Fisher— Disintegration of a Chalk Cliff. 



355 



Noticing a lofty chalk cliff, forming the face of an old quarry in 

 the neighbourhood of Lewes, I remarked that the action of the 

 weather upon the surface was to disintegrate it equally all over, so 

 that the face of the quarry remained vertical, while the stuff that 

 fell down formed a talus, whose surface was approximately a plane, 

 inclined to the horizon at that particular angle at which such 

 materials will stand. The question then occurred to my mind — 

 Wliat will be the profile of the solid chalk behind the talus ? 



The solution of this question is given in the note. The form of 

 the solid siu'face is there shown to be a semi-parabola, whose vertex 

 is at the base of the original cliff. 



It is evident that an old sea cliff deserted by the sea, or a 

 river cliff from which the stream had receded, woukl disinte- 

 grate after the same law. If any subsequent circumstance, such 

 as the return of the sea or river, should * remove the talus (and 

 it may be observed that the corollary proves that an under- 

 mining action would do so completely) we should have the 

 parabolic form disclosed. This is the shape observed in that 

 form of cliff known as a "ISTose." The imdermining action 

 of the sea upon a chalk cliff would of itself produce a vertical 

 wall. When, therefore, we see a cliff of a parabolic form, or 

 vertical below, and parabolic in the upper part, it seems to me 

 that we may expect to find that we have an ancient cliff, once 

 deserted by the waves, now attacked again, and the peculiar 

 form due to disintegration exposed by the removal of the talus. 



Note. 



Suppose C P to be the face of the cliff : A the bottom of the 

 quarry : T P the surface of the talus : and let the disintegration of 

 the face to Q E raise the talus to E Q. Then P Q will be a 

 portion of the curve whose form we are seeking. 



P p is perpendicular to E Q, Q q to C M, and E Q meets C M in 

 m. C M = a, and the angle P T M = a. Then, because the ma- 

 terial disintegrated from P has raised the talus to E Q, we shall 

 have in the limit — 



