"demolition" of Moseley's theory of glacial motion?

What initially drew my attention to Moseley’s work was a contemporary report by Doug Benn (11) of a short communication by Wallace (12) in 1871 to the Philosophical Magazine. Wallace was one of a fairly impressive range of critics advocating views that seem to have resulted in Moseley’s work on glacial motion now being less widely known and acknowledged than it would appear to deserve. After considerable criticism over the proceeding 2 years Wallace might have felt justified in his pronouncement that Moseley’s theory of contraction and expansion, then referred to as the “crawling theory”, had been “completely demolished”. The person said to have wielded the final blow of the demolition hammer, and this is what really caught my eye, was none other than James Croll (13). However, on careful reading of the contributions of Mathews (14), Ball (15), Wallace (12) and particularly Croll (13, 16) it is, in my view, very far from clear that an effective hatchet job had been delivered on the important contributions of Henry Moseley. A full account of all the deliberations leading up to the exchanges at the end of the 1860’s would require more space than is currently available. So here are just a few remarks relating to what appear to have been some of the most damaging of the criticisms together with Moseley’s and some of my own assessments of the validity of these criticisms.


Did Croll’s Comments Constitute a Demolition? Let me start from what appears to have been the last substantive comment on Moseley’s work. Wallace (12) claims that Croll (13, 16) demolished Moseley’s theory that the thermal energy causing expansion and contraction might be somehow responsible for providing the apparently missing force driving glacial motion. How he arrived at this conclusion is however baffling. To a very large extent Croll had concurred with Moseley’s conclusions that gravity acting alone could not conceivably be the sole agent causing the motion of glaciers. He also accepted that Moseley had demonstrated conclusively that a causal relationship exists between the incoming solar energy and the rate of motion experienced by glaciers. By arguing quite logically that the level of solar energy being transmitted could hardly be the result of glacial motions, Croll also concurred with Moseley that the motion of glaciers must therefore be the effect and the solar energy the cause in this relationship of dependence. The only substantive issue between Croll and Moseley would appear to be Croll’s insistence that the solar energy changed the material properties in a way that allowed the layers of ice within the body of the glacier to more easily slide one upon the other. In other words the heat increased the tendency for what we would now regard as visco-plastic flow. Croll’s arguments were ingenious but seemingly incorrect. He envisaged a process whereby the solar energy entering one molecule would be enough to break its bonds with its neighbouring molecules, allowing it to move relative to them, and in the process transfer the heat energy to these neighbouring molecules. These neighbouring molecules would in their turn do the same to their neighbours etc allowing a shear type failure to be propagated across the ice with such small mechanical force required that gravity alone would be enough. His notion of the molecules being able to move back and forth from the solid to liquid phase was founded upon the erroneous view that glacial ice remained fixed at freezing point (32oF). Like Ball, who argued that “no cause has been suggested that can tend sensibly to lower the temperature of the interior (of the glacier) below (32oF)” (15), Croll also seemed to believe there to be “nothing to lower the ice below freezing point; and as the sun’s rays do not raise the temperature of the ice above freezing point, the temperature must therefore remain unaltered” (13). In this he was quite wrong, as he was in his understanding that “heat entering the ice could not produce a mechanical pressure that would move the glacier; for heat produces contraction in volume not expansion” (13). This erroneous notion was seemingly based upon the observation that when subject to heat solid ice will occupy a smaller volume upon undergoing a phase change to form water.

Why Wallace considered Croll’s molecular explanation to provide a demolition of Moseley's views is therefore less than convincing. That he believed Croll to demolish Moseley’s views becomes even harder to understand when Wallace himself then goes on to point out the major fallacy in Croll's own explanation of the role solar energy might be playing in changing the material properties of the ice, the only real point of disagreement Croll had with Moseley. “If heat entering the glacier loosens the molecules in its passage and enables them to move insensibly into new positions, it is difficult to understand”, argues Wallace, “what causes the numerous longitudinal and transverse fissures of a glacier, the production of which is often attended by loud reports, and which indicate movement of masses, not molecules.” And Wallace quite correctly asks “how could molecular motion lead to that heavy grinding of the ice over its bed, which scores and wears down the hardest rocks, and whitens great rivers with its finely triturated mud?” If Wallace considers Croll’s explanation to be fallacious it is difficult to comprehend how he can then claim that it “demolishes (Moseley’s) theory”?

