Basin Erosion Research Articles

Global dynamics underlying sharp basin erosion in nonlinear driven oscillators.

For periodically driven damped oscillators with the ability to escape from a potential well, the erosion of the nonescaping basin of attraction begins at the homoclinic tangency of the stable and unstable manifolds of the hilltop saddle cycle. The consequent rate of erosion, however, is intrinsically dependent upon the manifold organization, which to a large extent is determined by the heteroclinic events following the homoclinic tangency. In this paper we outline how, under small parameter changes, there can exist a rapid erosion of the nonescaping basin.

Lobe dynamics and the escape from a potential well

Periodically-forced nonlinear oscillators that permit escape from a potential well frequently possess unstable periodic orbits whose invariant manifolds are homoclinically tangled. The trellises formed by such overlapping manifolds separate the Poincaré plane into regions (calledlobes) whose fates at successive time periods are amenable to analysis. The lobe configurations observed in simple escape systems are discussed, together with their interrelation with the location of periodic orbits and other invariant sets. Three applications of this procedure are illustrated: (i) a numerical technique for localizing the non-wandering set; (ii) a demonstration that the existence of a saddle possessing aboundedhomoclinically tangled unstable manifold branch implies the existence of safe open regions in the global basin of attraction; (iii) the proposal of definitions of global integrity and escape times which may be used to relate safe basin erosion to the evolution of a homoclinic tangle.

Cretaceous‐Eocene (Laramide) landscape development and Oligocene‐Pliocene drainage reorganization of transition zone and Colorado Plateau, Arizona

Landscape development of central and northern Arizona can no longer be ascribed mainly to events of Miocene and Pliocene age. New information on the age and distribution of older Cenozoic deposits has led to the recognition of a regional Cretaceous‐Paleocene(?) surface of erosion that conforms to major elements of the present topography and to the recognition that a formerly thick deposit of gravel accumulated on this regional surface of erosion. These relations cast new light on the history of evolution of the landscape and indicate a much greater age for the main landscape elements and a more complicated and prolonged history of erosion and deposition than has been previously supposed. The timing of events postulated for development of drainage on the Colorado Plateau can now be compared and partly reconciled with events recognized in the adjacent closely related Mountain Region (Transition Zone) of central Arizona. As a consequence of Late Cretaceous‐Paleocene (Laramide) compression, central and northern Arizona underwent at least 1200 m of uplift, documented by paleochannels cut into erosionally truncated Paleozoic strata on the Hualapai Plateau of the southwestern Colorado Plateau. During this time, a highly irregular erosion surface was developed on Proterozoic rocks across the Transition Zone south of the Mogollon Rim, the scarp of the Mogollon Rim was eroded to its present height (600–900 m), and an extensive stripped surface was developed on resistant upper Paleozoic strata north of the rim. Deposition of several hundred meters of Paleocene‐Eocene “Rim gravels” derived from highlands south and west of the region followed, covering much of the Cretaceous‐Paleocene erosion surface. Nearly complete burial of the rim is suggested by the distribution of remnants of the Rim gravels across the erosional scarps and on high plateau areas north of the rim. A second increment of uplift, apparently occurring in late Eocene time and apparently recorded by a series of fission track cooling ages from the Marble and Grand canyons, is inferred to have been responsible for ending deposition of the Rim gravels, for initiating differential uplift of contemporaneous deposits (Canaan Peak and Claron formations) to their positions in the high plateaus of central Utah, and for causing the drainage reorganization required to explain the extensive removal of Rim gravels from much of the region. A southerly flowing ancestral Verde River related to the drainage reorganization removed much of the older gravel cover from the Transition Zone of central Arizona, resulting in a younger regional erosion surface having 600–900 m of relief, a surface closely approximating the Cretaceous‐Paleocene erosion surface. Late Oligocene and early Miocene rocks locally rest unconformably on remnants of Rim gravels in the Transition Zone, indicating that the second episode of regional erosion had been completed by late Oligocene time. North of the Mogollon Rim, a west flowing(?) ancestral Colorado River is inferred to have become established on the Rim gravels, draining the interior parts of the Colorado Plateau and transporting detritus off the plateau. Exhumation of the Mogollon Rim and development of 600–900 m of topographic relief in the Transition Zone by an ancestral Verde River system suggests the potential for a comparable, coeval entrenchment of an ancestral Colorado River in Paleozoic strata north of the Mogollon Rim. Regional extension and volcanic activity ensued in late Oligocene to Pliocene time. The Oligocene erosion surface in the extensional basins of central Arizona became largely concealed by Miocene and Pliocene deposits as the Neogene climate became drier. In late Miocene and Pliocene time, perennial streams appear to have been lacking, transport of detritus appears to have been principally by flash flooding, little or no detritus appears to have been removed from the region, and much of the precipitation presumably moved by groundwater flow through the deposits of aggradation. A coeval episode of aggradation in the Grand Canyon is suggested by deposits that appear to have once choked much of the canyon. If this event parallels the episode of late Miocene and Pliocene aggradation recorded east, south, and west of the Grand Canyon, the Colorado River could have been incised to its present level by late Miocene time. A return to wetter conditions in late Pliocene time presumably was responsible for renewed erosion and reexcavation of older drainages and basins. An understanding of this Tertiary structural, erosional, and depositional history can be important for the geological analysis of geophysical transects across the region.

