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Today’s banner: metalworking layout tools, improvised, on a glass surface plate (also improvised).

We recently overheard an engineering student ask a really good question: where does precision come from? The manufacture of nearly every precision instrument derives that precision, ultimately, from something else that’s even more precise. Think about that. Infinite recursion, ad infinitum, ad nauseum… Where does it end? What’s the base case? It must be a platonic ideal. Perhaps it pulls itself out of its own navel or something. A realization of the Omphalos Hypothesis. It must invent itself.

We tripped over to the local engineering college’s library where we found a copy of Foundations of Mechanical Accuracy by Wayne R. Moore, 1970, The Moore Tool Company. The copy we found was forty years old. During the last forty years, exactly twelve people had read it. This made us sad. We determined to make up for this dearth of readers by reading it several times.

We discovered that, in fact, the base case is the perfect plane. In the 1830s James Whitworth gave us a simple (if arduous and tedious) method for establishing as a flat plane of reference the surface plate. Surface plates are made as large as needed, and since precision instruments are used to build really big things — think “naval engineering” — by large we mean large, heavy, and extremely rigid. Okay, they’re not as large as an aircraft carrier, but you could stretch out and take a nap on one. If you don’t mind a really hard mattress.

The best surface plates are made of cast iron, or ceramic, or even glass, and are flat to within a millionth of an inch. From this plane — as perfectly flat as we can make it — from this plane can be derived the straightedge, the square, and the precision ways of lathes and milling machines.

In Whitworth’s process, surface plates are manufactured in triplets. Each surface plate is repeatedly compared to the other two, mutually proving each other, their surfaces gradually refined by hand, using a scraper, until no imperfections can be detected. How are imperfections found? One way is to paint one surface with a pigment. Try to mate the surfaces of two plates: on the dry surface, any high spots get inked, and any low spots stay dry. When the pigment is uniformly transferred from the wet to the dry surface, we’ve reached the limit of our ability to detect imperfections.

But why make three at a time? It’s a matter of practicality. Surface plates are usually rectangular, so the only easy rotation is 180 degrees. Now image placing a horse’s saddle upside-down atop another saddle. (I know this seems like a totally unrelated tangent, but bear with me.) If the upside-down saddle is rotated ninety degrees, the two saddles will mate well, even though they’re not at all flat. Now rotate that upside-down saddle by 180 degrees. They still mate.

If you do this with a pair of rectangular surface plates with mirrored but matching saddle-shaped deformations, they will appear to mate well. Now suppose the third plate also has a mirrored deformation that mates well with the first plate. Well, it mirrors the first plate, but not the second. The second and third plates won’t mate. So three plates will detect this kind of deformation, allowing the maker to correct the problem.

These days you can’t get much flatter than a good pane of glass. Through an entirely different process, the Pilkington process, so-called “float glass” derives its flatness from gravity. It’s really cool (or rather, very hot): molten glass floats on the surface of molten metal, an alloy chosen to have a low melting point — lower than that of glass. The glass is allowed to cool enough to solidify on the surface of the molten metal. Then you just pluck it out of the pool of molten metal. Not with your bare hands.

As a surface plate in a production line or for large metalwork, a pane of glass would be utterly worthless. But for the hobbyist working on a very small scale, a good, thick pane of glass works great.

We’re going to try using a pane of glass as a surface plate, depending on it to draw really straight lines. We’ll use it derive the centerline of a 2-1/2″ workpiece of 1″x1″ extruded aluminum. (This will only work, by the way, if we know the faces of the workpiece are flat — which we assume but won’t confirm, but could confirm with the pigment trick — and that the faces are parallel. But if it works — if we establish a centerline and can prove it — the parallelism of the workpiece faces will also be confirmed.)

That’s a tube of oil paint from the local art supply store. It’s Prussian blue. Here it’s being smeared onto one face of a small piece of 1″x1″ extruded aluminum. The main reason we’re using it is that scribed lines on bare metal can be hard to see, but a line scribed through a layer of pigment is bright and easy-to-see. We could have used a felt-tipped marker. But we like Prussian blue — it reminds us of finger-painting. Here’s the completed coating:

The scribe is clamped into a dial indicator holder doohickey with a magnetic base, which is stuck to a small piece of flat metal (stolen from an engineer’s metalworking protractor). Here the tip of the scribe has been adjusted to point approximately at the centerline of the workpiece. We intend to find the exact centerline. By simply sliding our scribe-dial-indicator-holder-doohickey-with-a-magnetic-base across the glass surface plate, we scribe a short test line:

We flip the workpiece and try to rescribe the same line, without readjusting the scribe:

When we examine the two test lines, we find that — as expected — they don’t quite align:

Now we adjust the scribe tip. We adjust it to fall between the first two test lines. We then make a new pair of test lines. We repeat the process until the tests lines are as well-aligned as we can make them:

Then, sliding our doohickey, we try scribing a complete centerline. Then we test the centerline: we flip the workpiece, and without adjusting the scribe, we try again, and we check for agreement along the full length:

The scribed lines match, under unaided visual inspection. Just for the heck of it, we added crosshairs. Now comes the fun part: we inspect the line we made:

More detail! We must magnify! We stick the workpiece under a microscope. Here we’ve inkjetted a small millimeter ruler on paper, and we’ve placed it directly below the scribed line, for comparison under the scope:

Our centerline is the single vertical line. Pretty freakin’ spot-on. The parallel scribed lines are our crosshairs. For the heck of it we check the height of the scribe tip:

It lies on the 1/2″ mark, and to the limits of our visual inspection, the alignment is perfect.

Best wishes — stochastic