In any case Wallace’s ground for dismissing Croll’s explanation is a few paragraphs later itself contradicted by his support for the importance of the results from the ice beam bending tests conducted by Mathews and Osler (14). Mathews’s tests were supposed to show that the ice of the glacier moved in much the same way as an “imperfect fluid” – the term used for what we would now regard as viscous flow. Such a flow model advocated by Mathews and supported by many others such as Forbes (7), Ball (15) and Wallace (12), would itself be inconsistent with the violent tension tearing associated with the sudden rendering apart of ice masses to form fissures and crevices. If the small gravity forces are able to generate a viscous flow it remains difficult to really explain the very different orders of magnitude of force that would be needed to result in the “heavy grinding” action cited as making Croll’s theory untenable? But in any case it is far from clear that the results from the simple beam test reported by Mathews were really contrary to those used in support of the theory espoused by Moseley.

Did the Mathews Bending Tests Provide a Challenge? One of the central features of the arguments used by Moseley to support his thesis that gravity acting alone is not capable of explaining why glaciers move down gentle slopes, was the shearing capacity of ice. His experiments had shown that typical compacted ice samples failed in shear at stresses of around 75 lb/in2. These tests were conducted in air at temperatures well above freezing point. In a later communication (18) Moseley points out that the shear capacities at temperatures below zero are considerably higher. That the figure of 75 lb/in2 exceeded by a factor of 30 to 40 (in fact on the basis of the figures quoted this should have been 55 as used in his later contribution (18)) the average shear generated within a typical glacier by gravity acting alone, and hence exceeded by a factor of 30 to 40 the supposed shear stress required to cause the glacier to undergoing a shear flow failure, was a central part of the argument supporting Moseley's claim that glaciers would not move as a result of gravity alone. Mathews’s experiments on ice planks were supposed by many to disprove this central tenant of Moseley’s argument. But did they?

It is true that the shear stresses involved in Mathews’s tests were well below the levels of 75 lb/in2. And yet the beams tested displayed a tendency for major strains to develop, the greater parts of which were dependent on time. But to claim that this proves that ice undergoes visco-plastic, creep, straining at low shear stresses was even at the time somewhat perverse. The ice planks tested in bending under their own weight had span-to-depth ratios of between 30 and 40. At these levels of slenderness the components of vertical deformation resulting from shear action would be negligible; for such a slender beam almost the entire vertical deformation results from bending action and depends upon the magnitudes of the direct tension and compression stresses being generated on respectively the bottom and top fibres of the beam. Quick calculations suggest that these direct tensions and compressions would in Mathews’s experimental samples have been between 60 and 90 lb/in2; these would have been easily enough to cause tensile fracture of the ice and/or extensive creep deformation. And of course this is what Mathews observed. He makes it quite clear that on “the under surface of the plank near the point of flexure, (which is presumably the middle section of the beam) I noticed a number of very minute fissures extending a short distance into the ice”. He went on to claim that these fissures “were certainly not sufficient to account for the flexure of the plank”. On what basis he makes this claim is not clear. At direct flexural stress levels of these magnitudes it is remarkable that the beams did not suffer violent tensile fractures. That they did not would suggest strength levels for the ice at least as great as those found by Moseley. It seems highly improbable that these tests could in any way disprove the central tenant of Moseley’s theory in support of the impossibility of gravity alone propelling ice down typical alpine glaciers. The tests would certainly not support the inference that at very low shear stresses “a mass of ice may change its form under strains produced by the gravitation of its particles, without becoming fractured, and without returning to its original form when the strain ceases” (14). Moseley was aware of the shortcomings of the Mathews tests. As he remarked (18) “Mr Mathews’s experiment would … require to be greatly varied to bring it into analogy with the case of a glacier. If a glacier is supposed to descend by bending, the bending must be supposed to be in the plane of its surface or in the direction parallel to that plane, and not perpendicular to it, as it was in the case of the ice plank. To make his experiment apply to the case of the glacier, Mr Mathews should have placed his plank on the two bearers not flatwise, but edgewise. Indeed, looking at the proportion of the length to the width of a glacier, and considering that it is in the direction of its length that the bend must take place if it descends by bending, the plank ought rather to have been placed vertically on one of its ends”. He might have added that the length of the plank so orientated, in order to preserve the appropriate dimensional similitude, should have been the breadth of the Mathews’s test plank times the ratio of the glacier length to its width! On this basis the beam would no longer be acting in flexure. It would be deforming almost in pure shear, which, under the action of its small down-slope component, would be practically imperceptible. And this is of course the point Moseley was making.

