Saturday, February 17, 2024

"Keep Within the Compass", Cautionary Prints, c. 1785

Here: a well off and contented woman,  her space defined by the compass which is encompassed by a circle.

The print, dated 1785, is now in the British Museum. Prints like this showing women and men within the circle, scribed by the open compass, with corner vignettes, were common c.1780.

 The woman is sheltered by the compass. She is in a tranquil country setting with her dog and her wealth, her book. Beyond the circle is the vivid story of her possible dissolution: drink and gambling leading her to debtors' prison where she must break hemp. 

The words on the circle are, "keep within the compass and you shall be sure to avoid many troubles which others endure". On the swing arm of the compass is engraved, "Fear God'.

Googling the phrase running around the circle, "Keep within the Compass" brings up this image and a description of Free Masonry, including the idea of the circle as a symbol for God. 

Whoever wrote the entry ignored that well made, shiny compass with a serrated, adjustable swing arm, tapered legs with well defined knobs and sharp points ready to scribe that circle. The commentary only says that it shelters the woman.

Why did the print maker draw a compass so carefully if it wasn't part of the visual message? A shiny shimmering circle would have sufficed. The compass is a tool; here the tool of God, and the tool required to draw the circle.

I think the writer, and we as a culture, have forgotten common skills and so we no longer understand references and images our ancestors took for granted. 

As recently as 1950, compasses were tools, used every day by people who built with their hands: masons, carpenters, as well as architects and designers.  This image is an illustration from Basic Technical Drawing, published by The Macmillan Company in 1956 and 1962, written by Henry Cecil Spence. 

70+ years later we have almost no experience of geometry as practical knowledge, of compasses as instruments.




When the 'Keep within the Compass' print was first made the designs in patterns books included geometry as a matter of course.

Plate XXXVIII in William Pain's pattern book,  The Practical House Carpenter, printed in London in 1794, assumed that his readers used geometry: "...the height of the column... to be divided into 9 equal parts, one of which will be the diameter of the column at bottom..." 

His description for the pediment begins, "to find the pitch of the pediment set the compass at a..." His readers understood the compass cues: the letters and the dashed lines, the notation of lengths on the line along the left side. 




Here is Plate X in Asher Benjamin's  pattern book, The Country Builder's Assistant, printed in Greenfield, MA, in 1797.

His descriptions include 'diameters', 'arch lines' and notes about where to 'set the compass'.  He writes, "Divide the height of the  column into 10 parts, one of which is the diameter of the column."

The compass was used for measuring as well as a layout.






This sculpture of James Watt. the Scottish engineer, carved about 1820, during his life time, shows him using a compass to design the steam engine.

The compass was an engineer's design tool.




James Watts' little compass is a measuring and design tool, a tool for thinking carefully, thoughtfully.


Here are 2 more historic prints of people within the compass and pictures in the corners of their desolution if they do not keep within the compass. 

 The gentlewoman is finely dressed with a devoted pup and a chest of jewels and garments beside her, a purse on her arm, a book in her hand. She keeps within the circle drawn by the compass. The sky is a lovely blue.

Clockwise from the upper right: The gentlewoman drinks, does not tend to her baby or her sewing.

She gambles and plays cards. losing her money.

The constable (in blue, an official someone) takes her off to debtors prison

where she must break hemp to help make the ropes for the English navy, and will be flogged if she doesn't.

 And, in case you needed reminding,  "Prudence produceth esteem".

Here is the gentleman, prosperous with land, servants, crops, a mill. He is finely dressed and well fed. 

In the corners are his downfall because he did not "keep within the compass": wine and women, gambling in the upper corners. 

His investments, his goods and ships, are lost at sea so that he too ends up in debtors' prison.


The final words: "Industry produceth wealth"







In case you wondered: God knows about compasses. Here He is creating the world, from the frontispiece of a  German Bible, c. 1250.







My thanks to Patrick Kennedy (of Historicorp and PTN)  who introduced me to these images several years ago.

