Mr. Hopkins on the Mechanism of Glacial Motion. 159 



rections of maximum and minimum tension, when the mass is 

 brought into its state of internal constraint, then will the ele- 

 ment still retain its rectangular form, its linear dimensions 

 only being changed. Other elements about the same point 

 will be more or less distorted from rectangularity, according 

 to their angular positions. 



1 7. These results may be well exhibited geometrically by 

 an extension of the diagram, fig. 1 . Take M N' at right 



Fig. 5. 



angles to M N, and complete the parallelogram N N ; take 

 N' 7i' = L ^ = N n and complete the parallelogram 7i n' . Then, 

 while the physical points at L, N and N' move respectively to 

 /, n and ?«', that at L' will move to /', since L'/' = 2 L/, and 

 the relative velocity at L' = twice that at L. Now if lines be 

 drawn bisecting the angles NMn and N'Mn', and these lines 

 make angles of 45° with /V<7', it is easily seen that N'M?i' 

 must =NM?z. Consequently, the parallelogram ML' being 

 rectangular, M«'/'« will be so likewise, and will therefore be 

 an element of no distortion. If N n be indefinitely small, 

 Mn and M w' will make angles of 45^ with the direction of 

 motion, and will therefore coincide with the directions of maxi- 

 mum and minimum tension (art. 5.). 



We also thus arrive at the conclusion that M ?z and Mw' 

 are directions in which there is no tangential force ; for if 

 there were any such forces acting on the element M w'Z'w, it 

 could not retain its rectangularity. All these deductions, by 

 different methods, are in perfect harmony with each other. 



If we assume, as the result of our previous investigations, 

 that the directions of maximum and minimum tension are co- 

 incident with the lines of no tangential action, the geometrical 

 construction given above will serve to determine those direc- 

 tions when the relative motion N n is not small. 



