158 Mr. Hopkins on the Mechanism of Glacial Motion. 



would be sensibly correct as applied to a mass of the enormous 

 extent of a glacier, or of any considerable continuous portion 

 of it. 



15. Some of the preceding results may be still further elu- 

 cidated. If Xj = and Y, = 0, the only force acting on an 

 element of the mass will be /!, and it has been shown (arts. 6. 

 and 9.) that 9 will then =45 . Let^grs be an element ori- 

 ginally square. As al- Yia. 4. 



ready explained, it will 



be acted on by two ^^^j^' 



couples of forces^/, as 



represented in the • ^^^ k^ 



figure. It is seen at ^ '^''^ '^^ 



once, that the greatest 



tension produced by 



these forces must be in ^ 



a direction parallel to ^ 



the diagonal r q, or .''' 



supposing the devia- 



tion from rectangu- "^ 



larity very small (for the reason assigned in the note, art. 9), 



in a direction making an angle of 45° with p q, as before 



proved. Also, it is easily seen that there will be compression 



in the direction perpendicular to r q, and likewise that the 



compression must be greater in that direction than any other. 



The maximum tension (R) and the maximum pressure — (r) 



may be easily expressed; for the whole tangential force on pq 



=J'i,pqi its resolved part parallel to rg' =y).j9 5'.cos45'^. 



Similarly, the resolved part of the force on qs=jf^ .qs. cos 45°. 



Therefore 



(R)p q . sin 45° —frV^* ^os 45°, 



or (R) =/, 



Similarly, we obtain — if) =yj. 



These same values would be obtained from equations (3.) 



(art. 10.), putting Xj = and Yj = 0. 



16. We thus see also how the two forces (R) and {r) pro- 

 duce the same effect on the element pqrs^ in distorting it 

 from its original rectangular form, as the tangential forces J\. 

 If, however, we should take a rectangular element whose sides 

 were perpendicular respectively to the forces (R) and (r), it is 

 manifest that no distortion would be produced in it by (R) 

 and (r). In fact the tangential forces on such an element 

 would = 0. And in all cases, if we take a rectangular ele- 

 ment of the mass in its original state of no constraint, such 

 that the sides of that element shall be perpendicular to the di- 



