A solution for the steady flow of a cold ice sheet is recalled, which takes account of the heat released by deformation. As this strain heating increases the strain velocity, the bottom temperature may be unstable. A set of five equations with five unknowns is written, which allows the surface profile and the bottom temperature to be computed step by step by an iterative process. This has been done by computer for three very different models of ice sheets. and in each case with three distinct values of the constant B in Glen’s ice flow law. It was found in every case that steady-state temperature profiles could not be computed beyond a moderate distance from the ice divide. The correct value of B for bottom ice may be deduced from the actual surface profile. At the bottom of Greenland ice sheet, B ≈ 2.18 bar −3 year−1. This is about thirteen times bigger than for the bulk of the alpine glaciers.

Statistical results of measurements of glacier variations in Switzerland 1891–1965 are compared with deviations from average temperature and precipitation in summer for stations above 2000 m. The result is interpreted in terms of meso-scale glacier–weather relations. A correlation between glacier mass budget and deviation from the average height of the 500 mbar surface indicates the importance of cyclonic and anticyclonic conditions during the ablation period, and therefore of the frequency of certain Grosswetterlagen which has been studied for the period 1881–1965. The pattern of the difference of Grosswetterlagen favourable and unfavourable for glaciers resembles the pattern of glacier variations and also of mass-budget data. Atmospheric circulation in zonal and meridional forms, as expressed by the frequency of Grosswetterlagen has to be considered by seasons. There is no simple relation between the intensity of zonal circulation and glacier variation. Glacier recession of the last few decades seems to be caused by the fact that meso-scale weather conditions mainly in the ablation season have become much less cyclonic than in the decades 1886–95 and 1906–15.

If glacial till contains more than a certain minimum boulder content, it is dilatant and requires a much larger stress to initiate shear deformation than to sustain it. If the stress level at the glacier–terrain interface drops below a certain critical level, or the till reaches its critical boulder-content density, then the till beneath the glacier packs into stable obstructions. These are shaped into streamlined forms by the glacier and are found distributed at random in drumlin fields. Due to drumlin coalescence there is a normal distribution of drumlin axes about the direction of ice movement.

Earlier theories of Weertman and the present author are reviewed and compared; both are insufficient to account for the facts observed at the tongue of the Allalingletscher.

A calculation of the stresses and heat flow at the bed of a glacier with a sinusoidal profile is given which takes account of any degree of subglacial cavitation. The sliding due to plasticity and that due to pressure melting are related to this degree of cavitation and it is shown that these two terms are additive. There results an expression for the friction fω in terms of the total sliding velocity u and the height of the bumps a. For a given and large enough value of u, fω(a) exhibits two maxima which are equal and independent of u.

The paper then considers a more realistic model of the bed consisting of a superposition of sine waves all having the same roughness r, and a decreasing in a geometrical progression. The biggest a may be inferred from the overall profile of the bedrock; the resulting frictional force can be regarded either as part of the total frictional force f in an overall view for which f = ρgh sin α holds, or else as a correction to such a value on the small scale (the best point of view for crevasse studies). To a first approximation Coulomb’s law of friction holds provided one takes account of the interstitial water pressure at the ice-rock interface.

This interstitial pressure p is next related to the thickness of the glacier h. If the subglacial hydraulic system is at atmospheric pressure, p is proportional to h. Next, if the sliding velocity is not too large, the surface slope approaches 1.6r ≈ 0.12 and kinematic waves (which move four times as fast as the ice) disappear rapidly. If the hydraulic system is not at atmospheric pressure the surface slope is smaller and flow instabilities can occur.

Data from stake measurements, marker boards and pits along a 136 km trail crossing the Thule peninsula sector of the Greenland ice sheet have been used to determine both the regional and local distribution of snow accumulation, On a regional scale trend surfaces of mean annual accumulation can be adequately predicted from a model using distance from moisture source and elevation as independent parameters. A series of step- or wave-like features break the smooth profile of the ice. sheet and cause profound changes in accumulation rates on a local scale. The accumulation pattern over these features can be predicted from surface slope and departure from regional elevation. Profiles of’ surface and subsurface topography indicate a direct relationship between subsurface hills and step-like features, but cannot be quantitatively accounted for by existing ice-flow theory. Detailed accumulation studies in conjunction with a program of spirit leveling in the vicinity of Camp Century has revealed the development a shallow valley-like feature. Within this feature accumulation rates have increased indicating that it is the result of flow phenomena.