To see the prints at a bigger scale look for the British Museum website and  'Keep within the Compass' online.








































   * William Pain, The Practical House Carpenter, 1794, 5th edition, London; Plate 38. Reproduction from British Library by Gale Ecco Print Editions




The ones sold as toys lack sharp points. They are useless because they skitter across the paper.  Without a fixed point for a center a compass can not draw a circle.

Tuesday, January 9, 2024

The Practical Geometry of the Parson Barnard House: Addendum


How did the builders of the Parson Barnard House actually use Practical Geometry?
Did they have to draw arcs with twine every time they wanted to measure something? 

Probably not. I think that they knew the geometry so well that they could take short cuts in laying out a house .*

Consider a carpenter's education in 1715, when this house was built.  A boy would have been apprenticed to a carpenter when he was about 11 years old. Along with woodworking skills he would have learned the fundamentals of geometry: how to use a compass and line for measuring lengths, how to lay out basic shapes with a compass and a straight edge. 

After 7 years of training the apprentice became a journeymen. He would have traveled and worked for other carpenters. He would have broaden his understanding of practical geometry and understood how geometry works. He would have been able to skip steps.


The previous posts on the Parson Barnard House** explored the geometry used to lay out the house frame and window locations on the front facade. 



The width chosen for the sill, about 18 feet, was the dimension used for the layout. The room sizes and the overall width and length of the house come from that first length. The bent's rectangle comes from using the sill length as the radius of the daisy wheel by which the framers laid out rectangles.



 The sill length was also the beam length for all the bents.  

The diagonals are the Lines which true the rectangle's corners and mark the location of the 2nd fl. beam. See earlier posts**




The chimney mass is the only part of the house with unrelated dimensions. Built of brick, it used the 3/4/5 rectangle.**


The carpenters would have staked a line at one end of the house for the exterior of the foundation 1-2.
Then they laid out the length, 18ft, and staked it 1-2. They laid out a right angle (here shown as a 3/4/5 triangle), and extended that line 1-3 18 ft. - marking the second side of the square; they didn't need to swing the arc. from 2 to locate 3, marking 3 corners of the square: 1, 2, and 3




The 18 ft. Lines arced from the corners 2 and 3 would cross, locating the 4th point. The carpenters didn't need to draw the arcs, just where they crossed.



Then they would check to be sure it was true, just as builders do today.


Matching diagonals across the square would confirm the carpenters' accuracy.  1-2 = 3-4

The Parson Barnard House geometry uses the length A for its floor plan and its bents. That length comes from the arcs of the length of the bent. It could have been found by 1) folding the Line (about 18 ft long, the length of the bent) in half, marking that point - shown here on the bottom line of the square  - and then 2) marking where the arcs cross (dot).  A length from the base to the arcs' intersection, the dashed line A, could be transferred to the side of the square, giving the width of a room, the height of the bent.  (NB: Geometry requires 2 points in order to draw a straight Line.) 

The carpenters only needed to find this length once. They could have marked it on a plank for reference until the frame was complete, then used the plank as sheathing for the walls or roof. 

Some of these layouts have been found and saved: Eastfield Village in East Nassau, NY, ( has some which they noticed on the roof sheathing when the Inn was dismantled and  moved to the site.  Unfortunately, because we have lost most of our understanding of practical geometry, those doing restoration rarely look for such notations left by earlier craftsmen. 

*NB: When I teach, the students and I swing the twine in arcs to mark the corners of a house foundation. It was easy, fun, and exciting as we see the shape come into being.  

** see: 

 *** Brick walls are built row by row. 2 Lines and the 3/4/5  keep them true vertically and horizontally.

Tuesday, December 12, 2023

The Practical Geometry of the Parson Barnard House: Its Assymmetry

The Parson Barnard House, Part 3.*

The front  elevation is asymmetrical.  Did you notice?

The door at the Parson Barnard House is not in the center of the front of the house. But, yes - it's the focal point. The pediment, the surround, the red paint, the chimney above reinforce its importance. The paired windows on each side create a space between them where  the door belongs.  





