Wednesday, April 20, 2022

Hinges in Dividers and Calipers


 At their most basic, dividers consist of two legs hinged at one end. The hinge joint has to serve two somewhat opposing functions; it has to be loose enough to allow the legs to be moved apart and tight enough to prevent the legs from too easily moving when set. Many of the variations in construction of dividers focus on resolving these opposing actions.  The hinge end of a pair of dividers is typically forged into two or more plates or leaves which are then pierced and fastened together with a rivet or less often with a threaded nut. For the moment I am going to exclude wooden, bent-wood dividers such as the traditional European cooper’s dividers and metal spring dividers from this discussion.

The flat hinge leaves can slide past each other and allow the legs to move. At the same time the contact surfaces provide friction which keeps the legs from moving too freely. The greater the surface area in contact, the greater the potential friction. The most common way to increase the surface area is to increase the number of leaves that make up the hinge.  The simplest hinge with two plates or leaves is called a lap joint. This is typical of craftsman-made wooden and metal dividers, flat stock calipers and many more recent dividers such as those made by Starrett. Two-leaf examples are generally supplemented with stout outside washers.

                                                                    

Two-leaf hinge with washers

 A three-leaf  hinge has two leaves on one leg and one leaf on the other leg, creating a box or knuckle joint. This has the advantage of enclosing the end of one leg within the end of the other leg which keeps the hinge more secure and doubles the surface area and thus the friction provided by the leaves. Without a doubt, this is the most common hinge type found on antique dividers.

                                                                        

Three-leaf hinge with brass spacers

I have yet to see an example with four leaves. This arrangement would have the disadvantage of offsetting the contact of the legs by a significant amount. A more complex variation utilizes five leaves. Again, the more leaves in contact, the more friction available. In a five-leaf hinge one of the leg ends is split into three leaves, the other into two leaves. It strikes me that this is probably not an easy task for the blacksmith, but then my forging background is non-existent. In constructing the hinge   the maker can flatten one leg end and split it or saw it twice, the other leg once. Alternatively, three separate pieces of iron could be welded  to each other along most of their length leaving three flattened ends. The early types of five-leaf hinge often show what I believe is termed a “coldshut” or crack at the base of the leaf extending a bit down the leg.  The presence of a coldshut would  argue that the leaves were not created by sawing.  A blacksmith out there will have to explain to us how these hinges are created. A well-wrought five-leaf hinge is a significant plus in the value of a tool. A recent responder to my post on the Old Tools Listserv mentions he has seen seven-leaf hinges (4+3). These have to be extremely uncommon. Is there a law of diminishing returns when it comes to the number of leaves in a hinge of a pair of dividers

Five-leaf hinge with coldshut


Five-leaf hinge, sawn

                   

 Washers are often added under the rivet ends of two, three and five leaf dividers. In exceptionally well-crafted five- leaf hinges, brass washers are inserted between the leaves. The brass in contact with the iron provides even greater friction than iron on iron and reduces wear that can occur when two surfaces of the same metal (except hardened steel) are in contact. It is common to find leaf hinge dividers flattened at the top of the joint by a hammer in a crude attempt to tighten the hinge.   

                                                                                
Flattened hinge

 

The shape of the outside surface of the hinge rivet is often a good indication of the age of the tool. Brass “ball joint” (square joint) dividers where the rivet faces are rounded and often faceted are typical of the 18th century and earlier. In the late 18th and early 19th century iron and steel, flat “rule joint” dividers appear, especially in England.  The name derives from the hinges resemblance to a traditional boxwood folding rule joint. They often have concentric rings on the flat outside surface of the hinge. Cone shaped three-dimensional joint ends show up in the 19th century and possibly earlier.                         


        

Ball, rule and cone shaped hinges




                                                                                            Two additional hinge shape variations 

                           

An alternative to the use of a rivet to hold the joint together is found in many early drafting set dividers and some larger non-drafting examples. This type uses what is now referred to as a “2 hole pig nut” screw/machine bolt. These fasteners allow the joint to be loosened or tightened with the use of an appropriate two pin key (often missing from the drafting set). Collecting drafting instruments is a field all to itself. William Ford Stanley’s Mathematical Drawing and Measuring Instruments (1900, 7thed, Spon, London) gives a detailed account of the many different kinds of drafting instruments. This source is available in its entirety on line (www.books.google.com). Drafting dividers free from sets often turn up in sales. They are often quite complex and generally finely crafted of brass, steel or even precious metals.

