Box making department of the T.B. Williams Tobacco Company late 1800’s (Wiki Commons)
Yes it’s fine to think inside the box for a change, especially when there’s no need to think at all! At least not if your goal is to divide the box into any number of divisions. Thanks to the geometry of diagonal lines that occur inherently within a square, you need only a straightedge to reveal these fractions. This truth/tool allows you to lay out the baffles that will keep the bottles of spirits from rattling or worse. Of course there are easier ways to come up with these fractions (the sector springs to mind), but this is still a great way to construct by hand and observe by eye these geometric patterns as they spring to life.
See if you can follow the steps below which I’ve sketched on a sheet of graph paper. Why don’t you grab some paper and follow along too? Bet your kid can (and would like to) help you out! Get out a pair of dividers so you can confirm that the intersections do indeed produce perfectly spaced segments along a line.
Now isolate the first square…
…and continue by drawing a pair of diagonal lines as shown in green in the next sketch:
Next draw a horizontal line through the points that have been given to you where the (green) diagonals cross the first set. If you set your dividers to the intersections along this new horizontal line, you’ll find there are exactly/precisely/perfectly three equal-length segments. Now let’s draw another set of diagonals and connect their intersections with the original diagonals with a horizontal line:
As your dividers will reveal to you, that line is now automagically broken into four equal segments. Let’s continue the process with two more sets of lines (I really do highly recommend that you stop right now and grab a sheet of graph paper and watch this happen in real time through your own hands and eyes).
You’ll discover the red lines produces fifth segments while the yellow produce sevenths along their horizontals. Add another set (in blue here) of diagonals and horizontal and you come up with ninths:
Keep going if you like:
You’ll get ninths, elevenths and thirteenths – and on to infinity I suppose. What if you want an even number of divisions along a horizontal line, say tenths along the line of fifths? Well they are there waiting for you to discover with your dividers!
It was a spacious shop, well lit and outfitted with a tidy mix of old and new equipment. “I’m working on a dining table and chairs for a client in Miami,” [my host] told me. “Quite a famous bloke, actually. To tell the truth, he’s got such a big name that I’m not allowed to say it. Not that that’s anything out of the ordinary in my world. These days it’s rare for me to work for anyone who’s not routinely written up in Esquire or Vanity Fair, that sort of thing.”
“Which part of London are you from?” I asked, curious as to the origin of his accent.
Ignoring my question, he turned his head to the right, saying “Come an’ take a look at this table and chairs” as he strode toward his workbench. The dining set was inspired by the work of French Art Deco designer Emile-Jacques Ruhlmann. The table, made of rosewood, was stunning. A cross between Deco and neoclassical, it had an extending top that could seat an intimate foursome or expand to accommodate 10. It was waiting to be finished, as soon as the chairs were ready.
“Double tenons hidden in those miters around the seat,” he remarked. “Ever use those darlin’s? I’m telling you, they are quite the challenge to pull off. But what a sturdy bit of join’ry they are. Those chairs will last forever. On the other hand, so will everything I make. That’s one of the reasons my clients are willing to wait years for an opening in my schedule.”
“I took a look at your website,” he went on. “Nice enough work, but really….’Period-authentic furniture and built-ins?’ It’s all been done before, ‘ain’t it? You couldn’t pay me to do that type of guff for common punters. On the other ‘and, someone’s got to do it, so I daresay it might as well be you.”
Now that he’d established I didn’t even rank high enough to engage in a pissing match (not that I am ever inclined to take part in such b.s.) I thought he might answer my question. “Which part of London are you from?” I asked again.
You can read the scintillating remainder of this tale and learn the origin of my host’s accent in Making Things Work.
Once upon a time, 10′ poles were a tool common to a number of trades including linemen and cemetery workers. What they touched with their 10′ poles – high-voltage power lines and corpses respectively – is not something most people would want to touch, not even with an 11′ pole.
