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viii and elabo&shy;ration of Hirt’s. Apart from the Welsh examples the section contains nothing new except the notes on the place of a in the system (v (2)) and the treatment of long diph&shy;thongs (vii (5)). In the discus&shy;sion of philo&shy;logical questions generally my obliga&shy;tion to Brugmann’s great work is so obvious as hardly to need statement; for the writing of pre&shy;historic forms his scheme has been adopted, and is departed from in only one partic&shy;ular: ₑr, ₑn etc. are used here, as by Hirt, instead of r̥r, n̥n etc. I have also learnt much from Meillet’s brilliant Intro&shy;duction, and have borrowed from him the con&shy;venient use of the term “sonant” to denote the sounds which oscillate between vowels and conso&shy;nants in Pr. Ar. In the search for the origin and cognates of Welsh vocables I have made extensive use of Walde’s Wörter&shy;buch, which contains, in a concise form and fully indexed, a vast collec&shy;tion of the results of recent investi&shy;gation in this field; Boisacq’s Diction&shy;naire I have also found most valuable. For the purposes of Keltic philology I have consulted with much profit Thurney&shy;sen’s admirable grammar of Old Irish. The sections treating of the deri&shy;vation of sounds are fuller than they were origi&shy;nally intended to be; and with the material thus provided I was led further to attempt to trace to their origin all inflex&shy;ions and important grammat&shy;ical forms. But in order to save space I have generally given only the expla&shy;nation which seemed to me in each case the most probable; thus the fact that Pedersen’s equation of W. ynteu with Ir. intī or his deri&shy;vation of eiδ-aw from *esi̯o is not mentioned does not neces&shy;sarily mean that it has not been consid&shy;ered, but that I regard it as less likely than the expla&shy;nation offered in the text.

I have to express my gratitude to Dr. Gwenogvryn Evans, who was kind enough to lend me for the purposes of this work his manu&shy;script referred to as, his tran&shy;scripts of numerous poems by G.Gr., G.Gl., Gu.O., D.N., D.E., H.D., I.F. and Ỻ., and to furnish me with proofs of before it was issued, and of