                                                                        

       Slotted screw hinge on Stoddard, pat.1885                                                                  

"Pig nose" screws





Today's Mystery Dividers No. 2

Twelve inch, inside calipers, unmarked. Most likely user made, not old, but very well constructed, possibly by Rube Goldberg and Associates. Fine adjustment knob to the left. Middle knurled knob on right allows for transfer measurement.

                                                            

Mystery dividers #2
                    



Tuesday, April 5, 2022

The Symbolism of Dividers

                                                    

                                                 William Blake: Newton

There are few tools that carry the degree of symbolism associated with dividers. They are commonly depicted in prints and paintings of the Renaissance and earlier. Because dividers played such a key role in geometry, geography and architecture, in Renaissance art they came to represent science and learning in general. 

It is claimed by some scholars that the Chinese Book of History references dividers and squares about 2000 BCE. Probably the earliest portrayal of dividers (compasses) is found in Chinese art from the 7th to the 9th century CE. Pictured below are the intertwined figures of Nuwa and Fuxi, one holding a square and plumb bob, the other a pair of dividers. Dividers are often shown associated with squares. The dividers are often interpreted to represent the heavens while the square represents the earth. 

 
China:   Nuwa and Fuxi

Dividers are even mentioned in the Bible in Proverbs 8:27  “…when he prepared the heavens, I was there. When he set a compass upon the face of the deep”. This is the quote associated with William Blake’s well known etching Ancient of Days inspired by the lines appearing in John Milton’s Paradise Lost, book VII:  

                                    In his hand

            He took the golden Compasses prepar’d

            In God’s Eternal store to circumscribe

            This Universe, and all created things:

            One foot he center’d and the other turn’d

            Round through the vast profunditie obscure.

            And said, thus farr extend, thus farr thy bounds,

            This be thy just Circumference, O World.


                                                        God the Geometer, 13th. century                      William Blake: The Ancient of Days            

I am not aware of dividers showing up in Greek art, but Greek mythology, as presented by the Roman poet Ovid, tells the story of Perdix who is said to have invented dividers as well as the saw. These inventions got him in trouble with his jealous uncle Daedalus who tossed him off a tower. 

The Latin word for dividers is Circinus. Dividers appear on Roman stone funerary reliefs and Roman-era dug dividers, calipers and proportional dividers are held in several European museum collections. There is even a southern hemisphere astronomical constellation Circinus representing a pair of dividers.

                                                                                                

                            
                          Roman Funerary Relief                                                          Constellation Circinus                                                                                               


Surprisingly, dividers do not seem to have been used in Egyptian construction. At least I’m not aware they appear in any Egyptian hieroglyphics or as tomb artifacts. Likewise, I’m not aware of representations of dividers in any ancient New World cultures. 

There are numerous 15th, 16th and 17th century European portraits of individuals holding dividers. In these cases the tools usually represent the occupation or degree of learning of the subject in the painting

                                                                             

Vermeer: The Geographer

Holbein the Younger: Nicholas Kratzer
                                                                                    

                                                                                                                             
Bellini: Man With A Pair of Dividers

The best known representation of dividers is likely the Masonic seal.  Much has been written on the meaning of Masonic symbols, but generally the dividers are said to show the need to circumscribe our desires and keep passions within bounds.

Masonic Symbol
                                                                               
Dividers appear on  a number of London guild coats of arms. Below is the one for the Worshipful Company of Carpenters. Guilds for joiners and masons also utilize dividers in their coat of arms

                                                                              

 
                                                                

The flag of the former East Germany (GDR) shows a pair of dividers at its center which represents the intelligentsia while the hammer and sheath of wheat are symbols of the workers and farmers respectively.

                                                         

East German Flag