Hi Raymond. Thanks very much for your reply and helpful suggestions.
I set about checking the spindle first and ideally would have liked to own a 3MT test bar, but find it difficult to justify the cost of this as my preferred maker is Arrand and hsi cost about £80. There are other and cheaper versions available, but I wouldn't dream of buying one as they publish no information about accuracy. I settled for the next best thing and mounted a ground bar (silver steel) in a collet in the spindle and was pleased to find no deviation from the vertical that I could measre over 4". Rotating the bar, there was no measurable wobble at the collet and 4" away I detected 0.001" TIR. I reckon I should be happy with that – would you agree?
Next I followed your suggestion with the scope mounted (after removing the 3MT arbor and cleaning the contact faces). Initially it was a bit out and I adjusted it to be spot on. Then I freed the taper and re-engaged it at 90deg and the cross hairs were off centre. I repeated this at 180deg and 270deg and at all these positions the scope was off centre ny as much as 0.012". Which is not good news. I found the place where it was correct and marked the spindle, removed the scope and re-inserted it in the same place, but very disappointingly, it was now out by about .006".
I think all this means that the scope is inaccurate, but I don't have any idea what I can do to correct it.
Best wishes
Bernard