Prof. Sedgwick on the Geology of the Valley of Dent. 79 



1 and 2, and similarly 13 the moment of the lines 1 and 3, &c., the 

 forces are as 



^ 23. 34. 42 : ^34.41.13 : v/41 .12.24 : v/l2.23.31. 



Calling the four forces P lf P 2 , P 3 , P 4 , it follows as a corollary that 



we have 



P X P 2 . 12 = 12 . 34v/l3.42 . V'l4.23 = P 3 P 4 . 34 ; 



viz. the product of any two of the forces into the moment of the 

 lines along which they act is equal to the product of the other two 

 forces into the moment of the lines along which they act, — which is 

 equivalent to Chasles's theorem, that, representing a force by a finite 

 line of proportional magnitude, then in whatever way a system of 

 forces is resolved into two forces, the volume of the tetrahedron 

 formed by joining the extremities of the two representative lines is 

 constant. 



November 13. — By Professor Sedgwick, F.R.S., "A Sketch of the 

 Geology of the Valley of Dent, with some account of a destructive 

 Avalanche which fell in the year 1752." 



The valley of Dent lies in the north-west corner of Yorkshire, 

 which is thrust in between Westmoreland and Lancashire, beyond 

 the natural limits of the county. The upper part of the valley is 

 excavated in the carboniferous groups which are continued south- 

 wards into Nottinghamshire, and northwards into Durham and 

 Northumberland, and through the greatest part of their range form 

 the watershed between the east and west coasts of England. All 

 the valleys that drain down to the land are partly formed in rocks 

 of the carboniferous age. In the upper part of Dent Dale, which is 

 one of these tributaries, the great scar-limestone appears only near 

 the bottom of the valley, while the sides are formed of soft shale 

 alternating with harder bands of sandstone and limestone ; and the 

 whole series is capped by mill-stone grit. The rainfall in some por- 

 tions of the Lake mountains is not less than 150 or 160 inches in the 

 year. Among the neighbouring carboniferous mountains the rain- 

 fall is much less ; but still it is at least three times the English 

 ' average ; and the winter fall of snow is in some years enormous. 

 Hence the becks, or mountain-streams, are often greatly swollen, and 

 the gills, or lateral branches, frequently descend in brawling torrents 

 from the mountain- side into the lower valley through deep ravines 

 and lateral valleys that have been excavated out of the shales and 

 sandstones in the course of past ages. On rare occasions a great fall of 

 snow, accompanied by a violent wind, will almost fill up the ravines 

 and lateral valleys, and form a dam across the descending water ; 

 and should there be a sudden thaw afterwards, the descending gills 

 may be held up for a while till the pressure of the water drives down 

 the barrier, and an avalanche is formed of mingled snow and water 

 (provincially called a brack), which rushes down with the roar of 

 thunder, and bears all before it into the beck below. On the 6th 

 of February, 1752, a very large one fell, destroying several houses 

 and farm buildings, and killing seven people, besides several head of 

 cattle. The following letter, written by an eye-witness, describes 



