708 
ME. HOPKINS ON THE THEOET OE THE MOTION OE GLACIEES. 
30. Formation of Longitudinal Crevasses. — Transverse crevasses, as above stated, 
are almost invariably formed in valleys the sides of which are approximately parallel ; 
longitudinal crevasses are as generally formed in valleys in which the sides are divergent, 
and usually perhaps when they become rather suddenly so. They are found almost 
exclusively at the lower ends of glaciers. The Ehone glacier affords the best-known 
example of crevasses of this kind, but M. Agassiz refers to a number of other cases, the 
greater part of which, however, appertain to small glaciers*. At the foot of the great 
ice-fall of the Rhone glacier, the valley expands largely, as is well known, and its incli- 
nation to the horizon becomes comparatively small. Thus the ice, accumulating at the 
bottom of the fall, exerts an enormous pressure a tergo on the ice immediately before it, 
and this pressure is propagated onwards in directions which radiate from the bottom of 
the fall. It is manifest that the force along each radiating line will be a great pressui’e. 
Again, if we conceive the whole mass divided into concentric rings perpendicular at 
each point to the above-mentioned radiating lines, the pressure along these lines will 
extend the ring, and produce in it a great tension at every point, perpendicular to the 
dii’ection of the radial pressure above mentioned. Hence if we take any one of these 
radiating lines as the axis of x, the radial pressure at any point upon it will be denoted by 
— A, and the tension upon it in the direction perpendicular to the axis of x, will be B. 
The former will be a principal pressure, and the latter a principal tension ; and if 
crevasses be formed at all, they must be in directions perpendicular to that of B ; i. e. 
they must be radial, as they are always observed to be. The glacier of the Rhone is 
only a type, as regards longitudinal crevasses, of all other glaciers in which they exist. 
31. An explanation of the phenomena of transverse crevasses, essentially the same as 
that above given, though founded on a more restricted mechanical and mathematical 
analysis of the general problem, was given by me some seventeen years ago. I am not 
aware that any doubt was entertained as to its validity, but I am also not aware of 
any glacialist having recognized it previously to Dr. Tyndall. M. Agassiz has given an 
explanation f both of the transverse and longitudinal crevasses, involving apparently 
the notion of the oblique tension which, I have proved, must necessarily exist in a 
determinate direction. The mechanical reasoning employed, however, is too vague to 
constitute a mechanical explanation of the phenomena. Moreover his work was 
published in 1847, three or four years after my memoir containing the preceding explana- 
tion was printed in the Transactions of the Cambridge Philosophical Society. Principal 
Foebes, also, speaks of a drag from the sides towards the centre of a glacier J, but mth 
the view apparently, not of explaining the formation of transverse crevasses, but of 
the veins in cases of the veined structure. His “ lines of greatest strain” must therefore, 
I conceive, mean the same lines mechanically, not as my lines of greatest normal 
tension, to which the crevasses are unquestionably due, but my lines of greatest tangential 
action. If he supposed these two directSns to be identical, it was a manifest error ; for 
* Systeme Glaciaire, p. 324. f Ibid. p. 320 et seq. 
X Occasional Papers, p. 57 ; also last chapter of his ‘ Travels.’ 
