C. Davison — Form of Rock- Surface under a Talus. 65 



a transition fauna between the zones of A. planorbis and A. angulatus, 

 not so well developed perhaps in other districts. 



Under these circumstances, should the zone of A. angulatus he 

 eventually exposed, and with more exposures, an assemblage of 

 fossils be found in the clays containing Mg. catenatum, then those 

 clays should be placed in the position of a subzone — the subzone of 

 A. catenatum. For the present, however, it might be termed the 

 '•' Catenatus bed," and separated on those grounds from the zones of 

 A. planorbis below and A. angulatus above. 



The occurrence of the interesting zone of A. semicostatus is an 

 example of the fluctuations of the zones of the Lias formation in 

 districts or areas, and how species perhaps only of secondary import- 

 ance in one zone, under certain conditions of environment may be 

 of capital importance in another. 



I have to acknowledge the assistance of Prof. Blake, of Notting- 

 ham, who has kindly determined many of the fossils for me, and also 

 that of Mr. E. F. Bates, of Leicester. 



V. — Note on the Form of the Uneroded Surface of Eock 



UNDERNEATH A TaLTJS. 



By Charles Davison, M.A. ; 

 Mathematical Master at King Edward's School, Birmingham. 



IN the case of a vertical cliff, Mr. Fisher has shown that the 

 uneroded surface of rock underneath a talus is in the form of 

 a semi-parabola. 1 The object of this note is to show that the form 

 is parabolic, even if the cliff be not initially vertical, assuming, with 

 Mr. Fisher, (1) that the cliff- face is weathered uniformly at all 

 points, and (2) that the disintegrated material is spread evenly over 

 the surface of the talus, so as to maintain it always at the same 

 slope. The proposition may be proved analytically, as in Mr. 

 Fisher's paper, or geometrically as follows. 



1 Eev. 0. Fisher, " On the Disintegration of a Chalk Cliff," Geol. Mag. (18G6), 

 Vol. III. pp. 354-356. 



DECADE III. TOL. III. — NO. II. 5 



