Among the earliest monuments of the Buddhist faith as propagated through India by king Asoka in the third century B.C. is a peculiar class of structure known as a stupa, and since Fergusson (1) first put forward the idea at the end of the last century it has been vaguely realized that these monuments were in all probability a formalized version of nothing more or less than a specialized type of prehistoric (and pre-Buddhist) round cairn. The possible implications of this prototype's peculiar features in reference not only in oriental, but in European archaeology, were pointed out by Mr Harold Peake with characteristic acumen (2), but no convenient summary of the relevant Indian material has appeared in an English archaeological journal, and a recent discovery in Jaipur State has thrown most interesting light on the subject at large. It seems therefore desirable to bring the results of the Bairat excavations before a wider archaeological public than that reached by the original report by the excavator, the late Rai Bahadur D. R. Sahni, and to consider it in relation to the wider question of the origins of the stupa and of the curious features which are presented in formalized guise on the elaborate monuments which represent the supreme artistic achievements of the Sunga Dynasty in the closing centuries of the pre-Christian era. I am deeply indebted to Mr Peake not only for material amplifying his original thesis, but for stimulating discussion and correspondence on the whole question. The latter part of this paper is in fact to such a degree based on his ideas that it amounts to an appendix in which I have paraphrased views exprcssed by him and shared by myself.