.58 Mr. HOPKINS, ON THE MOTION OF GLACIERS. 



and when, during this motion, it has passed forward a certain distance, a succeeding one originates 

 at the same point, moves forward in the same manner, and ultimately disappears at the same 

 point as those which have preceded it. . ,. , ^ , . , 



If the sides of the containing valley be divergent, the longitudinal fissures predominate, and 

 diverge from the axis of the glacier in a manner accordant with the divergency of the sides. 



8. The continued convexity of a crevasse turned towards the upper extremity for a great 

 leno-th of time would manifestly be inconsistent with the fact already stated, that the central 

 pardon of a glacier moves considerably faster than its sides ; for such relative motion must have 

 the effect of continually lessening and ultimately destroying the convexity. Let us examine^how long 

 a time it might require to produce this efTect. 



Let PA'' be a transverse fissure when first formed in a gla- 

 cier, of which NO is the axis. We may, for an approxima- 

 tion, suppose PN^ to be the arc of a circle whose center is 

 O . Since N will move faster than P, the position and form 

 of the fissure' wiU change, but, as the change will depend only 

 on the relative motions of different points of the PN ^, we may 

 here suppose P to remain at rest, and the other points of the 

 fissure to move only with their relative motion. It will be suf- 

 ficiently near for our purpose if we suppose this motion such 

 that the fissure shall always retain the form of the arc of a 

 circle. Suppose it to come into the position PN after a time 

 t, and let O then be its center of curvature. We may first 

 examine what change of curvature will take place in the fissure in 

 the time t, the curvature being measured by the angle PON. 



Let PON = e, PON^ = e, , and PO = r, PO^ = r, ; and 

 let V be the relative velocity of JV. Then 

 NN = vt, 

 and r vers. 9 = r, vers. 9^ - vt (l)- 



Also, if 6 = sin of the arc PN, , 



r sin = b, 



Hence (l) becomes 



lid r sin 9, = b. 



vers. 9 vers. 9, v 



sin 9 sin 9, b 



9 0, V 



tan - = tan — — - t, 



2 2 6 



which gives the curvature at the time t. 



If e, and, therefore, 9 be not too large, we shall have approximately 



iiv 



Q = e-—t; 







or if 9 and 0, be expressed in degrees, 



^„ /180 2« Y 



