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.

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.

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.

If the surface of Berendon Glacier, British Columbia, Canada, rose by 19 m above its 1963 level at a certain point near the terminus it would reach the entrance to a mining tunnel. Computations are made to see whether this is likely in the near future.

We calculate the changes in mass balance that would be necessary to make the glacier, which is now retreating, start to advance and reach the tunnel in 40 years and 20 years respectively. The method fits polynomials to the advance—retreat data and then uses the λ coefficients of Nye (1963[b]) to infer the corresponding mass balance behaviour. It is concluded that if the mean mass balance should increase smoothly to +70 cm/year, which is a high but possible value, by the year 2003, the ice would reach the tunnel portal in 2003. But, even assuming a rather drastic deterioration in the climate in the future and a concomitant increase of the mean mass balance, the ice will not reach the tunnel portal within the next 20 years.

The deformation and the state of stress in the frontal part of a floating glacier is analysed by a method analogous with the beam theory, applied in engineering practice for determining stresses and deflections of a beans of an elastic material. Very rough approximations are made, the most severe being that of assuming the viscosity of the ice constant. Curves showing the progress in time of the deflections and the stresses in the frontal part of the glacier are given for the case of an infinitely wide glacier. The curves show, that the stresses are greatest at a cross-section situated at a distance of about the thickness of the glacier from the front, and that the stresses are of a magnitude which very likely will lead to fracture, resulting in the formation of an iceberg. It is shown that the magnitude of the icebergs as well as the frequency of the calving is a function of the thickness, the density, and the temperature of the glacier. Observations from nature supporting the theory are described. Finally other calving mechanisms for floating glaciers are briefly discussed.

A block of ice from Blue Glacier. Washington, was successively sectioned at close intervals as a means of determining exact crystal shape in three dimensions. Two crystals occupying over 20 per cent of the entire sample are used as examples, and their volumes calculated. These crystals were found to be much larger and more complex in shape than expected from thin-section examination alone. The surface-to-volume ratio was calculated using a simple relationship between the length of lines in a grid crossing the crystal and grid-line intercepts with the crystal boundary. From this ratio the surface area of each crystal was calculated.

A measurement of irregularity or jaggedness is introduced in order to compare crystals of different size with one another. This is necessary because surface-to-volume ratio of a body of the same shape decreases as the size increases.

Data on the physical properties of seasonal alpine snow have been collected from the Beartooth Mountains near Cooke City, Montana (elevation ≈3000 m) and the Bridger Range near Bozeman, Montana (elevation ≈2200 m). Systematic measurements of snow density, temperature, structure, ram and Canadian hardness, centrifugal tensile strength and shear strength measured with a shear box and several types of shear vanes are included. Test results were grouped according to gross snow types (cohesive fine-grained “winter” snow. depth hoar, new snow, etc.) and whether the snow was wet or dry. Then interrelations between the different test parameters were studied. A plot of ram number versus density for winter snow gave a log-linear relation similar to that suggested for polar snows. Both shear-vane and centrifugal-tensile results when plotted as a function of porosity are well described by the negative exponential relation suggested by Ballard and Feldt. Depth hoar and wet snow invariably have lower strength values at any given density. There is an excellent one-to-one agreement between values obtained with the shear vane and the shear box.

Several field experiments were performed to study the sources of error in making in-situ mechanical tests on snow without utilizing a pit wall. Statistical analysis of the results shows that the main factor contributing to the experimental scatter is lateral inhomogeneity in the snow cover. There was no significant difference between the results of different operators. The standard deviation of a group of strength tests is shown to be directly proportional to the mean value of the group. This indicates that a logarithmic transformation should be made in handling snow strength results in order to stabilize the variance. It is emphasized that the systematic relations between snow properties invariably become obscured when different snow “types” are indiscriminately grouped together.

The rate of snow accumulation has been measured at the U.S.S.R. station situated at the Pole of Relative Inaccessibility (eastern Antarctic plateau). Five independent methods were used. The results, expressed in g cm−2 year−1, are as follows:

1. (1) Accumulation-stake measurements show an accumulation of 3·1±0·5 in 1965. A maximum value of 3·6 for the 6–year interval 1959–65 is derived from snow-thickness measurements.

2. (2) Firn stratigraphy was found difficult to interpret in terms of annual layers. An upper limit of 12 g cm−2 year−1 is suggested.