Three outlet glaciers of the highland ice of Ny Friesland are described, in which englacial debris, derived from the glacier bed, occurs in thick bands which dip steeply up-glacier. As the glacier wastes down this debris is released on the surface to form thick supraglacial tills, which may remain on the glacier surface, or flow down it and onto bedded deposits which fringe the glacier in the proglacial zone. A frequent result of this latter process is the production of multi-till sequences which result from a single glacier retreat phase rather than multiple advance and retreat. The sedimentological features and fabrics of englacial debris bands and flow tills are described, and a mechanism for the formation of “controlled” and “uncontrolled” hummocky moraine is suggested. Many flow tills are identical to the compact fine-grained tills common in lowland glacial deposits of Pleistocene age in Europe and North America, and it is suggested that some of the latter could be flow tills.

An analysis is made of the rate of bubble coalescence in an ice mass that is deforming. A total strain of at least 8 is required before appreciable coalescence occurs. The analysis has been applied to deforming ice shelves and ice sheets. No appreciable coalescence is expected in ice shelves but coalescence should occur in ice sheets (or glaciers) if the shear strain-rate at the bottom surface is of the order of 0·075/year or larger. Measurements of bubble concentration are capable of setting limits on paleo-strain-rates of the present ice sheets. Bubble migration down temperature gradients presents complications to the study of bubble coalescence.

A diffusion equation is obtained that describes the mechanical dispersion of a dilute mixture of solid particles within an ice matrix that is undergoing deformation. It is shown that within the limits of time intervals and strain-rates appropriate to the movement of glaciers and ice sheets, the dispersal distance usually is no larger than a distance about one order of magnitude greater than the size of the particles themselves.

Recent glacial deposits in the Indian Peaks area of the Colorado Front Range have been dated lichenometricaily, using a growth curve developed locally for Rhizocarpon geographicum. Radiocarbon dates, where available, tend to support the lichen chronology. Three distinct intervals of glaciation, each consisting of several minor pulsations, have occurred in the area during the past 4500 years. The earliest advance (Temple Lake Stade) is dated at 2500–700 b.c. A later advance (Arikaree Stade) began in about a.d. 100 and ended in a.d. 1000. The most recent advance (Gannett Peak Stade) is dated at a.d. 1650–1850. It remains to be seen whether the Arikaree Stade was purely a local development or whether glaciers were advancing elsewhere in the cordilleran region during this interval. Alluviation on the plains east of the Colorado Front Range seems to have occurred during the waning stages of mountain glaciation.

Observations on Tunsbergdalsbreen show that an ice-dammed lake, Store Brimkjelen, overflowed on to the surface of the glacier. The lake lifted a section of the glacier and formed a long irregular crevasse along the line of dislocation.

Field measurements are presented of dielectric absorption in Antarctic snow and ice at frequencies of a few hundred megahertz. They are compared with measurements by other authors at very high frequencies. The dielectric absorption in ice at these frequencies is accounted for in terms of absorption bands both at radio frequencies and in the infrared. Bands at radio frequencies are caused by a relaxation mechanism which depends upon the temperature and the impurity content of the ice. These two factors are therefore included in an account of the dielectric absorption in ice at very high frequencies.

Ice samples from a 121 m core, representing the total thickness of the Meighen Ice Cap near its highest point, were studied for ice fabric, firn- and dirt-layer distribution. The absence of a strongly preferred fabric between the surface and the base of the ice cap at the core site suggests an absence of past or present ice movement at this point. From the variations of ice texture, am- and dirt-layer distribution with depth it is concluded that the ice cap post-dates the climatic optimum and has never been much thicker than it is at present. There is a possible relic ablation surface at a depth of 50 m which is estimated to be at least 500–600 years old.

Application of the gas law to fourth-place density measurements of ice samples from two deep drill holes at “Byrd” station and “Little America V”, Antarctica, shows that virtually all density increase beyond the pore close-off density (0.830 g cm−3) can be attributed to compression of the entrapped bubbles of air. Data from “Byrd” station also indicate that the lag between overburden pressure and bubble pressure, initially 4–5 kg cm−2 at pore close-off, diminishes to less than 1.0 kg cm−2 at about 200 m depth. By substituting the overburden pressure for the bubble pressure in the pressure-density relationship based on the gas law, one can determine ice densities below 200 m more accurately than they can be measured per se on cores, because of the relaxation that occurs in samples recovered from high confining pressures. This relaxation, resulting in a progressive increase in the bulk volume of the ice with time, is generally attributed to decompression of the entrapped air bubbles following removal of the ice from high confining pressures. However. calculations of the stress in ice due to bubble pressure, together with measurements of bubble sizes in cores from various depths at “Byrd” station, both tend to indicate that there has been negligible decompression of the inclosed bubbles. It is suggested that most of this relaxation may be due to the formation of micro-cracks in the ice. Anomalous bubble pressure–density relations at “Little America V” tend to confirm abundant petrographic evidence of the existence of considerable deformation in the upper part of the Ross Ice Shelf.