The paired windows are not equally spaced from the door, see A and A. The spaces between each set of windows are also unequal, see B and B, nor are the distances from the corners equal. see C and C. * *




The frame, the posts and beams, with the door and second floor window centered under the chimney, more or less.** 

The post and beam frame is structure here; it is not the design.





The windows could have been centered in each bay and the house would look like this: simple, direct, and a little crooked, boring.

Note: this looks very much like today's subdivision Colonials with the obligatory 2 windows on  either side of a door. It's acceptable, but that's all.



Instead, the carpenter built this. He gave us balance and grace, a lively facade.

This image is from 2021. The first floor windows in the HABS drawing have been replaced with windows with panes which match the early second floor windows.  


What did the carpenter consider?  

First: the Hall was the larger room; the Parlor, smaller. The front door could not be not centered on the front wall. 

Second: the door needed to swing so that people could go directly into the Hall to the right, the main room of the house. The door must also swing back, fully open, for easy access to parlor.

The drawing shows the door swing with black arrows, The vertical red line is the center of the entry hall, but not the center of the front facade, nor the center of the space between the windows on either side.

The porch is no longer there. It did not date to the early construction.

Third: the 2 main rooms of the house, the Hall and the Parlor, face south. That orientation allowed for maximum sunshine which gave (and still gives) both light and warmth to the interior. Placing two windows on the south wall in each room (and at least one on the east and west walls) was essential. 

Fourth: the parlor was the formal room. It was the parson's study/office; he was the most important person in the town. It required a pair of balanced windows, gracefully placed.

Fifth:The carpenter was using simple geometries: the square derived from a circle. He knew how to use diagonals to divide lines in half. He used the arcs of the square to set a smaller distance as shown here.***

We see today that he had a sense of design, a 'good eye'. Unfortunately, we don't know who he was.    


The window placement came from that geometry and the carpenter's visual understanding of the house: how that facade would 'speak' to those coming as well as to those already in the house. 

Bents were raised one after another, set into the sill below; the plates added above. The carpenter would have laid out the bents  along the sill and the plate on the framing floor before the raising. He would have cut the stud pockets along with those for the posts. The window frames were probably added later as they were hung from the beams at the ceilings, but he would have known the sizes of the windows he planned to install.

The geometry  of the window spacing  in the Hall used the distance from the exterior bent to the center bent in the Hall as a radius. The arcs of the semicircle and its reverse cross at 2 points, once on each side.The secondary arcs cross the semicircles 4 times at their 1/4 points. 2 straight lines with dots on their ends position the outer sides of the windows. 

This layout is 2 4 arc stars side by side.***

The placement of the Parlor windows follows the same geometry. 

I have drawn an alternate way to layout those locations. To read a simpler solution skip to the last paragraph!

Just as in the Hall the length of the arcs chosen is the distance from the right side of the post at the right of the parlor to the right side of the center post. Those 4 arcs cross top and bottom. The line with a dot at each end comes from the 2 points where the arcs cross. It locates the right side of the right window.  

The 4 arc star has 4 points. Those points allow the original square to be divided into 4 equal smaller squares. They also give the length between the window and the right post. That length, drawn here with arrows, gives the distance from the left window to the exterior wall, also a black line with arrows.

Or consider this: the carpenter knotted his twine (his Line) to mark the width of the parlor, outside of the corner post to the inside of the 3rd post. He folded the Line in half, and then again. He now had 4 equal lengths  which he could have marked on the sill and the beams.The outside lengths located the left and right edges of the windows. He folded a shorter Line to locate the windows in the Parlor.**** He would have known his geometry so well he could use short cuts. I write about this is my next post: 

* the link to my posts on the House for the practical geometry of the frame    

http: s:// and 

**The HABS drawing, c. 1934, shows a larger surround and pediment. These were updates to the house, removed to reveal the original 1715 doorway.

 *** I often find this '4 arc star' when I explore Practical Geometry. It follows naturally from the square derived from a radius. The radius is often the width of a room, the length of a beam. It easily provided 2 points for dividing a space in half either way. It is often the width of a room, as it is in this house. I have found no name for this geometry so I am naming it here: the 4 arc star .   