The morphological development of the Wadden Sea Island of Jordsand since the storm surges in 1976

Jespersen, Margot & Erik Rasmussen: The morphological development of the Wadden Sea Island of Jordsand since the storm surges in 1976. Geografisk Tidsskrift 91: 11–18. Copenhagen 1991. Jordsand is the smallest island in the Danish Wadden Sea. For centuries it has been eroded by the sea and is expected to have disappeared at the turn of this century. Since 1972 the authors have carried out investigations of erosion and accumulation on the island. In this paper a briefstatement of the morphological development of the island is given for the period 1976–88. Furthermore, the development of two adjacent morphological elements, the high-sand and the erosion basin, is described.

Systematic Dynamic Mapping and Analysis of Small Basin Erosion Environment Based on Aerial Remote Sensing Information

Systematic Dynamic Mapping and Analysis of Small Basin Erosion Environment Based on Aerial Remote Sensing Information

Incursive fractals: a robust mechanism of basin erosion preceding the optimal escape from a potential well

Comparative cell-to-cell mappings of the basins of driven oscillators with cubic and quartic potential wells show remarkable qualitative and quantitative correlations. We conclude that the recently identified erosion by incursive fractals is a robust phenomenon facilitating the optimal escape from a well.

Ship stability criteria based on chaotic transients from incursive fractals

This article surveys some recent findings in the nonlinear dynamics of driven oscillators that appear to offer a new approach to the quantification of ship stability in waves. The major discovery is that in situations where the resonant motions can escape over a local maximum of the potential energy (as in capsize), there is always likely to be a sudden reduction in area of the safe basin of attraction in the space of the starting conditions. This is associated with a gross striation of the basin, and can occur at a forcing magnitude that is a small fraction of that at which the final steadystate motions lose their stability. It is argued that this well-defined basin erosion could form the basis of a new design criterion based on transient motions. This approach has the twin advantages of being both conceptually simpler and at the same time more relevant than one based on a stability analysis of the steady state rolling motions which can be dangerously non-conservative.

Epidemiology and evaluation of an interdisciplinary rehabilitation program in chronic back pain

Assessment of ship survivability is a main requirement that must be satisfied before the ship isoperated. Some assessments of ship survivability which has been applied by IMO such as Intact Stability and Damage Stability in calm water needs to be developed. Sometimes ships are operated in rough water with irregular waves, so the future criteria of ship stability should be associated with ship motion and capsizinginthewaves. Ship capsizing isalways correlated with non-linier ship motion. This paper discusses how to modify intact stability criteria to be righting lever arm onthecalm waterwhich can be used to assess ship survivability from capsizing in the waves using safe basin erosion method. The results shows that the modified IMO‘s Intact Stability Criteria can be considered as assesment of survival of ship capsizing. And the bilge keels have significat effect for improving the survivability of ship capsizing.

