I have a Nikon D1X camera which I use for some medical Ophthalmologic
photography. Hooked to a operating microscope there is no lens used
and the focus is fixed as is the light source on the m'scope. There is
the capability of choosing one of the settings, "M","A","S",or "P". If
I set "M" and a shutter speed of 1/125 of a second, I get pictures all
over the map in exposure probably because distance from the eye varies
with each exposure. Setting "A" and "P" also gives me some pictures
which appear very underexposed.

I would like to know what the best setting would be that is more dependable.

The camera's autoexposure programs must be confused by the subject.  I
don't have the D1X, but in general, I'd suggest two things:

1. Set the camera to autobracket so that it takes three shots at
+1.5EV, -1.5EV, and (what it thinks) is the correct exposure.

2. Display the realtime histogram (if it has it).  The exposure will
be correct if must of the bars are in the middle of the graph.