ME. HOPKINS ON THE THEOET OF THE MOTION OF GLACIEES. 
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before, and let a b, dV be two lines of marginal structure, representing the two systems 
of lines to which they respectively belong. A particle in the tributary glacier will move 
parallel to the side of the glacier till it arrives, for instance, at h, a point near the section 
O A, and will afterwards move parallel to the axis O X. When the particle at a arrives 
at O, suppose the particle which was simultaneously at h to have arrived a,t c, be being 
parallel to O X ; then will O c be the position in the united glacier of the physical line 
of structure which before occupied the position a b. But the velocity with which a par- 
ticle will move from 5 to c in the central part of the united glacier, will be considerably 
greater than that with which a particle will move from a to O along the side of the 
tributary. Consequently the distance b c will be considerably greater than a b, and O c 
will make a proportionately smaller angle with O X than a b makes with the side a O 
of the tributary. Hence, if the lines of marginal structure approximate to parallelism 
to the sides in the tributary, the same lines, forming those of the longitudinal structure 
in the central portion of the united glacier, will approximate still nearer to parallelism 
with each other and with O X. Subsequently this approximation to parallelism will 
decrease, since a particle will move rather faster along O X than along b c ; but assuming 
always that the divergency is small in the marginal structure of the tributary, a simple 
calculation shows that it will not become considerable in the united glacier except at 
distances from the junction equal to many multiples of the whole breadth of the 
glacier*. Such, at least, would be the case with the glacier of the Aar. If, on the 
contrary, the lines of marginal structure in the tributaries should make a considerable 
angle with the sides of the glacier, they would also make a considerable, though 
smaller angle with the axis of the united glacier, and their inclination to that axis 
would afterwards increase more rapidly. 
Taking the opposite flank of the glacier, suppose two particles on the same line of 
structure to be simultaneously at d and b'’, and reasoning as before, suppose b' to have 
moved parallel to the side of the united glacier to d while d moves to A. Then will 
A d be the resulting position of the same line of structure as previously occupied the 
position d V. In this case, however, V d will be nearly equal to d A, since the velocities 
along the margins of the combined glacier and the tributaries will probably be much 
the same. Hence the directions of the marginal lines of structure with reference to 
the sides of the valleys, will be less changed than those of the longitudinal structure 
with reference to the axis O X. 
I have above supposed the absence of any transverse lines of structure on the central 
portion of the tributary glaciers. If, however, they exist so as to complete the loops of 
the curves (mm!) (flg. 17), they will of course also exist, by the transmission we are here 
assuming, in the combined glacier, in the forms of similar loops, as represented in the 
figure. 
58. If we compare the forms of the marginal structural curves in a canal-shaped 
glacier (represented in fig. 7, art. 42), resulting from the immediate action of the forces 
* This calculation is founded on data supplied by M. Agassiz in bis ‘ Systeme Glaciaire,’ p. 451. 
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