Fourth type. _Cups surrounded by a series of concentric, but incomplete rings having a straight radial groove._--This type constitutes perhaps the most common form of the circular carvings. The rings generally touch the radial line at both extremities, but sometimes they terminate on each side of it without touching it. The radial groove occasionally extends considerably beyond the outer circle, and in most cases it runs in a more or less downward direction on the stone or rock. Sometimes it runs on and unites into a common line with other ducts or grooves coming from other circles, till thus several series of concentric rings are conjoined into a larger or smaller cluster, united together by the extension of their radial branch-like grooves. Fifth type. _Cups surrounded by concentric rings and flexed lines._--The number of inclosing or concentric rings is generally fewer in this type than in the two last preceding types, and seldom exceeds two or three in number. Sixth type. _Concentric rings without a central cup._--In many cases the concentric rings of the types already described appear without a central cup or depression, which is most frequently wanting in the complete concentric circles of the third type. Seventh type. _Concentric circular lines of the form of a spiral or volute._--The central beginning of the spiral line is usually, but not always, marked by a cup-like excavation. It often occurs that two, three, or more of these various types are found on the same stone or rock, a fact indicating that they are intimately allied to each other. Prof. Simpson presents what he calls “the chief deviations from the principal types” reproduced here as Fig. 148. [Illustration: FIG. 148.--Variants of cup sculptures.] The first four designs represent cups connected by grooves, which is a noticeable and frequently occurring feature. In Fig. 149 views of sculptured rock surfaces at Auchnabreach, Argyleshire, Scotland, are given. Simple cups, cups surrounded by one ring or by concentric rings, with radial grooves and spirals, appear here promiscuously mingled. Fig. 150 exhibits isolated as well as connected cups, a cup surrounded by a ring, and concentric rings with radial grooves, on a standing stone (menhir), belonging to a group of seven at Ballymenach, in the parish of Kilmichael-Glassary, in Argyleshire, Scotland. [Illustration: FIG. 149.--Cup sculptures at Auchnabreach, Scotland.] [Illustration: FIG. 150.--Cup sculptures at Ballymenach, Scotland.] Dr. Berthold Seeman remarks concerning the characters in Fig. 105, supra, copied from a rock in Chiriqui, Panama, that he discovers in it a great resemblance to those of Northumberland, Scotland, and other parts of Great Britain. He says, as quoted by Dr. Rau (_d_):