Studies of crystal–bubble relations at “Byrd” station revealed that the concentration of bubbles in ice remains remarkably constant at approximately 220 bubbles/cm3. Bubbles and crystals were found to be present in approximately equal numbers at pore close-off at 64 m depth, at which level the average bubble diameter was 0·95 mm, decreasing to 0.49 mm at 116 m and to 0·33 mm at 279 m. Despite a ten-fold increase in the size of crystals between 64 and 279 m, the bubbles showed no tendency to migrate to grain boundaries during recrystallization of the ice. The observation that most of the bubbles had assumed substantially spherical shapes by 120 m depth points to essentially hydrostatic conditions in the upper layers of the ice sheet at “Byrd” station.

The use of the two-phase system ice–water to illustrate the effects on equilibrium of both hydrostatic and non-hydrostatic stresses has been a recurrent theme in the history of thermodynamic theory. The effects of hydrostatic pressure on the melting point of ice are firmly established by theory and experiment. Those of non-hydrostatic stress are still a subject of debate today; several theorists have predicted ice re-crystallization under such stress, but the magnitude of any slight melting-point depression is not known with certainty. The recrystallization of ice caused by local variations in hydrostatic stress was predicted and experimentally confirmed over a century ago. Cavities deep within temperate glaciers provide a suitable environment for the occurrence of this latter phenomenon. A water-filled cavity intersected by a tunnel in nearly stagnant ice of the Blue Glacier, Washington State, U.S.A., was lined with large and unusual single ice crystals which apparently owe their origin to the effects of hydrostatic stress. Even the minute differences in pressure melting point around this cavity are adequate to remove the heat of fusion as ice forms within it. There is evidence that interstitial movement of melt water in the surrounding ice also contributes to the heat and mass transfer. The form of these crystals indicates that they grew into slightly supercooled water. It is suggested that this growth pattern is sustained by the existence of oriented stresses at the cavity walls.

The heat balance of an Alaskan mountain glacier located close to the sea is calculated for a period of 16 d in midsummer—a period which is typical of the summer in this region in its high cloudiness and in its temperature and humidity conditions. The radiative and the combined sensible and latent heat components are found to contribute equally to the observed high rate of ice melting.

The formation of hexagonal and cubic forms of ice was studied by the use of a cold stage in an electron microscope within the temperature range −90° to −180° C. Ice crystal specimens were made on cold substrates, i.e. a collodion film, gold foil, or copper grid on the specimen holder of the cold stage. The hexagonal form of ice formed on the cold substrates at temperatures from−90° to−100° C. At −100° to −130° C, both hexagonal and cubic forms of ice were detected. From −130° to −160° C only cubic ice was found. At temperatures below −160° C, minute crystals of cubic ice were detected. No transformation of the structural form of ice from hexagonal to cubic or from cubic to hexagonal occurred when the temperature of the specimens was varied in the range −90° to −160° C. The lattice constants of hexagonal and cubic ice, and the coefficient of thermal expansion of ice were calculated from the experimental results.

Avalanche data were obtained by direct observation of the Vaughan Lewis Icefall. Magnitude, time and location of each ice fall were recorded and the resulting data were analyzed statistically. An inverse relationship was found between the relative frequency and the magnitude of the avalanches. A significant diurnal variation in avalanche rate was also detected. During the early morning hours the avalanche rate reached a maximum. No secondary increase in the avalanche frequency was observed during the evening cooling period. The data indicated that a given ice fall results in an increased probability of an ice fall occurring shortly thereafter. After approximately 4 min the effect of a given avalanche no longer correlates with succeeding avalanches.

In a recent paper Robin has developed a method of calculating the relation between bed and surface topography of an ice sheet. He found that by including the effect of longitudinal strains in the equilibrium equation the correlation between theory and observation could be much improved. This paper is concerned with the mathematical justification of the assumption made by Robin.