**** He could also have transferred his dimensions to a pole. Carpenters today use a 'pole' to make sure  clapboards and window casings line up around a house. It is a thin board, a piece of scrap, that can be propped up against the house wall and easily moved from location to location,


Monday, November 20, 2023

The Practical Geometry of the Parson Barnard House: the Bents


This is the second part of my study of the use of geometry in the layout and design of the Parson Barnard House, in North Andover, Massachusetts.

Here's the house. The left section, the 'front', was built in 1715; the saltbox added in 1720. The rear extension to the right came in the 1950's. 


For my first post on the Parson Barnard House please see the link at the bottom of this page.*




The first floor plan shows the 2 back wings. The middle section, labeled kitchen, back hall, and study is the 1720 saltbox addition. The laundry and entry spaces were added 230 years later.



The geometry of the first and second floor plans match. The posts and beams of the second floor match those of the first floor.

The plan shows a step down into the saltbox addition.




The side elevation also shows this step down. The dashed lines locates the floors and the step down.



The layout Lines locate the inside edge of the posts and the inside width between the posts on either corner of the house. Together they outline 3 sides of a rectangle, the layout for the bents of the frame.  The radii of the arcs is the width of the frame. They cross at the placement for the lower side of the beam which supports the attic floor joists. It is the upper beam of the bents that frame the house.  

This use of geometry matches the way the parlor width was determined. The thin black Line marks the rectangle which is the inside of the bent.






The rectangle from that layout crossed with its diagonals. Where the Lines cross is the height of the beam which carries the second floor joists. 

*See note below for more information.

For reference here is the geometry of the first floor plan with the Hall on the right, a square; the Parlor on the left, a rectangle whose width is laid out by the arcs. This geometry is laid out from the inside edges of the posts. 




When the same geometry is used to lay out the bent using the width from the outside of one post to the other as the dimension, the crossing of the arcs is at the upper side of the attic beam.

**Look back at the elevation of the house with the rectangle derived from the interior dimensions. Note that the second floor and attic windows - which appear to be original - are centered on the space. Using the outer dimensions the windows are no longer centered.





Here is the design for the 6 bents for the Parson Barnard House (without the braces). This simple layout requires only basic knowledge of Practical Geometry. 

The bottom red line is the sill.



Do the layout differences I've shown here - between the use of the inside and the outside widths - provide evidence that the interior widths were used? Or do they simply mean the drawing is too small, my lines too thick or not perfectly placed, that the attic framing might yield other information for an accurate assessment?



Tuesday, November 7, 2023

The Practical Geometry of the Parson Barnard House: the Floor Plan

The Parson Barnard House, North Andover, Massachusetts, built in 1715. This picture was taken in 2022.

The original house is the front (left) section: 2 rooms up and down, each with a fireplace. The chimney in the middle served all the fireplaces and acted as a radiator.

The saltbox extension was added c.1720. The rear wing dates to the 1950's.






John Abbott measured and drew the floor plans and elevations of the house for HABS in 1934. At that time it was thought that Simon Bradstreet had lived here. Now we know the families of the Reverend Thomas Barnard and his son, the Reverend John Barnard, were the first residents from 1715  to 1757.


Here are the tools a  Massachusetts Bay Colony carpenter had in 1715 for planning and laying out buildings*. He used a compass, a square, horizontal and vertical levels, a straight edge marked in regular increments (which might or might not be inches) and a line with a spool on one end and a plumb bob on the other. The builder also had an awl, chalk, charcoal, and an 8 or 10 ft. rod.

His square was small and might not have a true 90* corner. His inch, foot, rod, varied from those of other carpenters. He would have learned his skills as an apprentice to a master carpenter, become a journeyman, then a full-fledged carpenter. His training would have included practical geometry. Tape measures had not been invented, paper was precious. He drew plans on framing floors, on sheathing, on dirt. He did not need to be literate.

