352 Geological Society : — 



representing two Solitary Waves of similar circumstances 

 except for their different directions of propagation, and 

 meeting at the plane x = at the time t = 0. This will serve 

 in place of a single wave reflected at the wall x = 0. 



Still neglecting the small term, F t and F 2 are each sepa- 

 rately solutions of (5); and therefore the terms which remain 

 in (5) unsatisfied become 



2c{F 1 "F 3 '-F 2 "F 1 '}. 



Replacing Fi and F 2 by the function a tanh, this becomes 



4:a?m d c sech 3 m(ci +<^)sech 3 m(ct — x) sinh 2mct, . (9) 



From this expression, or from general considerations, we see 

 that if ct + x and ct— x are widely different from zero, the 

 term will be very small. Also when x and ct are small, its 

 value may be estimated as 



Aa 2 m 3 c sinh 2mct, 



which, as both m and ct are small, is of the order of the 

 terms we are neglecting. The expression reaches its maximum, 

 about 2"3m 3 a 2 c, at the wall, at the time given by cosh 2mct=^ 

 before or after the crest of the wave reaches the wall, being 

 both temporary and local. 



The condition that (3) may approximately give the form of 

 the free surface is therefore closely satisfied, and the mathe- 

 matical theory agrees with the experimental investigation 

 that the direct reflexion of a Solitary Wave will have an incon- 

 siderable effect upon its contour and progress. 



XXXV. Proceedings of Learned Societies. 



GEOLOGICAL SOCIETY. 

 [Continued from p. 268.] 



April 25th, 1900.— J. J. Teall, Esq., M.A., F.R.S., President, 

 in the Chair. 

 T^HE following communications were read : — 

 -"- 1. ' On a complete Skeleton of an Anomodont Reptile from 

 the Bunter Sandstone of Reichen, near Basel, giving new Evidence 

 of the Relation of the Anomodontia to the Monotremata.' By Prof. 

 H. G. Seeley, E.R.S., P.L.S., Y.P.G.S. 



2. ' On Longmyndian Inliers at Old Radnor and Huntley (Glou- 

 cestershire).' By Charles Callaway, M.A., D.Sc, P.G.S. 



The grits, with some associated slaty bands, forming a ridge near 

 Old Radnor were considered by Sir Roderick Murchison to be May 

 Hill Sandstone. The author has discovered that one of the beds of 

 Woolhope Limestone, dipping westward, is crowded with rounded 

 and angular fragments of grit bearing a general resemblance to the 



