238 Mr. Hopkins on the Mechanism of Glacial Motion. 



structure at right angles, which I have found empirically to be 

 the case." 



The error in this reasoning will be at once apparent to 

 any one who has followed the simple reasoning by which, in 

 articles 4 and 5 of my last letter, I have determined the line 

 of greatest extension. The Professor's conclusion is equiva- 

 lent to the assertion that the line M /, in the figure of the 

 articles just referred to, is the line in question, instead of M n, 

 as I have distinctly demonstrated it to be. These directions 

 differ by nearly 45° if the extensibility of ice be small, as I 

 conceive it to be, and could not even approximately coincide 

 unless the extensibility were very great *, as is easily seen by 

 referring to the construction given in art. 17 of my previous 

 letter, for determining the lines of no tangential action and 

 maximum and minimum tension. 



If we consider the Professor's reasoning with reference to 

 my analytical investigations, it will appear obvious that his 

 error consists in the omission of all consideration of the effects 

 of the tangential forces, those forces, in fact, which give to 

 the problem its distinctive character t- His conclusion would 

 be true provided each loop P' Q' (fig. 5) were indefinitely nar- 

 row and entirely unconnected with the contiguous portions of 

 the mass, forming an independent physical line of very small 

 section. In such case the whole tension would act in the di- 

 rection of the line at each point. 



2. Nor if the Professor's reasoning were correct, should we 

 be able to account for the fact of the convexity of the trans- 

 verse curves of fracture being turned towards the upper end 

 of the glacier; or, which is equivalent, for the fact that the 

 inclination of the transverse fissures to the axis of the glacier 

 is less at points near the sides than near the centre, where it 

 approximates to a right angle, except in the cases of diver- 

 gent glaciers. This fact, with the exception of those places 

 where there are local disturbing causes, is perhaps as well esta- 

 blished as that of glacial motion itself. The inadequacy of 

 the Professor's reasoning to explain it will appear at once by 

 the annexed diagram, in which two loops only are represented. 

 It is manifest that any curve line, as M N, which meets any 

 number of such loops, must have its convexity turned towards 



* The extensibility is here supposed to be measured by the extension 

 which glacial ice would bear without fracture, in a comparatively short 

 time (art. 27, Second Letter) . 



f In my first memoir I was guilty of the same omission, before I attempt- 

 ed any accurate analysis of the problem. The fact is, that the exact in- 

 fluence of the forces in question is extremely difficult to detect by means 

 of mere general and popular reasoning, though very clear and certain when 

 seen as the interpretation of a mathematical analysis of the problem. 