Using a compass, a straight edge and a scribe a carpenter could layout the plan on a board, then step off the plan on the site with his rod or his compass, set his lines, and true them. This is the same order in which we layout buildings today; we simply use more modern tools.

This is the floor plan of the original house.
Noted in black are the sills, the posts and beams for the first floor frame . 

 The carpenter knew the first floor would have a Hall - on the right labeled 'living room', and a Parlor - on the left called the 'dining room'. 


Between them, in the center of the house would be the chimney stack with a separate flue for each of 4 fireplaces.

Here is the chimney above the roof with articulated flues.  

These spaces add up to a house about 18 ft. wide by 42 ft. long.



The width and length of the house were stepped off with a compass or marked on a length of twine. The exterior of the house would have been staked.  3 foot units could have been stepped off 6 times for the width and 7 times for the length. Layout with a rod marked in feet would probably have been faster. A chalk line might have been snapped. Lines could have been tied to stakes for the men digging the foundation. Diagonals would have trued the foundation. All of this is similar to how we layout buildings today.

Stone foundations of  pre-1900 houses tend to be vertical on the inside of the wall, the basement side, battened into the soil on the exterior. 2 lines would be required to accurately set the top of the foundation - where the sill would sit, where the outside wall of the house would stand.   

The length of the beams of the frame, approximately 18 ft., probably determined the house width.  

The Hall, the biggest room, was a multi- purpose room, used for cooking, chores, gathering. Often set in the southeast corner of the house, it had sunshine from early morning to late afternoon.  Here the room is square with a beam to support the 2nd floor across its center. The arc of the 18' width locates the posts.

Note that the dimensions appear to begin at the inner side of the right hand posts, indicating that while the exterior of the foundation was laid 18 ft. x 42 ft., the layout for the timber frame appears to have been set from the sill and those first posts. 

Laying out the geometry from the inside of the frame would have been a practical choice. The sills would not cover the line, but located beside it. Truing a rectangle by checking its diagonals to the outside corner of a post would be tricky, especially after the posts were in place. The framing timbers also needed to set to the line. And, the outside of a stone foundation could be irregular - as field stones are - without compromising the bearing of the frame on the foundation. 

This length, this inside dimension, would also have been the one the framers used to lay out the mortise and tenon joints on the beams.

Next to the Hall is the chimney stack. In plan it is a 3/4/5 rectangle often used by masons to keep the bricks plumb and level during construction. The fireplaces fit within, their fires creating a massive heat sink.  

The entry and staircase fit into the leftover space in front of the stack.



The Parlor, the room to the left, was used for business and formal occasions, to welcome and entertain visitors. Sometimes it was also the master bedroom.

It was smaller than the Hall and also had a centered beam.  The arcs cross at the outside edge of the wall, setting the width of the room. 

The length of that width could easily be measured from the layout of the Hall. Here the arcs cross, giving 2 points for drawing a line which, extended, is the width of the Parlor. Note the black line with arrows.

Yes, if the line which measured the width of the square of the Hall  had been folded in half and marked, it also would have given the point needed to determine the width of the parlor. In either instance the framer needed to understand the geometry. Geometry was a tool. It was practical. It is also why the proportions of these buildings are graceful; why they speak to us.



The Parson Barnard House, seem from its front garden in 2022.

 Note that the geometry of the house is so strong that the front door of the house seems to be in the middle of the facade. Actually the right side is wider than the left side. The windows on the left  are closer together than those on the right and the wall spaces between the door and the windows on either side are not equal. 

The geometry of the frame and the elevations will be another post.  

* the image is the frontispiece  for  Giancomo Barozzi Da Vignola, *Canon of the Five Orders  of Architecture, translated by John Leeke, published by William Sherwin, 1669. 

** A square can be laid out by a compass. Square corners can be determined and proved by a daisy wheel. Here is the visual explanation: the width A-B as the radius of the circle and locates the 6 points of the circumference A, B, C, D, E, F, G. Then: Lines A-F and B-E are perpendicular to A-B. Line G-C locates the end (west) wall  of the Parlor.

For more information and a tutorial see: