Got the dynamic re-scaling working ok now with Uwe's help.
Qt Code: 
  1. const QwtScaleDiv &scaleDiv = axisScaleDiv(QwtPlot::xTop);
  2.     const double center = (scaleDiv.lowerBound() + scaleDiv.range() / 2) + diff * 2;
  3.     const double width_2 = scaleDiv.range() / 2 ;
  4.     QwtPlot::setAxisScale(QwtPlot::xTop, center - width_2, center + width_2, 10000);
  5.     setAxisScaleDraw(QwtPlot::xTop, new NewScaleDraw());
  6.     replot();
To copy to clipboard, switch view to plain text mode 
Scale shows as 10 major divisions with 4 minor divisions - good so far.
But, the grid has 6 major divisions with 3 minor divisions - not so good. Need it to line up with the scale.
Here is how the grid was created
Qt Code: 
  2.     grid->enableX(true);
  3.     grid->enableY(true);
  4.     grid->enableXMin(true);
  5.     grid->enableYMin(false);
  6.  
  7.     QPen* majPen = new QPen;
  8.     majPen->setWidth(1);
  9.     majPen->setStyle(Qt::SolidLine);
  10.  
  11.     QColor majColor;
  12.     majColor.setNamedColor("white");
  13.     majPen->setColor(majColor);
  14.  
  15.     QPen* minPen = new QPen;
  16.     minPen->setWidth(1);
  17.     minPen->setStyle(Qt::DotLine);
  18.  
  19.     QColor minColor;
  20.     minColor.setNamedColor("grey");
  21.     minPen->setColor(minColor);
  22.  
  23.     grid->setMajorPen(*majPen);
  24.     grid->setMinorPen(*minPen);
  25.  
  26.     grid->attach(this);
To copy to clipboard, switch view to plain text mode 
So what am I doing wrong that the grid doesn't line up with the scale?
Thanks for any assistance.