Integrity measures quantifying the erosion of smooth and fractal basins of attraction

The phase portraits of a dissipative dynamical system are characterized by the existence of one or more stable attractors, which typically include point equilibria, periodic oscillations (harmonic and subharmonic), quasi-periodic solutions and chaotic attractors. Each attractor is embedded in its own domain or basin of attraction, bounded by a separatrix' associated with an unstable saddle solution. Under the variation of a control parameter, as the attractors move and bifurcate, the basins also undergo corresponding changes and metamorphoses. These changes in size and shape are usually continuous but can be discontinuous as when an attractor vanishes, along with its basin, at a saddle-node bifurcation. Associated with the homoclinic tangling of the invariant manifolds of the saddle solution, basin boundaries can also change in nature from smooth to fractal. In this paper, the escape of a driven oscillator from a cubic potential well, as an archetypal example, is used to explore the engineering significance of the basin erosions that occur under increased forcing. Various measures of engineering integrity of the constrained attractor are introduced: a global measure assesses the overall basin area; a local measure assesses the distance from the attractor to the basin boundary; and a velocity measure is related to the size of impulse that could be sustained without failure. Since engineering systems may be subjected to pulse loads of finite duration, attention is given to both the absolute and transient basin boudaries. The significant erosion of these at homoclinic tangencies is particularly highlighted in the present study, the fractal basins having a severely reduced integrity under all three criteria.

Late quaternary spatial and temporal changes in clay- and silt-size mineral assemblages of fiord and shelf cores, western Baffin Bay, northwest North Atlantic

Clay- and silt-size mineral assemblages are described from eight piston cores from the fiords and shelf on the western margin of Baffin Bay, Arctic Canada. Radiocarbon dates indicate that all the cores extend back in time to the last local glacial/interglacial transition (i.e. 8–10 ka); four extend back to between 10 and 12 ka, and HU77-021-156, located on the Southeast Baffin Island shelf, includes the entire late Foxe glacial stage. Silt- and clay-size particles constitute ca 40 and 55%, respectively, by weight of the bulk sediment. The clay-size fraction is dominated by mica; feldspars and quartz are the main constituents of the silt fraction. The fiord sediments are mainly composed of local mineralogies, but on the shelf, and at times in the fiords, exotic mineral species occur. The most important of these are detrital carbonates, derived from erosion of the Paleozoic basins in Arctic Canada and/or northwest Greenland. Both calcite and dolomite occur; calcite is the major carbonate mineral in the “southern” cores, whereas dolomite is the most abundant in cores north of 66°N. Higher inputs of carbonate species occur during regional deglaciation, 7–10 ka, and during the last 5 ka (probably reflecting increased iceberg production from northwest Greenland). Thus variations in the precentages of the carbonate minerals indicate significant shifts in Late Quaternary glacial-sediment source areas and oceanographic regimes.

An extension of the grid-based hydrological model CEQUEAU to suspended sediment movement through drainage basins

This paper presents an original attempt to describe an integrated conceptual approach to the genesis and transport of suspended solids (SS). The key points of this approach are that: (1) the hydrological representation is provided by a numerical model (CEQUEAU) which is also used to define the spatial square grid for the transport of suspended solids, and (2) the model makes use of two main functions: 1. (a) a production function which considers drainage basin erosion and river bank erosion. For both of these it evaluates the amount of material, in each granulometric class, that is available for transportation; 2. (b) a transport function which takes into account the sedimentation/resuspension phenomena that occur within the river during hydrological events. One of the advantages of this approach is that it permits the isolation of a particular granulometric class of SS that might be ecologically important, such as the adsorption of toxic material on fine particles. This model, which is part of a conceptual water quality model called CEQUAL, has been tested on the Ste-Anne de la Pérade river, and the accuracy of the results is discussed.

Stable-isotope evidence for low-temperature kaolinitic weathering and post-formational hydrogen-isotope exchange in permian kaolinites

Depleted δ 18O- and δD-values of +6.1 to +9.4‰ and −107 to −94‰, respectively, have been obtained from kaolinite samples of early Permian (Sakmarian-Artinskian) age from the Gunnedah Basin, eastern Australia. The samples come from kaolinite clayrocks representing both in situ kaolinitic weathering profiles and the eroded and re-deposited products of this weathering developed in the Quirindi-Wingen and Boggabri-Gunnedah areas of New South Wales, Australia. The clayrocks were produced by the intense surficial weathering of an underlying volcanic sequence, with subsequent erosion and re-deposition in basins flanking the volcanic pile. The calculated isotopic composition of meteoric water in equilibrium with kaolinite from the clayrocks had δ 18O of ⩽ −17‰ and δD of ⩽ −125‰, indicating polar or sub-polar temperatures of condensation. As kaolinite formation cannot occur below the freezing point of water, the highly depleted isotopic results obtained from the samples suggest equilibrium with waters partly derived from deglaciation of the Gondwanan landmass, an event which consequently must have been well underway in eastern Australia by the Sakmarian-Artinskian. The climate prevailing at the time of kaolinite formation is unlikely to have been warmer than cool temperate, a conclusion which is difficult to reconcile with the classical interpretation of kaolinitic weathering as a tropical or subtropical phenomenon. This suggests that high rates of infiltration, efficient leaching of soluble cations, and good drainage are of more importance to kaolinite formation than the temperature at which the process operates. Oxygen-isotope exchange in the kaolinite samples since formation is thought to have been negligible, however, marked post-formational hydrogen-isotope exchange is demonstrable at temperatures not exceeding ∼ 80°C and probably considerably lower in some cases.