Carpenters, however, were quite happy with the 10′, or as the drawing suggests, any length of stick divided into 10 equal segments. For in their hands lay a tool critical to the efficiency and accuracy of their layout work. As we discuss in our book “From Truths to Tools” a right angle can be formed by a triangle composed of three whole-number leg lengths. In the simplest triplet, the leg lengths are three, four and five “whatevers.” The 10′ pole simply employs a doubling of those numbers: six, eight and 10, which are measured in this case with the imperial feet of some long-dead king. (If you think feet stink, you could measure out the pole in the cubits {forearm lengths} of some even longer-dead pharaoh.)
As demonstrated below – lifted from the book – we can construct a “proof” of this particular triplet using a straightedge and dividers. Be aware that there are many more whole-number triplet combinations – perhaps an infinite amount.
The sketch below shows the pole in use aligning a post square (and therefore plumb) to a level floor:
It’s a simple enough procedure: After fixing the base of the post to the desired location on the floor system, you use the pole to lay out a mark 6′ up from the bottom of the post. Next, you lay out a mark 8′ away from the post on the floor. When the full 10′ length of the pole fits exactly between the mark on the floor and on the post face, your post will be exactly square to the floor. Turns out that this layout problem (among many others as you’ll discover in the book) can be beat with a stick!
I’ve lost track of how many times people have written “So great to see a woman in the magazine!” following the publication of a project feature. For years I’d roll my eyes and think Never mind my gender. WHAT ABOUT THE WORK?
It’s thorny, this issue of gender representation in woodworking. You can say pretty much the same about race. When you’re the odd one out, it’s easy for readers to see only what makes you different. Which is galling when, for you, what matters is the work.
While I was on hold during a recent phone call, I glanced at Instagram and found myself tagged by Sarah Marriage at A Workshop of Our Own. She was commenting on a post by Phoebe Kuo. “Have you heard about our woodshop drinking game?” asked Sarah. “You take a shot every time you see a woman depicted working in the field of woodworking (ie, not a customer service rep with a headset asking you to call today) in a woodworking periodical. It’s usually safe for the woodshop because you never take a shot!”
Of course she was exaggerating (a little), as she acknowledged by referring to a recent issue of Fine Woodworking. I replied with a comment listing a few other publications that have recently featured work by women: Woodcraft, Furniture & Cabinetmaking, and most recently a cover feature in Popular Woodworking. But as I continued working into the evening and ruminated on Sarah’s remark, her point sank in: It’s important to go beyond publishing work by women to publishing images of women working. While it was exceedingly rare to see a woman in a workshop or on a building site just three decades ago when I started in the field, it’s verging on common today. But outside of publications directed specifically at women, the percentage of females to males in woodworking publications is still low.
Image from www.awfullibrarybooks.net. (Yes, that is the title of the site.)
This dearth of representation is not due solely to sexism. There are also some distinctly prosaic explanations, among them:
some women are so busy with commissioned work and other activities that they don’t want to take the time, which can be considerable, to propose, write, and do the hands-on work for an article, and
while some of us are set up to photograph ourselves, others (guilty!) are not. As a result, in publications that use photographs provided by authors, work by women is published more often than images ofwomen doing the work.
For years I felt like gagging at the mention of gender in relation to my profession. It wasn’t just the unintentionally demeaning remarks — “Did your husband teach you to do this?” It was the focus on the novelty of finding a woman in a field populated primarily by men. I just wanted to be Nancy Hiller, not a token female. Sarah and Megan Fitzpatrick have expressed the same frustration; no doubt many other women have, too. So why are we now paying so much attention to gender and calling for more images of women woodworkers?
Because we all need role models.
As a young woodworker, my models were men. Even without wanting to, I fell into the role of “cute tough-girl in the shop.” That was how others (though thankfully not all of them) made clear they saw me. I was “decorative,” to use a frequently cited word. This worked fine as long as I was thin. But when I gained 40 pounds in response to a devastating heartbreak, the reactions to the female in the shop turned to pity — and occasionally disdain, such as when the foreman at one of the shops where I worked greeted me with a hearty “MOO” when I arrived one Saturday morning to put in some extra hours on a deadline-sensitive job. (Note: Despite my appearance, I was still doing the work.)
