J. Sophinson — On New British Graptolites. 501 



gradually flattens, following however a concaTe line ; and when it enters a river, 

 which has become navigable, passes into a parabola. In Fig. 3 the convex part is 

 marked Hill H H ; and the concave part, Valley, V V ; and the convex or 

 concave form of the surface enables us to divide a hill from a valley broadly. A new 

 definition of a hill might be land situated above a valley having a convex form or 

 surface, and that of a valley might be land situated below a hill, and concave in form. 



The different powers of (a -j- V) require a different number of divisions of the base 

 line of the curve as well as different co-efficients, thus giving great variety to this 

 form of the curve, while still preserving the feature of convexity and concavity 

 pointed out. Hard rocks, or alternations of hard and soft, produce considerable 

 deviations. No curve could be general in nature without great flexibility and variety, 

 and the author thinks that Hogarth, who first tried to represent natural forms by 

 particular curves, would have chosen the binomial as the line of grace, had he been 

 aware of its properties. 



The curves Hogarth has drawn have little variety, and therefore do not represent 

 nature. Hard rocks do not always put on rugged features or outlines, they are 

 sometimes denuded into smooth curves. In passing over the most varied formations, 

 hills of identical contour but of diflerent materials may be seen. The harder rocks 

 have greater stability, and therefore are altogether larger, and. stand up higher. May 

 Hill and Shooters Hill, for instance, difi'er in size, but not in contour. No one can 

 tell in all cases the formation from the surface alone. Tou may be certain that you 

 are not looking at clay, but rock may put on various forms. 



III. — On some New Species of Graptolites from the South of 



Scotland. 



By John Hopkinson, F.G.S., F.E.M.S. 



(PLATE XII.) 



IN this communication I purpose describing a few new forms of 

 Graptolites which. I have obtained at various times from the 

 Llandeilo rocks of the south of Scotland. Of one species, first col- 

 lected at Mofifat in 1866, a brief diagnosis has previously been given, 

 and the names of two others, from the lead-mining district of 

 Lanarkshire, have already been published. One of these also occurs 

 near Mofifat. The remaining species are all from one or other of 

 these richly fossiliferous districts. Of their position in the geological 

 series I need only say here that the black, more or less carbonaceous, 

 shale in which they occur, appears, from the fossils it contains, to 

 correspond to the higher portion of the Llandeilo flags of "Wales ; 

 that it is almost immediately succeeded by a series of beds (the Gala 

 group) containing fossils of Caradoc or Bala age ; and that the un- 

 fossiliferous flagstone, or greywacke, in which it occurs, reposes on 

 rocks which have yielded to the persevering search of Prof. Elliot 

 and Messrs. Lapworth and Wilson a few fossils of Cambrian age. 



The Lanarkshire graptolitic shale is considered by Prof Geikie 

 to form "an upper part of the Mofifat group," ^ but while decisive 

 strati graphical evidence is wanting, from the evidence afforded by 

 the fossils it seems more probable that but one band of graptolitic 

 shale runs through the Llandeilo rocks of the south of Scotland, 

 there being in this band several distinct zones, each marked by a 

 different assemblage of fossils, but with many species in common. 



Several of these new species were collected in the course of a few 

 days' walking tour in these districts, during part of which I had 

 the advantage of the company of Mr. Chas. Lapworth, of Galashiels, 

 1 Erit. Assoc. Report for 1871, Sections, p. 96. 



