Mr. R. D. Oldham on the Modulus of Cohesion of Ice, 245 

 both of which, when the slope vanishes, become 



L=^f4 (X.) 



i being the thickness at the commencement of the level ground, 

 and I at the extreme point to which motion could be commu- 

 nicated. 



I would here call special attention to one point proved by 

 the above formulae, and which is at first sight totally opposed 

 to the idea one might naturally form of what was actually the 

 case, — namely, that the resistance which would be opposed to 

 a glacier moving as a whole through any depression that might 

 lie in its path is shown (by formula V.) to increase as the 

 slope leading out of that depression diminishes, and approxi- 

 mately in the ratio of the cotangent of the angle of slope: 

 thus, for an angle of V the resistance would be ten times that 

 for an angle of 10', for an angle of 10' about ten times 

 that due to a slope of 1° 40', and for a slope of 5° about one fifth 

 that due to a slope of 1°. This is of the greatest importance; 

 for wherever the theory of glacial erosion is upheld, especial 

 emphasis is laid on the fact that the hollows in which lakes 

 are situated are of but insignificant depth compared with their 

 length — a fact which investigation shows to be the very point 

 that would make the excavation of lake-basins of any great 

 size by these means not only improbable but absolutely im- 

 possible. 



But as formulae, in the state of formulae, are distasteful and 

 unintelligible to many, I will apply the formulae deduced above 

 to actual examples; and for this purpose I shall begin by con- 

 sidering the case of the Lake of Geneva, as it is the one con- 

 cerning which I can obtain the most perfect data, and which, 

 through the wide-spread circulation of Professor Ramsay's 

 ' Physical Geography and Geology of Great Britain,' and 

 from the fact that it was selected as an illustration in his 

 original memoir, is best known. From Professor Ramsay I 

 take the following data : — extreme length 45 miles ; extreme 

 depth 984 feet, say 1000 feet (for the lake must have been 

 at least that depth originally) ; distance of greatest depth from 

 lower end 25 miles, — giving a slope into the lake of 33' and 

 out of the lake as 26', taking both as uniform. 



Now the pressure necessary to force the glacier en masse 

 through the lake is, by (VI.), 



T = fjJ) (cot 6+ cot /3). 

 Here D = 1000, p is taken at '2, cot 0= 132*22, and cot/3 = 

 104*17 ; whence 



T=47,278; 



