Mr. Hopkins on the Mechanism of Glacial Motion. 157 



X= (R)cos2 5+ (^Osin^a 



But by equation (1.) 



Xj — Y, 



cos 2 9 = 



tljerefore 



X = Xi, 



as it ought to be. Similarly, 



/= {(R)-(r)}sinficos5 



= Y^(Xi-Y,)2 + 4.y;^sin2 5 



=/. 



by substitution from equation (1.). 



14?. It should here be borne in mind that, in the preceding 

 investigations, the internal tensions are supposed to be insuffi- 

 cient to break the continuity of the mass, and that, conse- 

 quently, our results are independent of the law according to 

 which the cohesion may vary from one point to another, the 

 consideration of which only becomes necessary when we have 

 to determine the directions of fracture. It is also important 

 to remark that the preceding results are independent of the 

 degree of relative displacements of different elements of the 

 mass, the continuity remaining unbroken ; it is not necessary 

 that the displacements should be small. Again, it should be 

 observed, that, to render these results absolutely accurate, 

 we must suppose the line j) s (fig. 2) of infinitesimal mag- 

 nitude, but still containing a great number of molecules form- 

 ing so many points of action on each side of this lifie of sepa- 

 ration. This hypothesis would not be strictly applicable in 

 the extreme limit, to a mass of which the perfect continuity 

 should be interrupted by innumerable ipores of sensible mag- 

 nitude, in every part. Ifj however, ip s be of finite length, so 

 as to contain a great many points of contact, there will be no 

 sensible error in our results as applied to a mass constituted 

 as just mentioned, provided the resultant of the actions at the 

 points of contact pass through a point oi'p s not deviating sen- 

 sibly from its middle point. Thus if ^ s should be conceived 

 to be several inches, or even several feet in length, our results 



