Many thanks to the folks who have emailed me to help solve the mystery plus
much more. At Wayne Sippola's suggestion, I'm posting his response which is
both helpful to me and perhaps of interest to others with a similar dividing
head. --Buddy (Wayne's email follows)

I don't have an account to post to RCM so I thought I would send an email
directly to you. Feel free to post to RCM - someone else may be able to use
this. I believe the screw you speak of is for adjusting end shake of the
worm shaft. I have what sounds like the same kind of dividing head and that
screw is locked in place with a setscrew accessible from through one of the
holes on the direct dividing face plate (bottom right when you are looking
at the end of the spindle). To use the direct dividing plate, take off the
crank and the 3 screws holding the dividing plate and you will see 2 allen
headed cap screws. Loosen these and you can rotate the housing that the
worm shaft rides in. This housing is eccentric and will rotate the worm
away from the wheel. This is also how you remove play from between the worm
and wheel. If you remove the two screws, you can slide out the eccentric
with the worm shaft - not much to it.
Last week I used mine to drill 183 holes around the face of a 6" disk -
to make another dividing plate for cutting 366 teeth for a calendar
mechanism. I did a minor modification to allow differential indexing. I
will describe in case it may be of some use to you. I removed the 3 screws
which hold the dividing plate in place. I had to drill and thread one small
hole on the side of the dividing head to mount a small strip of steel (3-4"
piece of hacksaw blade) with a pin to fit the dividing head holes. This pin
enters the holes from the back of the dividing plate. With the spindle
vertical, this strip of steel with the index pin goes horizontally from the
top edge of the dividing plate to near the left side of the dividing head
(still on the portion which rotates the spindle from horizontal to
vertical). As it is held with one screw, it can be loosened and swiveled up
or down to different hole circles although it will only reach to the outer
couple of holes on a plate, due to the eccentric mount for the worm is in
the way.
From a set of differential index tables, 183 can be divided by moving
the crank 1 24/41 + 8/49. The added index pin enters from the back of the
49 hole ring, and the normal index pin with the sector set for 24 holes in
the 41 hole ring (please note that as you do not count the hole the pin is
in, the sector actually spans 25 holes). 1. Turn the crank one round plus
the width of the sector (24 holes). 2. Turn the dividing plate (the crank
moves with it) 8 holes using the added index pin. To help prevent errors, I
had a sheet of 10 thou steel behind the index plate with the space for the 8
holes (again, actually 9 holes) cut out - I would rotate one edge against
the added index pin, then rotate the shim steel and the index plate until
the other edge of the shim steel cutout was against the pin - 8 holes later.
Harder to explain than do. Took just over an hour or about 20 seconds per
hole. No mistakes thankfully. Differential dividing is not always quite
exact, but if you calculate it out the spacing of the last hole is a few
tenths out - not a problem.
The point is that it is a simple mod for this kind of dividing head to
do differential indexing which vastly increases the number of divisions you
can do. The drawback to this method is that the added index pin will only
reach the outer couple of holes on the plate. Hope you find this useful,

Wayne Sippola
Elizabeth City, NC
RCM Lurker