ME. HOPKINS ON THE THEOEY OF THE MOTION OF GLACIEES. 
741 
nearly =Fi. Consequently Fj will he much more likely to attain the magnitude F, su^- 
cient to dislocate the mass, if the glacier slide over its hed as described in art. 8, than if it 
were attached to its bed so as not to slide at all, and its whole motion should be that due 
to the molecular mobility of its particles alone. 
The above equation expresses the condition of the mass being on the point of disloca- 
tion in terms invohlng the tangential cohesion ; it will be easy to express it in terms of 
the normal cohesion. Generally, instead of the forces A, B, F acting on any element, we 
may substitute the forces (art. 29), acting in their proper directions as determined 
by the values of a. Let fig. 19 represent one side of the glacier with the lateral 
plane B E ; then, since at any point (R) Fig. 19 . 
in that plane = F„ p^— — F„ and ^ 
tan 2a = oo, we may substitute for Fj 
acting tangentially along E B, two other B S 
forces, viz. a tension =F, along R M, and 
a pressure = Fj along N R, both directions 
making angles of 45° with B R. Conse- 
quently an equal tension and pressure similarly applied at each point of the lateral 
vertical planes, would by hypothesis balance the tendency of the mass to descend in the 
du’ection B R. Now F, acting at an angle 5 on B R Avill produce a force =F, cos 5 on a 
unit of surface of B R. Therefore the tension Fj acting along R M will produce a force 
on the same unit, of which the resolved part along R B will 
=Fi cos 45°. cos 45°, 
~ 2 ■ 
Similarly, the pressure F, along N R will produce a force the resolved part of which along 
F 
R B will also = y. These together =F„ and the whole supporting force on the two 
lateral vertical planes will =2'F^ac, Fj being now the measure of a pressure or a tension 
acting normally on a unit of surface. Therefore 
and 
2Fi«c=iy(z5c sin t, 
- Sin/. 
Consequently a glacier like that we have been considering, will necessarily be dislocated 
by its own weight resolved along the plane of its bed, if its normal cohesive power be 
less than the weight of a column of glacial ice whose transverse section is unity, and 
whose length = semiwidth of the glacier multiplied by the sine of the inclination of 
its bed to the horizon. If the glacier were a mile wide and its inclination about 5°, it 
would be necessary, in order that it should not be dislocated, that its cohesive power 
should be such that a vertical cylindrical column of glacial ice about 200 feet long 
should be capable of supporting itself when suspended by its upper extremity. This 
would be the measure of the greatest tension j?,(=F,) at any point along either of the 
MDCCCLXII. 5 I 