Before leaving the subject of Mathews’s tests it is worth commenting upon another seemingly erroneous interpretation of them used to undermine the arguments of Moseley. Mathews observes that the deformed shapes of the ice beams were similar to the transverse shapes of the surface ice flow on glaciers (14). He conceded, almost in line with Moseley’s suggestion, the validity of an experiment in which the planks might be placed with their longer cross-section dimensions parallel to the flow of the glacier. While he recognised the need to allow for a greatly reduced gravitational component in this orientation he did not it seems make any allowance for the considerably increased flexural stiffness and strength that would result from this orientation. Even for the thicker of his two test beams the flexural stiffness would be more than 6 times as great as when oriented with the shorter side parallel to the loading. Making allowance for the reduction by approximately 12 in the down-slope gravity force that would be acting and it becomes clear that the shear stresses would be lower by a factor of 12 compared with those in his reported tests. But more significant given their role in the behaviour in Mathews’s tests, the flexural stresses would be reduced by a factor of nearly 30 and the flexural deformations by roughly 75. And this is with a beam having a span to depth ratio 12. For a glacier of width, say, 360 ft this would correspond with a strip between adjacent lateral crevices of just 30 ft. Over most sections of a glacier the spacings between substantial lateral fissures are observed to be very much greater than this, and even if they were so closely spaced the stresses and their accompanying deformations would be most unlikely to account for the observed flow of glacier ice.

Neglect of Failure Zone Localisation: Another common criticism levelled at Moseley’s idealised model of glacial motion was that he assumed the whole “bulk or weight of the glacier, or any portion of it to which the formula of the shearing force may be applied, (would involve) the whole mass shear(ing) at once by the action of gravity on the same mass” (12). Wallace argued that this “does not recognise the possibility of one portion of the glacier acting by its own weight to shear another and much smaller portion”. He opined that this must surely occur as a result of the “irregularity of the bed in which every glacier moves”. With evident logic he added that this would result in the ice “mass (being) everywhere in varying states of tension and compression”. This would mean that at “at any moment, therefore, the whole descending weight of a portion of the glacier containing perhaps thousands of cubic yards of ice, may act so as to cause the shearing of a few superficial feet where the tension is greatest.” Moseley had to some extent already countered (8) this argument with a simple example of a strip of glacial ice 1 in squared in cross-section and a mile in length being supported at its lower end on just three sides of the strip over a length of just 1 inch. He points out that the down-slope force of this 1 mile strip is 194.42 lb., when the slope is 4o 52’. If resisted by shear on just the 3 sides of the cubical inch this would exert a “resistance of 3x75 lbs., or 225 lbs. That resistance stops therefore the descent of this strip of ice, one mile long, having no other resistance than this opposed to its descent, by reason of its detachment from the rest. It is clear, then, that it could not have descended by its weight only when it adhered to the rest, and when its descent was opposed by the shear of its whole length”.

