*This paper is based on ones delivered to the Seventh International Congress of Celtic Studies on 15 vii 1983 and to the Philological Society on 14 times 1983. I am indebted to members of both audiences for helpful comments, and for advice on particular points I thank R. G. G. Coleman, G. C. Horrocks, K. H. Jackson, G. Khan, P. H. Matthews, O. J. Padel and J. H. W. Penney. Professors E. G. Quin and K. R. McCone kindly sent me some useful notes on a draft. My debt to my brother Nicholas Sims-Williams is as always very great. Responsibility for the argument rests, of course, with me.