I've got this sanding plate to use in the lathe-

http://tinyurl.com/q7hoar9

To use it, I have to put it in a chuck which fits in the lathe by the No 1
morse taper. You can see a witness mark on the spindle which is where the
chuck reaches to. Trouble is, the plate is so far from the headstock that it
wobbles, and sometimes comes loose in the chuck. Is it possible to get one
of these with a morse taper so I can put it straight in the lathe? I haven't
had any luck locally (Southern UK), and can't find one on ebay.

Steve