While this example is informative, it does not entirely address the issue raised by Wallace. When the ice is being resisted locally by some bedrock protrusion the force being delivered would need to take account of the depth of the glacier over the 1 mile length, assuming that is, a vertical crevice has formed downstream of the point at which the blockage has occurred. Under these circumstances it is conceivable, although unlikely, that the 1 mile section of unsupported ice could be delivering a force sufficient to produce the local fracture needed to unlock the movement. A point that none of the protagonists of the debates in the mid-18th C appear to have made is the following; although had he lived a little longer one suspects that Moseley would soon have done so. Imagine another experiment with a strip of ice 1 m in width but in a glacier having thickness t (m). The force to be resisted by a protruding obstruction on the glacier floor if it were required to resist the entire down-slope component of weight of a length of glacier equal to L (m), having the same slope as that considered by Moseley, would be 0.9 x t x L (kN). A closely related example was presented in Reference (4). If it is assumed that vertical sections of the glacier ice remain vertical during the deformation, then for just a 1oC increase in average temperature within a glacier having ice with a coefficient of thermal expansion 90 x 10-6 / oC and an elastic modulus of 10 x 10+6 kN/m2 would even over a short length of glacier exert a force of 900 x t kN on this same protrusion. That is, an unsupported length of glacier equal to 1000m would be required for gravity to deliver the same level of fracturing force onto a recalcitrant piece of protruding rock. It would seem to follow that if gravity acting alone is capable of causing failures in such circumstances then realistically small changes in average temperature, making due allowance for the thermal gradients through the thickness of the ice, would be even more likely to do so. Alternations in temperature could in such circumstances easily explain the occurrence of tensile cracking and compressive crushing action.

Basal Slippage or Material Deformation: Moseley had in his critique of current theories based upon the forces of gravity been strongly influenced by the observations of Tyndall (10) on the Mer de Glace. These showed that just a small proportion of the movement was due to the shear failure between the base of the glacier and the underlying rock. In his analysis Moseley (8,9) made allowance for the shear distortions within the body of the ice which accounted for the major part of the flow. For this he was criticised by Wallace who pointed out that in these analyses he “has neglected … the capability of ice when in a state of deliquescence to slide along a surface of small inclination, as demonstrated by the well-known experiment of William Hopkins.” Ball (15) reinforced this point by suggesting that “observation abundantly proves that the resistance offered by the bed of great glaciers to the sliding of the lower surface is very much less than even the smallest amount of shear force derived from (Moseley’s) several discordant observations”. We now know, of course, that the proportion of the motion that can be attributed to basal sliding as opposed to the material shearing of the body of the ice depends critically upon the nature and particularly the temperature of the glacier bed. Even at the time when knowledge of what happens at glacier beds was much more limited, Moseley replied, very reasonably, that among the resistances gravity would have to overcome “I reckon those of the sides and bottom of the channel to be as great as though the ice were frozen to them; and considering what are the obstacles in the actual channel from projecting rocks, bends in its direction, and frequent contractions, the assumption of a resistance at least equal to that which would result in the imaginary form of the glacier from the ice being frozen to its bottom and sides, is not perhaps unreasonable.” He continues a little later by noting that “the differential motion is in point of fact, by far the greater part of the motion of the glacier - thirteen fourteenths of it on the Aar Glacier, according to Professor Forbes (19); so that the resistance to the differential motion, measured by its work, is by far the greatest resistance.” Moseley reports (p148-149 (18)) confirmation from his own experiments that under the appropriate conditions a block of ice may “descend on an inclined plane by its weight alone – and therefore not to be mechanically impossible that a glacier should descend by its weight alone, if it descended as the block of ice did in (Hopkin’s) experiment. But it does not. There is an essential difference; and precisely in this difference lies the impossibility of the glacier descending by its own weight alone.” Moseley then goes on to reiterate that “the block of ice descended bodily; its parts did not move one over the another or alongside one another, but with a common motion of descent; whereas not less than thirteen fourteenths of the motion of the Glacier of the Aar is, according to Professor Forbes, not in common motion, but that of its particles one beside another and one over another, which is called the differential motion, and to which is opposed the resistance to shearing, which is at the rate of not less than 75 lbs. per square inch.” On this point Moseley concludes that “Mr Hopkin’s experiment leaves therefore more than thirteen fourteenths of the power necessary to cause the glacier to descend unaccounted for.”

