textbook. Basic description is attempted, and the bibliography has been specifically chosen to guide the reader toward a fuller treatment of his special ised interests. No fully satisfactory term has yet emerged to describe the processing of minerals, which is also called "ore dressing," "mineral dressing," "mineral engineering" and, in the University of London degree course "mineral technology." The dressing of ores was an excellent description of the older processes which aimed to break down rock to appropriate sizes, grade it, and separate the heavy fraction from the light one in each grade or size by gravity methods. The work done in the mill today goes far beyond these simple operations, and requires some knowledge of physical chemistry, particularly the branches which deal with the physics and chemistry of surfaces and of the interphase between solid particle and the surrounding liquid. At the same time, the engineer must not become so absorbed in the study of fundamental and applied technology as a physico-chemical science that he overlooks the mechanical, economic, and humanistic aspects oli his work. He is an engineer, a chemist, a physicist, and an administrator and, as such, should have a sound scientifj. c and cultural education. Technically, his work is to extract the valuable minerals from the ore sent to his mill; economically, it is to balance all the financial costs and returns in such a way as to ensure the maximum profit from the operation."

Cratons and Fold Belts of India, is a unique attempt at presenting geological characteristics and evolution of the fold belts and the cratonic areas of the Indian shield. The author has evaluated the different evolutionary models for each fold belt in light of all the currently available geological and geochronological informations that are clearly listed. Shortcomings, if any, of each model are stated and a viable geodynamic model is presented for each fold belt. The book is self-contained it includes an introduction to the processes of mountain building, especially plate tectonics theory with its application to the evolution of the Himalaya as an illustrative example so that the reader can better appreciate the novel approach to the evolution of Proterozoic fold belts. The author eschews a detailed account of the fold belts for a clear description of all the concepts that go into building models. It is primarily written for graduate students, teachers and for those geoscientists who aspire to know all about the Indian shield."

This volume contains a selection of papers presented to the Fourth International Symposium on Environmental Biogeochemistry (ISEB), and a conference on Biogeochemistry in Relation to Mining Industry and Environmental Pollution (Leaching Conferenc, held in Canberra, Aust ralia on August 26-31 and September 3-4, 1979, respectively. The ISEB were established to provide "a forum for uninhibited exchange of information and ideas among the biological, chemical, atmospheric and geolopical scientists working in the common area of biogeochemistry, encompassing soil and other earth sciences as weIL as the hydrosphere and atmosphere," By linking the fourth ISEB with the Leachinp Conference the scop.e of discussions was extended to encompass the application of biogeochemical processes to the mining industry. This wide-ranging philosophy is reflected in the breadth and diversity of the subjects covered in this book. The published papers are expanded versions of those presented at the meetings. They have all been scrutinized by at least one referee in addition to the editors. About 20% of the contributions to the meetings are not included, either because authors did not wish to publish or because the papers were not accepted by the editors."

Igneous petrology was to some extent essentially a descriptive sci ence until about 1960. The results were mainly obtained from field work, major element analyses, and microscopical studies. During the 1960's two simultaneous developments took place, plate tectonics became generally accepted, and the generation of magmas could now be related to the geodynamic features like convection cells and subduction zones. The other new feature was the development of new analytical apparatus which allowed high accuracy analyses of trace elements and isotopes. In addition it became possible to do ex perimental studies at pressures up to 100 kbar. During the 1970's a large amount of analytical data was obtained and it became evident that the igneous processes that control the compositions of magmas are not that simple to determine. The composition of a magma is controlled by the compositions of its source, the degree of partial melting, and the degree of fractionation. In order to understand the significance of these various processes the relationship between the physical processes and their geochemical consequences should be known. Presently there are several theories that attempt to explain the origin of the various magma types, and these theories can only be evaluated by turning the different ideas into quantitative models. We will so to speak have to do some book keeping for the various theories in order to see which ones are valid. the present book is intended as an introduction to the more fun damental aspects of quantitative igneous petrology."

In modern sediment research on contaminants five aspects are discussed which, in an overlapping succession, also reflect develop ment of knowledge on particle-associated pollutants during the past twenty-five years: (1) identification of sources and their distribution; (2) evaluation of solid/solution relations; (3) study of transfer mecha nisms to biological systems; (4) assessment of environment impact; and (5) selection and further development of remedial measures, in par ticular, of dredged materials. Scientific research and practical develop ment are still expanding in all these individual aspects. Similar to other waste materials, management of contaminated sed iments requires a holistic approach. This means that assessment of biogeochemical reactions, interfacial processes and transfer mecha nisms as well as the prognosis of long-term borderline conditions, in particular of capacity-controlling properties, should be an integrated part of the wider management scheme, i.e., the analytical and experi mental parameters should always be related to potential remediation options for a specific sediment problem. The underlying coordinated project, which was funded by the German Federal Ministry for Science and Technology (now the Federal Ministry for Education, Science, Research and Technology) provided excellent opportunities for multidisciplinary effort, bringing together biologists, chemists, engineers, geologists and other researchers. During its active phase, the group attracted much interest nationally and internationally. The group members highly appreciate the manifold contacts and invitations during the past five years."

Microscopy is a servant of all the sciences, and the microscopic examina tion of minerals is an important technique which should be mastered by all students of geology early in their careers. Advanced modern text books on both optics and mineralogy are available, and our intention is not that this new textbook should replace these but that it should serve as an introductory text or a first stepping-stone to the study of optical mineralogy. The present text has been written with full awareness that it will probably be used as a laboratory handbook, serving as a quick reference to the properties of minerals, but nevertheless care has been taken to present a systematic explanation of the use of the microscope as well as theoretical aspects of optical mineralogy. The book is therefore suitable for the novice either studying as an individual or participating in classwork. Both transmitted-light microscopy and reflected-light microscopy are dealt with, the former involving examination of transparent minerals in thin section and the latter involving examination of opaque minerals in polished section. Reflected-light microscopy is increasing in importance in undergraduate courses on ore mineralisation, but the main reason for combining the two aspects of microscopy is that it is no longer acceptable to neglect opaque minerals in the systematic petrographic study of rocks. Dual purpose microscopes incorporating transmitted- and reflected-light modes are readily available, and these are ideal for the study of polished thin sections."

During the last few years, carbonatites have received a considerable amount of attention. Some of this interest was no doubt kindled by the importance of volatiles in the Earth's mantle, particularly CO , by the fact that carbonatites 2 can be used to monitor the chemical evolution of the sub-continental upper mantle, and by the fact that carbonatites may be effective metasomatizing agents at both mantle and crustal levels. The interest in Oldoinyo Lengai has extended over at least 100 years, but it was not until the eruptions of 1960, when the unique carbonatitic nature of its lavas was recognized, that the volcano took on special significance in volcanology and igneous petrology. The recognition of carbonatitic flows coin cided with the first successful laboratory experiments carried out on carbonatitic melts. Since then, Oldoinyo Lengai has formed a cornerstone in all carbonatite discussions. It is probably true to say that the findings from Oldoinyo Lengai have dominated our ideas about carbonatites, in spite of the fact that the alkali rich, natrocarbonatitic lavas of Oldoinyo Lengai are markedly different from other carbonatites.

Early in this century, the newly discovered x-ray diffraction by crystals made a complete change in crystallography and in the whole science of the atomic structure of matter, thus giving a new impetus to the development of solid-state physics. