ATM mirror grinding mechanics

[Cary Chleborad <bennu@ns.net>]

Ok people, time to flex those brain cells!

One thing that has occupied my thoughts often when I'm grinding mirrors
is the question of what's going on in the grinding process.

We all know that if we maintain a 1/3 diameter coc stroke, the top
workpiece goes concave spherical and the bottom convex spherical.  As
long as we maintina this, the roc gets shorter and if we flip the whole
setup over the roc gets longer.  This is all we need to know to make a
mirror and that keeps most of us happy - not me.

Why does the top workpiece  want to go towards  concave and the bottom
convex? As far as I can invision both surfaces (i.e., the 10% zone on
both the mirror and tool) are getting equal grinding treatment. 
Obviously they are not, since one grinds away faster than the other. 
Follow this? Any Ideas? What happens if you grind the mirror and tool in
a verticle position?

-Cary Chleborad