While recent boreholes have confirmed that in many glaciers there is meltwater present which would allow low friction basal slippage (11), it has to be admitted that these must in general be the exception rather than the rule. Much of the data on basal conditions has been gathered in those regions of the glaciers where access is relatively easy. It is these very regions where it is most likely that warm beds will result in loss of adhesion of the ice to the bed and water at pressure will allow low shear slippage to take place. That this is the exception is evidenced by the erosive powers of glaciers within which the bed shear resistance must be considerable to generate the massive forces required to fracture and drag along the bed the rocks fragments from small to massive dimensions.

Crawling Model Inconsistent with Observation: Another issue that was addressed in the criticisms of Moseley’s supposed crawling motion is that it is inconsistent with important observations on glacial motion. Ball (15) remarks that he has met no one “practically conversant with the phenomenon of glaciers who could be brought seriously to discuss the theory”. He proceeded to list the assumptions in Moseley’s model that were at variance “with the facts of nature”. Apart from those already mentioned above, he maintains that glaciers do not present a continuous mass like a sheet of metal. Glaciers are, he observes, “more or less imperfectly welded separate portions, traversed by fissures, and whose upper surface is cut by deep rents extending to a depth very much greater than that subject to the influence of external changes in temperature.” However, Moseley’s model would equally well apply to the separate and largely continuous sheets of glacial ice lying between adjacent rifts. With these rifts acting as very effective conduits for the ingress of surface melt and other water they provide a very plausible means whereby surface solar energy could be transmitted into the body of the glacial blocks. Upon freezing this water would give out its latent heat causing considerable changes in temperature to large volumes of internal ice. The expansions and contractions needed to mobilise Moseley’s thermal ratchet would then be operating on relatively short lengths of the glacier. Any very small uphill motions occurring in these short sections of essentially continuous ice above the stagnation point for each of these finite length blocks would be largely undetectable. In any case if they did occur they would help to close the fissures and crevices, making it more likely that during the next warming cycle the expansion would be constrained and therefore add to the downward forces tending to produce motion.

While Moseley had not addressed the issue of the discontinuous nature of the deformations of glacial ice, it is more than possible that suitably extended his theory could have provided a convincing explanation for this discontinuous behaviour. As observed above few of the other theories being put forward at the time could account for these discontinuities. It is clear that at some locations and at some times glacial ice shows evidence of tensile behaviour whereas at others it may display properties more consistent with the existence of high compressive stress. It also seems fairly clear that these changes from tension to compression dominated forms of deformation response show strong cyclical patterns. There are few obvious reasons why an essentially continuous form of flow within the ice, as envisaged by the gravity inspired, visco-plastic, models of the type favoured by Forbes (7), and many others both in the mid 19th C and today, should give rise to such clear cyclical patterns of response. On the other hand Moseley’s theory is predicated on such cyclical patterns of behaviour. Add to Moseley’s gravity induced ratchet, acting on each of these to some extent discrete lengths of ice, that of the material ratchet (4) and it becomes entirely conceivable that alternations in temperature could be playing a major role in not only accounting for these forms of discontinuous behaviour but also in the very movement of glaciers.

In his fairly forthright dismissal of Moseley’s “crawling theory”, Forbes (7) raises very real doubts about the extent to which heat can flow to and from the interior of the glacier. Moseley’s adoption of the daily variations in air temperature as being indicative of the changes in temperature within the body of the ice to support his calculated motions, Forbes find “perfectly untenable”. While agreeing that the percolation of surface melt water into the fissures could account for the increases in temperature, due to its release of latent heat upon congelation, Forbes perceptively asks “how is the cold of the night to operate in reducing the temperature of the mass of the ice from 300 to 600 or more feet in thickness through the enormous average depression of 9.5oF?” He goes on to suggest that “the water so efficient by its percolation in raising the temperature (if necessary) to 32o, being frozen, is now powerless. Cold can be conveyed downward, or to speak more correctly, heat can be transmitted upwards through the ice only by the slow process of conduction, and this on the supposition that depression of superficial temperature is all that the theory might require.” Forbes quotes some of the temperature observations of De Saussure’s Travels, and points out that on many summer days the temperatures do not fall below zero at any hour during the night. “It is in the summer that the glacier moves fastest” Forbes continues, and “it is with my observations of motions in July that Mr Moseley compares the results of his theory: it is of no avail to say there are periods of the year when congelation penetrates at night some inches or even it may be some feet into the ice, and when therefore the sensible heat of the glacier may be said to vary, though, if regard be had to its vast thickness, it must be on an average and in the most extreme circumstances to an absolutely inappreciable degree.” It seems clear that Moseley’s attempt to explain measured movements of glaciers by reliance upon daily temperature variations was seriously flawed. These flaws were more so when one considers the final paragraph of Forbes’s contribution (7).

