ME. HOPKINS ON THE THEOET OF THE MOTION OF OLACIEES. 
707 
that direct longitudinal tension which might, at first sight, appear necessary to produce 
them. 
(2) If there be a considerable longitudinal tension, but no appreciable transverse 
pressure, we have 
i',=i{A+yA“+4F’}, 
F 
tan 2a=^- 
Hence ^ 1 , the maximum tension, will be increased, and therefore, also, the tendency to 
form a crevasse. Likewise the greatest value of a will be less than 45°, and the direc- 
tion of the crevasse, as we might expect, will be more nearly perpendicular to the axis 
of the glacier. 
(3) Many glacial valleys become narrower as we descend them, and consequently the 
mass of the glacier may enter each part of the valley as a wedge, and may frequently 
become more or less compressed. In such case B will be negative, and may become 
very large. We shall then have 
— B+\/ (A + B)^ + 4F^}, 
;),=i{A-B-x/(A+Bf+4F}, 
In this instance, as well as in the preceding one, will necessarily be a tension, and 
greatest (A and B being constant) where F is greatest, i. e. in the marginal portions of 
the glacier. For the like reason, a will also be greatest in those portions. It will vanish 
at the axis, where F vanishes. Hence, if the forces be sufficient to overcome the cohe- 
sion of the mass, a curvilinear crevasse may be formed extending across the glacier and 
meeting its axis at a right angle. This, however, is rarely the case, the transverse 
crevasses being formed, in general, in the lateral portions only of canal-shaped glaciers, 
where they will approximate more or less to straight lines. They are most likely to 
be formed where A is a considerable tension, which is less likely to be the case in 
converging valleys. 
It is important to observe that in all cases in which the expression for tan 2a is posi- 
tive, e. where B is algebraically less than A, a must lie between 0 and 45°, and con- 
sequently the inclination of a curved crevasse to a transverse line perpendicular to the 
axis must likewise always lie between the same limits. This rule is applicable, according 
to this theory, wherever transverse crevasses are likely to be formed*. 
* An open curvilinear fissure in its “progressive formation would be in some degree influenced bj other 
causes than the maximum tension at each point through which it might pass. Moreover, the cohesive 
power has been above supposed to be the same in every direction from any proposed point. There may, on 
the contrary, be planes of less cohesion, in which case if the cohesion along any such plane bear a smaller 
ratio to the internal tension perpendicular to it, than the cohesion perpendicular to the maximum tension 
bears to p^ the crevasse may be formed along the plane of least cohesion. I know no reason, however, to 
suppose that these causes are sufficient to modify in any essential degree the law enunciated in the text. 