Foreland basins

The characteristic pattern of the subsidence, deformation, uplift and erosion of foreland basins, or exogeosynclines, has long been recognized by geologists as an integral part of the geosynclinal cycle yet only descriptive models have been proposed. This evolution is quantified in terms of a model of regional isostatic adjustment of the lithosphere under the mass load of the adjacent migrating fold-thrust mountain belt. It is shown that the foredeep, which received the clastic wedge of detritus from the core of the orogen and the fold-thrust belt, owes its existence to downward flexure of the lithosphere by the fold-thrust belt. Additional depression occurs in response to the infilling sediment. The scale of the basin therefore reflects the degree of shortening in the orogen and the rheological properties of the underlying lithosphere. Subsidence reflects mass that accretes at a faster rate than mass wasting from the orogen, whereas regional uplift and erosion of the basin is attributed to the large-scale erosion of the fold-thrust belt that has been depressing the lithosphere. There is a complete coupling between the evolution of the foreland basin and its adjacent mountain belt through the lithospheric flexure. Lateral migration of the fold-thrust belt accounts for the progressive overriding and disruption of some foreland basins. The proposed model is tested by comparison with the structure of sections across the Alberta Foreland Basin of Western Canada. It is shown that a model in which mass loads continuously advance on to the craton in a series of pulses between the Upper Jurassic and the Eocene is consistent with observations. No successful models were found when the lithosphere was modelled as a uniform thin elastic plate. However, when the plate was allowed to relax stress according to a viscoelastic (Maxwell) rheology good agreement between observed and theoretical cross-sections was obtained. These results suggest that suitable values for the flexural rigidity, D, and relaxation time constant, τ, are 1025 Nm and 27.5 Myr. Models with significantly different D-τ parameter values failed to predict satisfactory results. Predictions of basin erosion, coal and shale compaction, and thermal metamorphism of coal are shown to be in agreement with observations. A significant result is that no change in geothermal gradient, with respect to that presently observed, is needed to explain coalification. This result confirms the view that subsidence of the basin was not thermally controlled, unlike Atlantic type marginal basins, and explains the high value of the flexural rigidity as that appropriate to an old, cool, thick lithospheric plate.

Simulation of Soil Erosion and Sedimentation in Small River Basins

Potential erosion and sedimentation for three small stream basins near Dodoma, Tan-zania are simulated using SOILCART, a computer program recently developed to assist in the investi-gation of soil erosion problems. Using only widely available generalized data, the predicted values of soil erosion and sedimentation derived from SOILCART compare favorably to measured values which required a 2-year field investigation. Potential areas of high erosion are identified that could be amelio-rated with proper management. The potential use of SOILCART in preliminary evaluation of erosion and sedimentation problems promises useful results, especially in areas where small dams are proposed.

Abstracts of Papers Presented at the Symposium But Not Published in Full in this Volume: Subglacial, Englacial, and Supraglacial Sediment Differentiation and Erosion in Glacial Basins

AbstractIf sediments being transported by glaciers in subglacial, englacial, and supraglacial situations can be differentiated on the basis of their textural characteristics, some potential exists for interpreting the relative importance of subglacial and sub-aerial periglacial processes in the excavation of glacial valleys, by examining the sediments in abandoned or active terminal moraines. Caution should be used with compound glacial valleys where subglacially eroded debris may become englacial as ice streams merge, be subsequently transported passively, and in terminal moraine deposits appear to represent sub-aerially derived sediments.

Abstracts of Papers Presented at the Symposium But Not Published in Full in this Volume: Subglacial, Englacial, and Supraglacial Sediment Differentiation and Erosion in Glacial Basins

Abstract If sediments being transported by glaciers in subglacial, englacial, and supraglacial situations can be differentiated on the basis of their textural characteristics, some potential exists for interpreting the relative importance of subglacial and sub-aerial periglacial processes in the excavation of glacial valleys, by examining the sediments in abandoned or active terminal moraines. Caution should be used with compound glacial valleys where subglacially eroded debris may become englacial as ice streams merge, be subsequently transported passively, and in terminal moraine deposits appear to represent sub-aerially derived sediments.

