Apprentice Sketchbook Summer 2011

Concave section on this base is a Scotia

Last weekend I had the privilege of attending the Ohio River Valley chapter of SAPFM (Society of American Period Furniture Makers). Don McConnell of Old Street Tools (Formerly Clark and Williams) presented – or should I say, let us pummel him with questions all day. Don generously shared with us his expert knowledge on wooden planes, both bench and moulding planes. All day I was struck with how these amazing tools are both simple, yet sophisticated. Watching Don stick some mouldings, it was apparent that a lowly hollow or round is capable of becoming a creative extension of the artisan himself. It brought to mind something I’ve been thinking about a lot. There’s no escaping the fact that we live in an age of technology, a grandchild of the industrial revolution from the 19th century. So much emphasis focused on machines and automation, all aimed at replacing muscle with machine power and eventually man himself from the picture. Industrial drawings are a key part of this equation and for much of my life in industry I was immersed in that world. As an apprentice in the mid seventies, I just caught the tail end of the hand drafting era where engineering departments had huge rooms filled with fleets of big cumbersome drafting boards. Thirty five years later we were downloading drawings directly into machine controllers with all the data needed to manufacture a part. Actually these “drawings” no longer contained any graphic images just code, but for some reason we still referred to them as prints or drawings. This type of drawing performs flawlessly in the industrial world of mass production. It matters not at all whether the human tending the machine is a mechanical savant, a recovering alcoholic, or both. The technology removes the human element. Every foible, stutter, shake, and mishap we are prone to, gets sidestepped. Makes perfect sense when you produce parts going into the landing gear on a fighter jet or delivers power to the wheel of a high speed rail line. Yet this steady march of progress that makes men the servants of machines is not without side effects.

One side effect I think about a lot is the difference between the way we think of drawings from a mass production, versus a creative standpoint. From a creative view a drawing is a completely different animal, something meant to pull the human element back into the creative process. These simple apprentice sketches are meant to do just that, pull you (with all your human foibles) back into the process. These are not meant to help you duplicate someone else’s idea, instead they are intended to help you visualize forms in your mind and build a spatial vocabulary. As you draw these with dividers and then freehand you create new bridges, tunnels, and roadways on a mental drafting board in your head. There’s nothing magical about these sketching exercises except they create some hooks in your mind you can latch your creative ideas onto. More and more when I have a choice that involves technology or even when choosing tools, I ask myself a simple question, “Does it exclude or enhance the human element?” Does it extend my skill and imagination? If the answer is no, that, tool, software, gadget ultimately ends up limiting creativity.

A Scotia is a mixti-linear form according to Gibbs

Now let’s turn to the exercise itself. James Gibbs in his circa 1732 “Rules For Drawing” describes a Scotia as a mixti-linear form. I tried looking up mixti-linear and both my giant print dictionary and the on line version came up blank. My guess is it means a line form containing multiple or different in this case radii. Combining curves with faster (sharper) and slower curvature is found in abundance in nature. A Scotia is often found at the base of columns on a classic order. It’s circular and usually encompasses more than a half circle and the curvature usually contains several radii.

I’ll let the drawing itself guide you. Draw this a few times with compass and then switch to free hand. Fill up a couple of pages of freehand Scotia’s and drill the form into your mental sketchpad.



I didn’t post this to explore the lost world of “mixti-linear” forms but I guess one of the fun things about a blog is not quite knowing where it will end up. That said I’m adding a snippet of a plate from Thomas Sheriton’s “The Cabinatemakers and Upholsterers Drawing Book” Circa 1793 showing several examples of mixtilinear forms. His explanation is as follows –

Of Mixtilineal figures. No 17 (refers to drawing) is of this kind; and every other figure that is bounded both by right and curved lines is called mixtilineal. Of these figures some are regular, and some irregular. When a figure of this kind is composed of equal curved and equal right lines, then it is call a regular mixtilineal figure; but when its sides and ends are formed of unequal curved and unequal right lines, then they are called irregular compound mixtilineal figures.

Now there’s a nugget to impress your freinds!

center left is regular mixtilinear form, to the right is an irregular mixtilinear

 George R. Walker

About walkerg

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11 Responses to Apprentice Sketchbook Summer 2011

  1. Andrew Yang says:

    Maybe more of an explanation of mixtilinear geometry than you want.

  2. walkerg says:


    I’ve seen the term mixti-linear used by Gibbs (circa 1730)and Sheraton (circa 1790). Both designers leaned on simple geometry to visualize and draw forms. My guess is the 18th century meaning is different than the modern mathematical definition. Thanks for the reference.


    • Andrew Yang says:

      Hi George,
      Not having anywhere near the knowledge of traditional design or woodworking, I would hazard to say that simple geometry today is far simpler than simple geometry from centuries past, much like woodworking. By my reckoning, your Scotia diagram is a clear (not so clear?) subset of the mixtilinear diagram from Wolfram.

      • walkerg says:


        Concerning geometry – based on the acheivements in the sciences in the 18th century, they were capable of tackling very complex problems. Yet when I refer to a simple or visual geometry, I’m aluding to the sort of practical geometry that artisans would have used to build furniture or buildings. A period craftsman could imagine a door opening as two squares or two circles (the height is twice the width). This ability to visualize with simple squares and circles was a powerful creative tool. I wouldn’t say woodworking today is simpler as much as based on a different model. Much of our woodworking today flows from industrial practices – thats why woodshop classes were called industrial arts. The pre-industrial model was based on individual artisans mastering a set of core skills both technical and design that produced a very different craft than we see today.


  3. Dean says:

    George, from what I could find on the web, “mixti” is a Latin word that translates to English as “to mix, mingle, blend”. So, I’m guessing “mixti-linear” might mean “mixed linear” or “blended linear” or maybe even “mingled linear”. Since I think of “linear” as a straight line, then maybe you could add the word “straight line” to these possible translations, or more simply “line”, in place of “linear”.

    • walkerg says:


      When I was looking this up I noticed the definition of Linear as – Pertaining to line. I also took for granted it meant straight as in linear bearings, but looking at Sheratons plates of mixti-linear forms it includes shapes with straight and curved lines.

      • Dean says:

        I was assuming (dangerous I know), that it was a case of intermixing lines with “whatever” other geometrical forms. Yeah, I know, I’m reaching. However, I think the Latin definition would still stand for the “mixti” part. Just a thought.

  4. walkerg says:

    Thanks for your questions, as a result I dug a little deeper and looked again at Sheraton’s plate and his definition. (I added both to original post). Now I knows what an irregular compound mixtilinear figure is! Not sure how I made this far in such utter ignorance!

  5. Dean says:

    Well, now that, that is settled, we can get back to our homework assignment and “…drill the form into your mental sketchpad.”

  6. Ruby Lee says:

    fantastic blog! what would you recommend as a good introduction to woodworking for a novice?

    • walkerg says:


      For a novice woodworker I’d highly recomend Jim Tolpins “New Traditional Woodworker”. You also might want to check out Chris Schwarz at Lost Art Press and his book “Joiner and Cabinetmaker”. Both are good overveiws of the foundation skills and tools needed to learn the craft. Both also are realistic about the tools you really need and the skills to master them.


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