﻿the Descent of Glaciers by their Weight only. 365 



_ Usint— (U 4 + U 5 )/cost . . 



*' u 1 + u 9 +u, {l) 



PQ=BC+^(AD-BC)=/3+-(^-a) = ^ + " 7(a ~^ ) - 

 BA V ' a x ' a 



Let the motion of the bottom of the glacier in the centre be 

 supposed to bear the same proportion to the motion at the top 

 in the centre that that of the bottom of the sides does to the top 



at the sides. Or let -;-=■ = ^r^ : whence ad= ~ '> 

 AD BC ' /3 



,'. M = h c+ f a {ad-bc)=y + f @ -y)=g [«/S + ,(«-/3)] ; 

 ... TQ- M - ^±-&=^> _ j [^+.(.-«j 



~V 8/ a ' 





mn=pq+ p- (PQ-^)= £ [«r/3 +a?(a— /3)] 



+ bV 0/ a 



ab(3 



Weight of prism' m n — w. mn dx dy. 



Work of the weights of the particles descending m n while m 

 descends from m to n = weight of prism x | mn sin i ; 



2 



,*. ^U sin t—\wmn dxdys'mi; (2') 



_ wab {u 3 -/ 3 3 ) {l3 3 -v 3) 

 U ~ 18/3 2 («-/3)(/3- r ) ' 



U = ^(« 2 + ^ + /3 2 )(^ + /37 + 7 2 ). ... (2) 