Mixed-Layer Kaolinite—Montmorillonite from the Yucatan Peninsula, Mexico

AbstractClay beds 1–2 m thick and interbedded with marine limestones probably of early Eocene age are composed of nearly pure mixed-layer kaolinite-montmorillonite. Particle size studies, electron micrographs, X-ray diffraction studies, chemical analyses, cation exchange experiments, DTA, and TGA indicate that clays from three different localities contain roughly equal proportions of randomly interlayered kaolinite and montmorillonite layers. The montmorillonite structural formulas average K0·2Na0·2Ca0·2Mg0·2(Al2·5Fe1·03+Mg0·5)(Al0·75Si7.25)O20+(OH)4−, with a deficiency of structural (OH) in either the montmorillonite or kaolinite layers. Nonexchangeable K+ indicates that a few layers are mica-like. Crystals are mostly round plates 1/10 to 1/20 μ across. The feature most diagnostic of the mixed-layer character is an X-ray reflection near 8 Å after heating at 300°C. The clays are inferred to have developed by weathering of volcanic ash and subsequent erosion and deposition in protected nearshore basins.

Development of Basin-in-Basin Honeycomb of Florida Bay and Northeastern Cuban Lagoon: ABSTRACT

This triangular, 1,000-sq mi, bimodally windy, subtropical lagoon is a honeycomb of closely spaced, interconnecting, suboval, pan-shaped basins individually upward of 10 mi long and 12 ft deep. It lies north-south between multiple mangrove-swamp belts along the Everglades shoreline and the emergent barrier reef of the Florida Keys and east-west between Biscayne Bay and a zone of broad, marly, sandy and shelly shoals facing the Gulf of Mexico, north of Vaca Key. Basin walls of Holocene marl (mostly shelly calcareous silt grading above to mangrove peat) stabilized by alternations of mangrove-swamp bands and marine grasses form a honeycomb pattern throughout the lagoon. Walls rise to 2.5 ft and basin floors are as deep as 11-12 ft msl. Bottoms are muddy or floored by shell concentrate. Near the are bottom exposures of the underlying hard Pleistocene Miami Limestone. Basin areas and depths increase irregularly southward from tiny, oval, fresh-water, marsh ponds of the Everglades border, by multiple mergings and irregular loss of separating walls, to form large, nearly smooth-sided bays along the barrier reef with its keys cut by tidal inlets. The honeycomb pattern of the geographic map appears below water as a more intricate though fragmentary basin-in-basin structure. Alignments of basins, trending roughly north-south between nearly continuous mangrove belts which mark former rill-valleys of the Everglades marsh, cross northeast-southwest alignments separated by walls which have been reinforced by shoreline storm-debris ramparts. Aqueous erosion of a contemporaneously gradually thickening marl-and-peat formation is indicated by suboval basin form maintaining a rough width/depth relation in a windy region (Price, 1947), while sediment accumulating, in step with rising sea level, produced Scholl's (1964) dated regional stratigraphy of the last 5,000 to 4,000 years. The basin-in-basin honeycomb is the result of conflict between (a) aqueous erosion in saline basins, and (b) the strong sediment potential of tropical paralic vegetation, while (c) the erosion continued during the slow transgression of an 8-mi-wide fresh/salt contact zone like that of today which passed across a rock basin at first lightly carpeted with Everglades marsh. Thus, salt-denuded rill-valley lows developed oriented lakes, which were drowned to form tidal bays. Shoaling of ponds, with mangrove occupation, alternates today with flushing-out of wave-eroded marl. Total volumes of walls and water are now roughly equal. Patches of a similar basin honeycomb occur along 270 mi of the northeastern Cuban lagoon behind its emergent barrier reef. Pleistocene examples occur in Florida and Cuba. Drowned oriented Carolina bay lakes give a somewhat similar pattern along a Chesapeake Bay shore. No process of accumulation adequate by itself to form such honeycombs is known. The genetic process was the drowning and embayment of oriented lakes formed by similar action from drowned marsh rills. End_of_Article - Last_Page 2168------------

