706 
ME. HOPKINS ON THE THEOET OF THE MOTION OF GLACIEES. 
pressure and_p2- It may be convenient to consider F an absolute positive quantity; 
and we may suppose, for such a glacier as that represented in fig. 2, that B=:0. In such 
case the preceding formula shows that one of the values (as aj of a must be small and 
positive when F is small, i. e. for any point P (fig. 2) near the axis Kx. Now the 
maximum tension at P must be due to the tension A parallel to A x, and that produced 
by the angular distortion of the element V qr s. The magnitude and direction of this 
latter tension are obtained by putting A=0 and B = 0 in the above formulae. This 
gives the greatest tension =:F, the least = — F, and tan2a=oo , or therefore a=45° or 
135°. From the inspection of the element, it is manifest that the first of these values of 
a corresponds to the greatest tension produced by the angular distortion. It is from 
this tension and A thaty), in the actual case of a glacier before us, must result. Con- 
sequently must act in some such direction as P ^ (fig. 2), where a in that figure is 
acute. The same result will hold if B be of finite magnitude, and algebraically less than 
A ; and thus and are distinguished from each other in the case before us, and by 
similar reasoning may be distinguished in any other case. 
29. Formation of Transverse Crevasses . — When the maximum normal tension is the 
force to which the cohesive power of a glacial mass first gives way, the result, as above 
observed, must be an open fissure, or crevasse, the direction of which must manifestly 
be perpendicular to that of the tension producing it. These crevasses approximate more 
or less to right angles with the glacial axis, and usually characterize canal-shaped valleys 
in which the sides are approximately parallel. In such cases B must be comparatively 
small ; if the valley be slightly convergent, it will be a small pressure, and therefore 
negative. When these crevasses exist more abundantly, A will doubtless be a large 
tension, though not necessarily so, as we shall see, for the production of a crevasse. 
(I) Taking the simplest case, let us first suppose A=0 and B=0. This may be very 
approximately true if the glacier descend without acceleration or retardation along a 
trough-like valley of uniform width and uniform inclination. We shall then have by 
the above equations, y)j = F, ^^3=— F, and tan2a= 00. Hence the direction of maxi- 
mum tension will make an angle ce=45° with the axis of the glacier [Kx) (fig. 2) towards 
which it will converge in descending. If, therefore, a fissure be formed at all, which can 
only be in the marginal regions where F is considerable, it must be in a du’ection per- 
pendicular to P and making an angle of 45° with the axis of the glacier. We have 
also for the maximum tangential action (art. 21), 
T2=KPi— P2) = F, 
equal, in this case, to and making an angle of 45° with the directions of^i andyja- I^ 
will therefore be parallel to the axes of x and y. Hence the maximum normal and tangen- 
tial forces make equal efibrts, in this case, to dislocate the mass. Let the tangential 
cohesive power of the mass be Fj ; the greatest value which can assume will then be 
also Fi ; and if the normal cohesive power (PJ be less than F,, the tension may 
assume a value (F) between Pj and Fj, by which a crevasse will be formed in the posi- 
tion above mentioned. Transverse crevasses may therefore be formed without any of 
