This is a follow-up to a thread from June 2004.  I'd bought an Apple 
Joystick //e off eBay and was looking for help with the adjustment 
controls on the bottom. Got a good reply from Raymond, but did some more 
fiddling tonight and I think I have the definitive answer.  So, here it 
is for Google posterity!

Look at the underside of the joystick. Hold it so you can read the 
writing. There are two knurled thumbwheels and 4 screw adjusters. On 
some models, these are labelled Y2, Y1, X1 and X2. Other models have no 
labels, so see diagrams below to understand the label references.

The screw adjusters are small, black & circular.  There is a large 
groove in the center of each screw adjuster which allows you to turn it 
with a screwdriver or your thumbnail.  If you look carefully, there is 
also a tiny raised line on only one side of each screw adjuster. In the
Y2 and Y1 grooves should always be vertical, X1 and X2 grooves should 
always be horizontal.

Self-centering mode: lines are pointing "out" (away from each other)
Floating mode: lines are pointing "in" (towards each other)

SWITCHING TO SELF-CENTERING:
Simply turn each screw 1/2 turn, so each pair of lines is pointing out 
(away from each other). The springs will engage one by one.

The underside should look like this when you are done:

      |||||||||||||                    <-- thumbwheel

<||                ||>                <-- Y2/Y1 screw adjusters

  Y2                Y1      ^
      Joystick //e     X1   =    _     <-- X1 screw adjuster
                                 _
                                 _
                                 _
                                 _     <-- thumbwheel
                                 _
                                 _
                                 _
                       X2   =        <-- X2 screw adjuster
                            v

SWITCHING TO FLOATING:
To switch from self-centering to floating is a little trickier:
1) Hold joystick upside down, oriented as per layout.
2) Move stick to bottom left corner (away from Y1/X1)
3) Turn Y1 half a turn so the tiny line is on the left
4) Turn X1 half a turn so the tiny line is on the bottom
5) Move stick to top right corner (towards Y1/X1)
6) Turn Y2 half a turn so the tiny line is on the right
7) Turn X2 half a turn so the tiny line is on the top

The underside should look like this when you are done:

      |||||||||||||                    <-- thumbwheel

  ||>              <||                 <-- Y2/Y1 screw adjusters

  Y2                Y1
      Joystick //e     X1   =    _     <-- X1 screw adjuster
                            v    _
                                 _
                                 _
                                 _     <-- thumbwheel
                                 _
                                 _
                            ^    _
                       X2   =          <-- X2 screw adjuster


THUMBWHEELS:
These are to assist you to synchronize the physical center (when the 
joystick is self-centering and you are not touching the stick) with the 
logical center (the midpoint values that the Apple is reading from the 
device). Kind of like V.HOLD and H.HOLD on a TV.  The game "Choplifter" 
is a good test case.  With the joystick self-centering, take off from 
the helipad then release the stick. If the chopper drifts up, down, left 
or right you can turn the wheels to eliminate the drift and achieve a 
stationary hover when the stick is centered.

Have fun!
Martin