Geological Society. 279 



real light is found. Similarly as regards the axioms of Geometry, 

 the expositions of meta-geoinetry by Helmholtz, Klein, Clifford, 

 Cay ley, and Poincare are examined and found wanting. The 

 fundamental question here is the nature of the axiom of parallels ; 

 and Mr. Berkeley shows that Euclid's axiom of parallels can be 

 broken up into two propositions, which exhibit a remarkable 

 analogy in thought process with the axioms of magnitude. He 

 concludes that the ordinary notion of direction has no logical 

 foothold in non-Euclidean space-conceptions. Here, however, 

 the whole difficulty comes to the front again in the question, 

 what is involved in the ordinary notion of direction? In. 

 reasoning about those fundamental almost a priori notions, we 

 seem to come round again to our starting point — like a '* straight " 

 line in elliptic space, it is quite permissible to define a straight 

 line as such that any part of it is the shortest distance between 

 its end points. If then we proceed to say that such a " straight" 

 line never changes direction, we get a definition of direction which 

 satisfies the familiar experimental notion of direction in Euclidean 

 space. But it does not seem necessarily to follow that the meta- 

 geometer is using this ordinary notion in his discussions of the 

 properties of elliptic and hyperbolic space geometric. This, 

 however, is the accusation made by Mr. Berkeley against these 

 mathematical mystics. No doubt they will find their own defence. 

 Whether or not we agree with the author in his conclusions, there 

 is no doubt that he has given us a book worthy of close study 

 on the part of all interested in these meta-geometrical questions< 



XXXI J I. Proceedings of Learned Societies. 



GEOLOGICAL SOCIETY. 



[Continued from p. 176.] 



November 9th, 1910.— Prof. W. W. Watts, Sc.D., M.Sc, E.R.S., 

 President, in the Chair. 



r PIIE following communications were read : — 



]. 'The llhsetic and Contiguous Deposits of West, Mid, and 

 Part of East Somerset.' By Linsdall Ilichardson, E.R.S.E., F.L.S., 

 E.G.S. 



This paper contains a detailed account of the Bhsetic strata of 

 Somerset, with the exception of a small area bordering upon 

 Bristol. The magnificent sections at Blue Anchor and Lilstoek 

 are described in detail, and correlated with those on the opposite 

 Glamorgan coast. The record by Prof. Boyd Dawkins of 

 characteristic Khaetic mollusca in the top portion (uppermost 

 14 feet or so) of the Grey Marls is confirmed, and the contention 

 for their recognition as Rhsetic is fully substantiated. The deposit 

 between the top of the fossiliferous Grey Marls or ' Sully Beds ? and 

 the main Bone-Bed at Blue Anchor measures 22 feet, and teems 

 with interesting Ilha2tic fossils, such as Pteromya crowcombeia 

 Moore. The beds above the Bone-Bed agree very well with those 



