An observation as to why the unusual 0.1227" hole spacing of the
Wurlitzer APP tracker bar [also used for Style 165 music rolls]
may have come about.

This, I believe, is because a metric leadscrew was used with a 40 to 1
dividing head.  One turn of the leadscrew would advance the drilling
table 1 millimeter [0.03937 inch].  The dividing head usually has 40
holes, allowing for divisions with the standard plate of 1/40th pi.  Two
of these holes are used, one to mark and one to keep the table steady.

What I think the machinist who made the master did was to advance the
dividing head two times; then, because of a marker pin, they do not
advance the last 1/40th of the division.

This means that the actual spacing is (Pi millimeters) - 1/40
millimeters.  This works out, when converted to Imperial, to exactly
0.1227 inches.

  pi millimeters (3.141579...) converted to Imperial is
  0.12368475... inch.
  .1227 inch converted to millimeters is exactly 3.11658 mm.
  Subtracting 3.11658 from pi gives 0.0250126...
  Taking the reciprocal of this, rounded to 0.025 mm, gives 40.

Which is saying the same that 1 mm divided by 40 is 0.025 mm.

Since this is the expected error between pi mm and 0.1227 converted to
mm, the slide could not advance, say, pi millimeters because of the pin
holding the drill steady, 1/40th of 1 millimeter.  The machinist turns
the handle of the divider around two times full, but stops just shy of
the third complete turn.

While this does not answer whether or not it was a mistake, or what
actually happened as to cause it to be reported as a mistake, I think
it shows how using a simple 40 to 1 dividing head and a metric
leadscrew to achieve a simple spacing that has such an odd repeat per
inch or millimeter, as the fundamental value used is pi millimeters.

Julie Porter