What would a mature, confident woman in a workshop look like? I had no idea. To be honest, the question didn’t even occur to me. Instead, I had a vague sense that I should get out of the field before the age of 40, because a mature woman in jeans and work boots would be, well, kind of scary. Or maybe people would assume, based on her work clothes and dusty appearance, that she was not very smart. She would definitely not look “professional” or “desirable.” I’m embarrassed to admit that I ever felt this way, that I had so thoroughly internalized female norms presented by advertising and publishing that 40 represented the end of the road for me as a woodworker.
This is one of the reasons why it’s important to present images of real women working. Not just demure young women with wood chips gathering on their chests while they use power tools, not just intentionally sexy babes using table saws, and not just tattooed tough-girls. We need to include women in mom-jeans and make-up, women of color, big strong women…you get the picture. In other words, we would like to see images of real women woodworkers, ideally in numbers proportionate to the population of women woodworkers, whether woodworking is their hobby or their job — pretty much as we do with men. (After all, not every man looks like Tommy Mac.)
As Megan pointed out in a recent Popular Woodworking editor’s letter, it’s hard to aspire to something for which you have no example. –Nancy Hiller, author of Making Things Work
Anissa Kapsales, editor at Fine WoodworkingAnne Briggs (a.k.a. Anne of All Trades)Ouida Vincent with her Dutch tool chestDenise GaulSarah Marriage (Photo by Allison Crowley)Ivy Siosi and Audim Culver of Siosi Design + Build (Photo: Anna Powell Teeter)
Video made by Frank Miller Lumber featuring what Raney Nelson would call “your humble narrator” (with apologies to Raney)
Or, translated from the Latin: “As Level as Water.” As we explored ancient layout tools at length in “From Truths to Tools,” it became quite clear that the artisans of antiquity were no dummies. For example, we see from their tools and works that they understood that there was a difference between the curved “level” of a horizontal line and the straight “level” of a sight line. In fact, when they used the term “horizontal” to name the latter they were alluding to “horos,” the horizon, the boundary between water and sky.
How did they know that the earth they stood on was a sphere? Two things for starters, according to source documents: They observed the arc-line shadow of the earth falling on the moon during a lunar eclipse, and they watched ships disappearing on the horizon from the hull to the top of the mast (as opposed to the ship simply getting smaller and smaller). Why is this so important? Try building an aqueduct so it works properly or digging a tunnel accurately through a mountain without accounting for this difference.
If the trough of the aqueduct were constructed to a sight (or laser!) line level, the water would flow toward the center because the center, relative to the earth’s surface, is downhill from either end. Another problem that could arise if the support columns were constructed to meet the trough at right angles, is that the columns would only be plumb in one location. They would all be parallel, but that doesn’t make them right! (Literally: the forces on the un-plumb columns would have some amount of shear in them, leading eventually to distortion and ultimately failure.)
In tunnel work, the opposite problem arises: if they relied solely on horizontal level as the digging progressed from start points established by sight lines shot around the mountain from surrounding benchmarks, the tunnel would not exit at the predicted opposing point. Digging from either end, one tunnel would travel above the other and they would never meet. Note that the gradient drop of the earth’s curve is about 8′ per mile – and it’s not an additive (linear) increase, but exponential to infinity. To grasp this intuitively, picture the earth constantly curving away from the sight line. Eventually, at a point just past a quarter of the way around the sphere, a line dropped down square from the sight line would never reach the earth’s surface.
The more George and I immersed ourselves in research for this book, the more we gleaned about the tools and works of the artisans of antiquity and the smarter they started looking to us. The corollary was the dumber the guys in the mirror looking back at us each morning started to look! Obviously, not only is there is still so much more to learn, there is so much more to relearn!
![IMG_2342[1]](https://blog.lostartpress.com/wp-content/uploads/2017/10/img_23421.jpg)