Moseley had condemned an earlier attempt by Charpentier to account for “glacier motion in terms of the daily congelation of water which percolates it, and the expansion of its mass consequent thereon” (5) by appealing to Forbes’s observation that in summer there is very little congelation of the melt water more than a few inches from the surface. In apparent contradiction of his own views Moseley asks how this dearth of water the expansion of which is supposed to explain the motion of glaciers could account for the observation that “it is summer that the daily motion of the glacier is greatest.” In this condemnation of Charpentier’s theory Forbes opines that Mr Moseley “clearly passes sentence on his own, which could not come into action until the other had produced its effects” (7). However, it is far from clear that in this respect Forbes’s observations can be relied upon. It is now well recognised that during the heat of summer the volumes of surface melt water, and indeed other precipitation possibly at elevated temperatures, percolating into the body of the glacier reach their maximum. Apart from some comparatively rare glaciers most of this water does transfer its higher heat energy into the colder ice. In some the surplus melt water reaching the glacier base is believed to contribute to a higher than normal level of basal slip. In those where basal slip is not greatly increased it seems clear that these greater volumes of congeling water will induce expansion by both the change in state and the increased temperature of the extant ice. Both these effects could be providing major contribution to the forward motion of the ice.

References used in this blog:

(4) Croll, James G A “The Movement of Glaciers”, submitted but rejected by the J of Glaciology, 2004.
(5) Moseley, Henry. “On the Descent of Glaciers”, Proc Roy Soc, 7, 1855, 333-342.
(6) Moseley, Henry. “On the Descent of a Solid Body on an Inclined Plane when subjected to alternations of Temperature”, Phil Mag, S.4, 38, August 1869, 99-118.
(7) Forbes, J. D. “Remarks on the Rev H Moseley’s Theory of the Descent of Glaciers”, Proc Roy Soc., vii, June 7, 1855, 411-417.
(8) Moseley, Henry. “On the Mechanical Possibility of the Descent of Glaciers by their Weight only”. Received, Oct. 1868, read before Royal Society, 7 Jan., 1869, reported Phil. Mag., 37, 229-235. Proc. Roy. Soc., xvii, Jan., 1869, pp202-207.
(9) Moseley, Henry. “On the Mechanical Impossibility of the Descent of Glaciers by their Weight only”, Phil Mag., 37, no 208, May, 1869, 363-370.
(10) Tyndall, “Surface Velocity Measurements of the Mer de Glace”, Phil. Trans. Royal Society, cxlix, part 1, 265-266.
(11) Benn, D. “The Theory of Glacial Motion”, http://www.edu/~smithch/wallace/S184.htm
(12) Wallace, A R. “The Theory of Glacial Motion”, Phil. Mag., February, 1871.
(13) Croll, James. “On the Physical Cause of the Motion of Glaciers”, discussion of Moseley’s papers references (5,8), Phil. Mag., March, 1869, 201-206.
(14) Mathews, W. “Mechanical Properties of Ice and their Relation to Glacier Motion”, Alpine Journal, Feb., 1870 and Nature, March 24, 1870, 534-535.
(15) Ball, J. “On the Cause of the Descent of Glaciers”, Phil. Mag., July, 1870, 1-10.
(16) Croll, James. “On the Cause of the Motion of Glaciers”, Phil. Mag., September, 1870, 153-170.
(17) Croll, James G A. “Comparisons of the Stresses in Glaciers when subject to Gravity and Thermal Loading”, to be submitted to J of Glaciology, 2005.
(18) Moseley, Henry. Reply to discussion of References (5,8). Phil. Mag., 42, no 278, August, 1871, 138-149.
(19) Forbes, Travels in the Alps of Savoy, .