Mr. Winch on the Geology of the Banks of the Tweed. 11 



included between the two surfaces. Similar reasoning may be 

 applied to the fluid contiguous to this new containing surface, 

 and so on throughout the whole of the mass. From this we 

 infer that the motion is at every point directed to the vertex 

 of the given cone. Also, let V = the velocity of the vertical 

 descent of the horizontal surface, and h its distance from the 

 vertex of the cone, and let us consider a point on this surface, 

 at which the direction of the velocity makes an angle & with 

 the axis. The velocity at this point = V sec and V sec $ 



c dy csin^ TT h? V sin 6 m, 



= - = ~ Hence ~ c = ---- There - 



f V sin 2 6 h* T/ , 



fore in general co = -^7- . If = the distance of any 



point from the vertex g sin 6 = y, and 



V h* 1 



cos 6 ' cos* 6 ' 



As the vertical velocity M cos varies as CQS ^ g , it is the 



same at all points of a plane perpendicular to the axis. Hence 

 the fluid descends in parallel slices ; that is, a portion which 

 at any instant is included between horizontal planes will al- 

 ways be included between horizontal planes. 

 Trin. Coll. Camb. Nov. 13, 1830. 



IV. Remarks on the Geology of the Banks of the Tweed, from 

 Carham, in Northumberland, to the Sea Coast at Berwick. 

 By N. J. WINCH, Esq. Secretary of the Natural History 

 Society of Newcastle-upon- Tyne*. 



f T 1 HE rocky strata which border the Tweed from Carham 

 Bourn, where the river begins to form the boundary be- 

 tween Northumberland and Scotland, to the sea shore at Ber- 

 wick, appearing to be associated in a manner so different from 

 the order generally considered by geologists as the natural 

 arrangement, will oblige me to abstain from theory altogether 

 in the following remarks. It is, therefore, my intention to lay 

 before the Society merely a series of notes lately made during 

 an examination of the north-eastern termination of our district, 

 accompanied by specimens which will serve to assist in verifying 

 the correctness of the observations. A superficial view of the 

 banks of this beautiful river presents a succession of eminences, 

 I can scarcely call them hills, chiefly composed of diluvium, con- 



* Read before the Natural History Society of Newcastle-upon-Tyne, 

 on the 20th of July last ; and now reprinted from the Transactions of that 

 Society. 



C 2 taining 