3. (3) 18O/16O ratios were measured along the upper 235 cm. Assuming that each maximum in the isotope profile corresponds to a summer season, the accumulation would be 8·6±0·9.

4. (4) Gross β radioactivity as a function of depth was measured on three firn sections. The 1955 radioactive fall-out horizon is clearly marked, enabling the derivation of an average accumulation of 3·0±0·3.

5. (5) The average accumulation over the last 80 years, derived from the 210Pb distribution with depth, is 3·1±0·3.

A multi-annual average accumulation rate of (3·0±0·3) is thus firmly established, as well as the validity of both the 210Pb method and the 1955 radioactive fall-out horizon method. Stratigraphie studies lead to uncertain results. Oxygen isotope variations give accumulation values which are too high by a factor of two at least.

Accumulation values of the same order of magnitude (2·8±0·2) were derived from radioactive fall-out measurements at the U.S. “Plateau” station.

Radiometers, suspended at a height of 15 m between two towers anchored to the bottom of the ice cover, have been used to measure the average or integrated albedo of the surface. The work was carried out in May 1967 at Tanquary Fiord, Ellesmere Island (lat. 81° 25′ N., long. 76° 50′ W.) during the period when the surface of the ice cover was undergoing rapid change. The albedo was observed to have a value of almost 1·0, for a fresh snow cover, and about 0·8 for a weathered snow cover. It decreased to 0·6 as the wind partially cleared the surface of snow and gradually to 0·5 with further deterioration of the snow. The onset of melting, produced when the daily mean temperature exceeded 0°C, rapidly lowered the albedo to a value of about 0·3.

Ablation polygons on snow have been examined, mainly in the Tatra Mountains, both by field observation and by experiment. The polygons are initiated under peculiar climatic conditions—mostly when the melting of snow is somewhat slow and is accompanied simultaneously by the metamorphism of snow. A thick snow cover appears to be a prerequisite of this process. A detailed analysis of the problem of dirt concentration in snow, due to ablation, reveals the major role played by adhesion in this process. The concentration of dirt is due to lateral movement of the material and this is intrinsically related to the micro-elements of the snow surface.

The origin and development of ablation polygons do not depend on the presence of dirt in the snow; on the contrary, the process of dirt concentration and its effects are dependent on the evolution of polygonal forms.

Among the important factors in the formation of melt water are: (1) The air and soil temperatures. (2) The presence or absence of debris on snow and ice. (3) The surface gradients of the glaciers. These gradients determine the areas of snow and ice in the zone where melting can occur as well as the amount of insolation. (4.) The orientation of snow and ice slopes. In general, in the Southern Hemisphere north-facing slopes receive more insolation than south-facing slopes.

The main source of the melt water is Wilson Piedmont Glacier, and the snowdrift-ice slabs are next in importance. The seasonal snowfall is not an important source, nor is the ice in the active zone. As no rain has ever been reported, all run-off is melt water.

The seasonal discharge of the Surko and Scheuren Rivers was roughly measured in 1957–58. It was found to be approximately 13 m3 s−1 d for the Surko River and approximately 19 m3 s−1 d for the Scheuren River, and it seems likely that the total seasonal discharge of all streams in the area was not far from 50 m3 s−1 d.

Thermal probes can carry instrumentation packages into polar ice sheets for geophysical investigations and long-term observations by remote measurement methods. They are self-contained surface-controlled devices. The development work at U.S. Army CRREL solved problems of materials, fabrication and heat-transfer analysis. The Philberth probe, named after its inventor, has demonstrated its performance capability in Greenland. The pendulum probe is a further development with increased performance and versatility. The probes are a tool to widen Man’s knowledge in glaciology and geophysics, and to increase his capability in seismics and possibly communications.

The measured β activities of firn samples from two sites on the Juneau Icefield are in good agreement with each other and with those of Greenland firn. A consistent pattern of β-activity variation can be identified far the fire layers from 1959 through 1962. The 1952–53 firn layer cannot be identified from the measured β activities.

An empirical formula, derived by the author for the seismic velocities of P waves in glaciers and ice caps, is used to determine the temperatures which can be deduced from the maximum and the mean vertical velocities. With the aid of several examples from previous publications, these temperatures are discussed and, as far as they are available, direct temperature measurements are compared with the derived temperatures.