"Without attempting to solve the mystery connected with these archaic lapidary cups and ring cuttings, I would venture to remark that there is one use for which some of these olden stone carvings were in all probability devoted--namely, ornamentation. From the very earliest historic periods in the architecture of Egypt, Assyria, Greece, etc., down to our own day, circles, single or double, and spirals, have formed, under various modifications, perhaps the most common fundamental types of lapidary decoration. In prehistoric times the same taste for circular sculpturings, however rough and rude, seems to have swayed the mind of archaic man. This observation as to the probable ornamental origin of our cup and ring carvings holds, in my opinion, far more strongly in respect to some antique stone cuttings in Ireland and in Brittany, than to the ruder and simpler forms that I have described as existing in Scotland and England. For instance, the cut single and double volutes, the complete and half-concentric circles, the zig-zag, and other patterns which cover almost entirely and completely some stones in those magnificent though rude western Pyramids that constitute the grand old mausolea of Ireland and Brittany, appear to be, in great part at least, of an ornamental character, whatever else their import may be." In a communication on the Great Pyramid, made to the Royal Society 16th December 1867, Professor Smyth most unexpectedly, and quite out of his way, took occasion to criticise severely the remarks contained in the preceding extract, on two grounds: _First_, He laid down that the term pyramid was misapplied, as the term referred only to figures and structures of a special mathematical form; being apparently quite unaware that, as shown in the text and notes, pp. 219 and 220, it was often applied archaeologically to sepulchral mounds and erections that were not faced, and which did not consist of a series of triangles meeting in an apex.