Mr. Handscombe has replied somewhat to my challenge that he prove his
claims.  Now I'd like to review his statement in general, all of which
involve not actual bench measurements, but something he discovered by
putting a gauge on three fully assembled, playing Duo-Arts and
measuring everything combined, as they sit from rebuilds or repairs
past.  This really isn't what we need, Paddy.  As I have already
stated, I can easily get a curved response from a Duo-Art box, simply
by shortening the springs with the adjuster.  If you will simply go to
Sam Harris' web page he has copied off for you to see, you will see what
Duo-Art intended with brand new springs in a bench testing setup.  So
first off, we will start with your purpose statement and here is how
you said it:

> I have absolutely no doubt that even though they utilized standard
> linear rate regulator springs, they were intentionally designed to
> give the upward concave exponential response curves ...

Immediately the reader says, "Uh-oh.  Craig has been saying the springs
were linear.  Paddy has already said in his first posting that the rate
of the box is determined by the springs.  And now Paddy is agreeing
further with Craig that the springs truly are linear.  So what we then
have at Paddy's house is a linear box whose overall response is bent.
That's exactly what Craig said can happen, but which is not desirable.
That is merely a crooked line -- not a purposely generated portion of
a parabolic curve.

When we look at a true square-law response curve, that means that at
a particular regular interval determined by a simple multiplier, the
pressure of the box keeps squaring.  This gives you a parabolic effect,
or some say, an exponential effect.  Were you to look at a parabolic
curve charted, even the flattest one you can imagine, it would look
nothing like anything a Duo-Art box could generate, especially one
which starts out parabolic and ends up flat (as you have already
intimated).  So although we can all be dazzled by the trapeze act they
call the Duo-Art expression box and mention how compound rotational
displacements on a sliding scale and the cosine law of pneumatic
collapse produces non-linear results of and by themselves, you fail to
take actual measurements under controlled bench conditions with fixed
loads to discover exactly what the designers intended to get out of the
box.

For instance, the regulators do weaken as they collapse (until the
cloth angle reaches 90 degrees to itself, then it's linear), but on the
other hand, the ratio between the distance from the regulator hook to
the center of the control lever pivot through the knife, versus the
length of the levering to it, is 3:1.  That means that Aeolian was
only tapping 1/3rd of the regulator's movement to counter the 2/3rds
accordion control.  As we go through the geometry of this box and
concern ourselves mainly with the overall response to accordion
collapse, we realize something very important: Our levers aren't moving
very far! That means, we are only tapping a very small percentage of
arc, and as any mathematician understands, at small angles, the cosine
can be regarded as roughly linear.  So despite all the talk about
sliding feet and arcing levers, the box is very simple, designed in
a rotational quadrant to simulate linearity.

If you wish to change certain aspects of its curve, you can change the
accordion levers' start positions by loosening their set clamps and
resetting zero then recharting the box (all the time on the bench, of
course, with a fixed load).  You will observe that it is this lever
alone that will linearize the box the most, but will not fine-tune it.
For each adjustment of this lever, everything else except accordion
movement has to be done over again.

I am presently adjusting a Duo-Art box, and in this case, the accordion
levers are adjusted at a backward angle at zero, such that when they
are drawn down vertically, parallel to the frame, each accordion is
drawn down almost exactly 9/16." As far as initial spring tension is
concerned, that still varies, but where I begin is always where Aeolian
says to begin -- just tight enough that they won't rattle when they
first pull up to zero intensity.

At any rate, if you wish to talk of the square law curve (which is the
curve that Mike Knudsen referred to,  and to whom you referred) you
will have to demonstrate how this box could possibly achieve it,
please.  My question is not how two already rebuilt American pianos
measure in Britain, after the fact, and after you have already stated
what you believed all along.  Put an expression box on the bench, give
it some fixed bleeds that do not change as the pressure changes (which
stacks and everything else attached to them do), and measure, with a
professional quality pair of low vacuum gauges for self-checking
accuracy, the overall curve of your boxes.  Not just one of them, but
perhaps 6 or a dozen of them.  You don't have to hurry.  Take your
time.  We'll wait.

In all of this however, you have not addressed your initial claims
which defame the American Duo-Art and extol the British model.  So I
am going to repeat the challenge I posited yesterday to you, and I for
one want an answer to these things.  I don't intend to let it go,
because you and Julian Dyer owe everyone an explanation.  I admit
ignorance of the British expression system and have not asserted myself
about them, at all.  I've never even seen one.  The only thing I know
for sure is this: The rolls are identical, except for the different
leaders and boxes.  I own British Duo-Art rolls too, and they play no
differently than their American counterparts.  Here is what I want to
know, and I hope you will address these issues:

It is now incumbent upon you both to prove that American Aeolian
Duo-Arts were wrongly designed and that they not only didn't know much
about music, but proved it by putting springs on their boxes having
rates differing by a factor of 2 when they should have been equal, and
that they were wrong to design a basically linear box (easily shown),
their music is "offensive" with that supercilious, "assaulting" crash
valve, that British Duo-Arts are able to achieve that full crash _and
more_ without the crash valve, but directly through their regulators,
and that Duo-Art rolls never used a theme expression equal to the
accompaniment, but always raised or lowered it.  It's still your serve.
Your first was obviously a net ball.  You have one left.  Just take
your time and hit it squarely over to me.

Please let us all know as soon as possible that you are preparing this
reply so we won't wonder that you have decided to forget it.  Thanks
fellows.  And by the way, even though we disagree, I enjoy your
postings.  It makes for some very lively conversations and clears the
air for facts to emerge.  But we must keep at it.  The truth only comes
at a price.  So I encourage you to keep studying.

Craig Brougher