architects with their compasses are part of my presentations: how I show people that we really did use geometry and compasses for design and layout.

I collect these images as someone else might collect old maps or historic recipes.

This is John Haviland, 1792-1852, an emigre to Philadelphia. He designed many Gothic inspired public works around Philadelphia.
The portrait is now in the NY Metropolitan Museum of Art. I have cropped it so his compass (which shines) can be clearly seen.

 Like Owen Biddle, Haviland taught 'carpenter's assistants' in Philadelphia. In 1833, 28 years after Biddle's death, he reprinted Biddle's pattern book.
He also wrote his own 3 volume pattern book, beginning in 1818. The Met has one copy; the other is in a library in Australia.I have not yet read it.

James Watt  (1736-1819) was a famous Scottish inventor and mechanical engineer.

Soon after he died Sir Francis Chantrey was asked to create this sculpture to honor him.
Watts is shown designing the double acting beam engine. a new and powerful steam engine which changed manufacturing. It drove machinery all over the world.
Note that he is designing with his compass.

This sculpture sits in the entry hall of the National Museum of Scotland in Edinburgh. It is on loan from the Heriot-Watt University in Edinburgh, named after him and George Heriot.
(Heriot (1563-1624) was a goldsmith who left his money to educate the orphaned sons of freemen in Edinburgh.)  

I had come to Edinburgh after presenting on Practical Geometry at the IPTW 2019 in Stirling, Scotland, September 5-7. I was enjoying the museum with friends, including a 3 yr old who needed to visit the sharks and dinosaurs, when I came upon James Watt.
What fun to share a 3 yr old's enthusiasm and come across one of mine in the process!

For an interesting look at James Watt and his world,  read this blog  written by an intern at the Engine Shed, the center (run by Historic Environment Scotland) where my IPTW conference had just been held.

Friday, June 14, 2019

Corn Cribs for the Indiana Barn Foundation Workshop and Keynote

July 19-20, 2019, I will give a workshop and the keynote address on Practical Geometry for the Indiana Barn Foundation at the Oakwood Retreat Center in Selma, Indiana.
Their website is :

The picture they used for their announcement is the one I use on my website: It's a farm house north of Boston built about 1830 which was designed using a wonderful combination of circles and squares. I hadn't planned to include it in the talk but now think, of course, I will.

One post about this house is here:

I might have chosen this picture of my corn crib as it is a barn out-building - and because it is red!

My post about the corn crib here:

2 more corn cribs will be part of the lecture and probably the workshop.
They are from different construction traditions in different parts of the States. utilitarian buildings, built without frill, their forms easy to understand and read. They all use geometry differently.

The front of the Knight corn crib in Flatbrookville, Sussex County, NJ, shown here, is one of 3 HABS photographs of the crib. taken in 1969.

This is the quote which accompanies the photographs and drawings.
"Within this farm group that developed between 1826 and 1910, two significant structures are the corn crib and hog barn. The corn crib is an excellent example of early corn cribs in the Delaware River Valley, featuring a frame that is hewn and pegged."
This corn crib in New Jersey is therefore about the same age as mine in Vermont; they are not the same.

Here are the HABS drawings.

 It is so different from  my Vermont corn crib that if the sides did not slant I would have thought it just a shed.

The layout is governed by its width. The posts are placed  by 2 red squares and the arc of the squares' diagonals.
The same sized  2 red squares and the arc of the diagonal determine the height of the crib and its roof.
A crew could lay out the plan on site with twine,
then layout the section of the crib on a framing floor with twine,  cut the frame and assemble it on site.

The slope of the walls is set by the square: the sills - noted in red - are located inside the lower corners of the square, the mid-plates - also red - are located on the outside of the upper corners. the slope continues up to the height of the upper square.  The red line on the right indicates that the height of the wall is divided in half by the center girt.
 The crib design could have begun with a line and its perpendicular. The line could be the width; the perpendicular could have been one wall. Then with twine the arcs - in red - could have located the posts - also in red.

The upper brace in the section falls on the point where the diagonals crosses the arcs of the side of the square - noted in red. 
I have seen this only once in New England. The center brace is on the line of the squares.
The lower brace is not located on the arcs. Instead it is centered between the floor and the mid-brace.

To see the HABS photographs and drawings, type the name and location "Knight corncrib... " into your browser.

Sunday, June 9, 2019


 June 9, 2019
subject to updating

This bibliography was first complied to accompany a lecture on Practical Geometry in 2016. It is now available whenever I present.

A list of books by and about builders and architects who used Practical Geometry; many are primary sources.
At the end are other sources, websites, and credits.
It does not include books I refer to in a specific post. For example: Audel's Carpenters and Builders Guide, Theo Audel & Co. Publisher, NYC, 1923, is footnoted at the end of that post:

A few are books on architectural history and technology which I reference regularly:  Bannister Fletcher's History and Knight's American Mechanical Dictionary.


Benjamin, Asher. The Country Builder’s Assistant, 1797, Dickman, printer, Greenfield, MA –
     reprint by Applewood Books, Bedford, MA.
                     *The American Builder’s Companion, 6th edition, RP &C Williams, Boston, 1827
Biddle, Owen. *Young Carpenter’s Assistant, published by Benjamin Johnson, Philadelphia,
Charles, FWB, The Great Barn of Bredon, Its Fire and Reconstruction, Oxbow Monograph 76,
     1997, Oxford Books, Oxford, UK.
Fletcher, Bannister, A History of Architecture on the Comparative Method, Charles Scribner’s
      Sons, NY, 17th Ed. 1967.
Gibbs, James. *Book on Architecture, London, 1728
                       Rules for Drawing the Several Parts of Architecture, printed by W. Bower for the
      author, London, 1732, ECCO print edition  
Green, Bryan Clark. In Jefferson’s Shadow, the Architecture of Thomas R. Blackburn, Princeton
       University Press, NY, 2006
Harris, Leslie. Robert Adam and Kedleston, The National Trust, London, 1987.
Knight, Edward H. American Mechanical Dictionary, Vol I, II, III; J.B. Ford & Co. NY, 1874.
Nicholson, Peter. The Carpenter’s New Guide, 1793, London; 10th ed., Philadelphia, 1830.
Palladio, Andreas. *The 4 Books of Architecture, 1570, translated and published by Isaac Ware,
      London, 1738.
Serlio, Sebastian. On Architecture, Lyon, France 1530, translated in1611, available on-line. 
       Translated by Vaughan Hart and Peter Hicks, 1996, Yale University Press, New Haven
Shaw, Edward. *The Modern Architect, Dayton & Wentworth, Boston, 1854
Smith, Laurie, The Geometrical Design of St. David’s Cathedral Nave Ceiling, A Geometer’s
      Perspective, The Geometrical Design Works, 2017, printed Exeter, UK.
Vitruvius, Marcus. *The Ten Books on Architecture, c. 10 BCE, translated by Morris Hicky
      Morgan, Harvard University Press, 1914.

*Reprinted by Dover Publications, Inc., Mineola, NY

     HABS drawings, Library of Congress, Washington, DC
     Denison Bingham Hull, Old First Church, Bennington, Vermont, c. 1935.
     James Platteter, barn frame for Green Mountain Timber Frames, 2014
     All others: Jane Griswold Radocchia
Web sites: (you are here!)  and
for Laurie Smith: and