I'll confess to a grammatical error: I should have said "faster, easier, and
more precise," not "or." Methods that are faster than using dividers are less
precise or harder, methods that are more precise are slower, and so on.

I don't think I'd win the race: I'm slow at the best of times, not precise
enough by nature to be a machinist, and I'm willing to allow the ruler trick to
be faster anyway. But I don't bother with the ruler trick, because with the
materials I use for the things I do at the scale I work to it is as precise to
mark by eye without bothering with the ruler. If I needed more precision than my
eye can give I would have to correct using dividers anyway, so why bother with
the ruler?

The eye as precise as a ruler? Well, I just checked on a 3-3/4" board with
rough-sawed edges, and was disappointed in my level of precision, but even so
the division into eight, done with only a sharpish pencil and checked with
dividers and a Starrett 6" rule calibrated to 64ths, was precise to 1/32", less
than the width of the kerf of the saw I would use to cut the battens apart and
on most days much less than the wobble of the kerf for me. Almost all the
variation was in the pieces at the edges of the board; if I throw these out (as
I learned to do in science classes many years ago), five of the six remaining
were dead on in 128ths and the sixth was under 1/32" off. That's not good enough
for machining metal, not good enough to get a motor to work or to do celestial
navigation, but its ample for what I do. The division into sixths was not as
good, 5/8" to 1/16" and if I throw out the top and bottom two were dead on and
two less than 1/32" under. Still
 better than I can saw.

Yeah, I'll confess that in practice I use a ruler a lot. But that's laziness,
not speed or precision.
____________________________________

OK, this is about to run off on a tangent here, but maybe its unfamiliarity will
interest someone. And some of this stuff was learned so long ago that I just
don't think about it.

Remember, most of what I do involves paper, so I always have scrap and offcuts
around. If I want a division into multiples of two I'll take a slip of waste,
mark the desired overall length from one end, fold the end to the mark, and
crease down.That gives a true half if you do it correctly and carefully. If you
want a rough quarter fold the halved slip in half; if you want a precise one
fold each half independently. If you want a third: fold the two halves in
without creasing and fiddle back and forth until they are as precise as you need
them, then crease. Sixths: fold into thirds, then halve the thirds. And so on.
Fifths are tricky without stepping off, but who needs fifths for anything unless
they are joined at the hip to decimal arithmetic and the metric system?

In binding there is a lot of use of the fact that it is very hard to construct a
true right angle in any situation, but very easy to get a right angle good
enough to fool the eye. Example? In marking the squared-off end of a two-by-four
for cutting you never march the lines around the board ABDC, because the lines
are unlikely to line up; you mark two adjacent sides from their shared arris,
then the other two from the diagonally opposite shared arris. A similar test: on
a piece of paper with a flat square like a drafting triangle mark a line, then a
right angle to that, then one to that, then one to that, and come back to the
original line. They are unlikely to line up. So what do you do if you want a
precise right angle for a pattern? Cut one side of a piece of paper straight
with a knife and straightedge (one of the most basic things you can do in
binding), mark where you want the right angle, and fold the piece of paper in
half, lining up the two
 halves of the straight side you just cut (one of the few things even more
basic).

I would never rely on the sides of a piece of paper being square to the ends to
a high level of precision; but it is more important to be able to get the
parallel edges truly parallel. The eye is very sensitive to out-of-parallel,
especially if the lines are close together, just as it is tolerant of
out-of-square. To get two sides precisely parallel one way is to fold the paper
top to bottom without creasing,line up the two corners on the left, and check
the other two corners; if they don't line up the top and bottom edges are of
different lengths which means that the side edges aren't really parallel, so I
nick the corner that sticks out on the right, allow the paper to unfold, and cut
the right edge true with knife and straightedge. I'd never check to see if two
edges were parallel by seeing if they are both at right angles to a shared
adjacent edge, because this will only work if **two** right angles are **both**
precise; rather, I'd always check to
 see that they are the same distance apart at the ends, using dividers or direct
measurement (as described above) or the equivalent of a story stick (in binding,
an offcut slip with pencil tics on it.)

Running out of steam here, I'm afraid, and no particular point reached. But a
lot of the techniques I learned for binding have close parallels in things that
can be done in woodworking, and a lot of the preferred choices are the result of
habits that come from binding. I avoid numbers as useless, just as someone who
must work in tolerances of thousandsths of an inch get a piece of machinery
running at all will rely on numbers as essential. As Peter said, there are times
when there is more than one way to skin a cat, and other times when there is
only one route through the maze.

Tom Conroy
Moving away from the temptation to a head-butting contest by (to adapt E.R.
Eddison's memorable simile) voiding much ink, like a squid.

PeterH in Perth wrote:
 
> Tom, lets have a race: There's 3 boards each 4+5/16" wide x
> 1' long. 
> Each 1' length has to be divided equally into battens. 
> One piece into 4 battens, one into 6 and the last into 8
> battens.
> 
> Ready, set go. 
> 
> My method is to get a rule and angle it across the board
> from the 
> 0" mark to the 6" mark (4 equal divisions of 1+1/2" ) and
> make 3 marks. 
> Next I move to the second 1' piece and again lay the rule
> across the board
> at an angle from the 0" mark to the 6" mark, and mark off 5
> marks at the 
> inch divisions. etc., etc. ...
> 
> Of course it (almost) goes without saying that (not just) in
> layout, there are 
> times when there is more than one way to skin a cat, and
> there are those times 
> when only one way will get you through the maze.
> 
> But what do I know? I have a nice set of Mitutoyo verniers,
> and my method for 
> using them is to place work inside the jaws, or the jaws
> inside work and lock 
> them up, then get my trusty steel rule and measure against
> it. Accuracy? 
> Within any one division of the rule. 
> 
> Cheers
> PeterH in Perth
> 

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