Origin of Erosional Surfaces in the Lebanon Valley, Pennsylvania

Summit elevations in the Lebanon Valley, part of the Great Valley, range from 440 o t 720 feet above msl (mean sea level). This range cannot be accounted for adequately by the peneplain concept. Although accordant summits, the chief evidence for peneplains, occur over large areas, summits are not accordant between adjacent areas within the valley. The Lebanon Valley is underlain in the south by carbonate rocks and in the north by shale. The major stream valley in the carbonate area is now partly occupied by segments of two streams, but at one time it was the location of one major stream —the ancestral Quittapahilla Creek—which was beheaded by a tributary to Swatara Creek. Landforms of the Lebanon Valley are probably the result of erosion within two separate stream systems—Swatara and ancestral Quittapahilla creeks—in which streams and interfluvial areas were in a state of erosional equilibrium. The land surface in equilibrium with the ancestral Quit-tapahilla Creek lies at a higher elevation than adjacent land surfaces that were in equilibrium with Swatara Creek. The land surface on the carbonate rocks, which is in the ancestral Quittapahilla Creek system, lies at a lower elevation than shale within the same system, but it commonly lies at a higher elevation than shale in adjacent parts of the Swatara Creek system. Accordance of summits is the result of uniform erosion of uniform rocks in basins whose discharge points are at the same elevation. Lack of accordant summits on uniform rocks is the result of erosion in basins whose discharge points differ in elevation.

Societies and Academies

LONDON. Royal Society, June 9.—Prof. C. S. Sherrington, president, in the chair.—Prof. C. S. Sherrington: Break-shock reflexes and “supra-maximal” contraction-response of mammalian nerve-muscle to single-shock stimuli. The maximal twitch-contraction of tibialis anticus muscle (cat) evoked by a single break-shock applied to the cut motor nerve exceeds the contraction evoked reflexly (spinal preparation) by a single break-shock applied to an afferent nerve. This is due to the reflex response being tetanic in nature. if the break-shock is strong it excites, even when applied to the motor nerve, a response of tetanic quality. The so-called “over-maximal twitch,” now termed “supra-maximal response,” is a response of this kind. A reaction of like kind probably obtains in the afferent nerve when the single-shock applied to it is of comparably high value. In this case there is also a tetanic reaction from afferent nerve-fibres themselves. With weaker break-shock stimuli the origin of the tetanic character of the reflex discharge lies in the centre itself. It arises there from a “charge” process which is relatively long-lasting in comparison with the cycle of a nerve-impulse, and increases in intensity and duration with the number of afferent fibres excited.—R. J. Ludford and J. B. Gatenby: Dictyo-kinesis in germs-cells, or the distribution of the Golgi apparatus during cell-division. Maturation mitoses in the germ-cells of Cavia, Mus, Helix, Limnæa, and Stenobothrus were examined. In all cases the Golgi apparatus breaks up into its constituent granules, and these are distributed haphazardly to the two daughter-cells at mitosis. In no case examined are they divided between the daughter-cells as equally as are the chromosomes. Hence the Golgi apparatus takes no important part in the transmission of factors from cell to cell.—Dr. F. W. Edridge-Green: The effect of red fatigue on the white equation. A white equation is formed fry means of a mixture of a red of λ6670–6770 A., a green of λ5144–5156 A., and a violet of λ4250–4267 A., matching a simple white. When the eye is fatigued with light viewed through a red glass, or with pure sp_ectral light in the region of λ6700 Å., and the equation is again made, about half the amount of green is required. The white equation and its match cannot be due to similar physiological processes, or both would change in the same ratio. When the fatiguing light is in the region of λ7800 Å., no difference is seen between the mixed and simple white.—E. Ponder: A method for investigating the hsemolytic activity of chemical substances. The relation between the time taken by a given quantity of hasmolytic substance and the temperature at which it acts is expressed by a hyperbola. The relation between the constants of such a hyperbola and the quantity of hsemolytic substance to which it applies are given. Certain general relations hold for all substances examined. Experimental and calculated results are compared.—W. H. Pearsall: The development of vegetation in the English lakes, considered in relation to the general evolution of glacial lakes and rock basins. The English lakes are of the same age (glacial), of similar origin, and lie among rocks possessing relatively uniform characters. The differences they show are due to variations in the rates of erosion and sedimentation of the lake basins; therefore it becomes possible to describe the stages in the post-glacial development of a rock basin, and also of its vegetation. The differences observed between primitive and evolved lakes are regarded as being dependent upon their physical condition.