Patience is a virtue, or so they say.  Unfortunately, if you wait for the simple weight of the mirror against the grit and tool to get rid of the radial lines, then death will come shortly before those lines are ground out.  So we removed the alligator and applied a bit of muscle to put more pressure on the tool (now on top of the mirror, since we wanted less curvature at the point) while grinding.  The machine turned the mirror and we all took turns manually moving the tool.  Later we proved we were smarter than the machine by putting weights on top of the tool to increase the pressure and putting the alligator back on so the machine would move the tool.  (or were we so smart?  This approach nearly proved disastrous during the polishing phase.)
After we finished the rough grinding, we moved onto the fine grinding...
Since the grinding machine produces random motions, the resulting surface must be approximately spherical.  This is simply because grinding removes any high spots and a spherical surface is the only surface that allows full contact regardless of the orientation of the surfaces (think of a small section of a ball-and-socket joint).  As the grinding progressed, we needed to make sure the curvature was staying approximately correct.  If the curvature was too shallow (longer focal length), we needed to deepen it (by working with the mirror on top).  If it was getting too deep (shorter focal length), then we needed to make it more shallow (by working with the tool on top).  Jim Sattler used his spherometer to measure the curvature.  At one point early in the grinding process, it became obvious that one mirror was significantly shallower than the other, which would be difficult to correct with our current methods, so we went back to the curve generator stage with that mirror to correct it quickly.  Our original target radius of curvature is 96 inches which will result in a focal length of 48 inches (f/6).  (Note: Since it's hard to be sure we'd cleaned all the grit out of the spaces between the tiles of the tool when changing to a finer grit, as a precaution we worked with the tool on the bottom for all but the first 2 coarsest grits.  That caused the radius to shrink, so over the course of grinding, the radius shrank to 88 inches (44" focal length, f/5.5).