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LXXI. On Lake-Basins. 

 By John Carrick Moore, Esq., F.G.S., tyc* 



PROFESSOR RAMSAY, in his able memoir in defence of 

 -*- his Glacial Theory of Lake-Basins, in the April Number of 

 this M agazine, lays down principles of the erosion produced by 

 a sliding body which, with the greatest deference, I cannot 

 believe to be sound. His words are, "Every physicist knows 

 that when such a body as glacier-ice descends a slope, the direct 

 vertical pressure of the ice will be proportional to its thickness 

 and weight and the angle of the slope over which it flows. If 

 the angle be 5°, the weight and erosive force of a given 

 thickness of ice will be so much, if 10° so much less, 20°, 

 less still, till at length, if. we imagine the fall to be over 

 a vertical fall of rock, the pressure against the wall (except 

 accidentally) will be nil. But when the same vast body of ice 

 has reached the plain, then motion and erosion would cease, 

 were it not for pressure from behind." By " the direct vertical 

 pressure of the ice," the Professor means that resolved portion 

 of the weight which is at right angles to the slope ; and this 

 resolved portion, which is stated rather loosely to be proportional 

 to the angle, is proportional to the cosine of the angle, a function 

 which up to 90° diminishes as the angle increases. It does not 

 appear to have struck Professor Ramsay as strange, that by 

 his theorem the erosive force is nothing at 90°, comes into 

 operation as the angle declines from 90°, goes on increasing 

 sine limite as the angle diminishes, and just when we expect 

 it to be a maximum, we are told it is nil as the angle vanishes. 

 It seems to me that Professor Ramsay has taken a wrong 

 measure of the erosive force. He says "the weight or ero- 

 sive force," as if the words were equivalent. But mere weight 

 does not erode ; weight in motion will. A body sliding down a 

 slope will tend to erode with a force compounded of the pressure 

 perpendicular to the slope and the velocity. Now the velocity 

 of sliding ice (as has been shown by Hopkins) is nearly uniform, 

 and therefore may be taken as proportional to the force in the 

 direction of the motion — that is, as the sine of the inclination 6 ; 

 therefore the erosive force is as the pressure vertical to the plane 

 X sin 6; that is, as weight x cos x sin 6; that is, as weight 

 x sin 26. This expression is in accordance with Professor 

 Ramsay's theory, that when the angle is 90°, the erosion is 0; 

 and again, when the angle is 0, the erosion is nothing : but it is 

 quite discordant from his view, that the erosion is greater at an 



* Communicated by the Author. 



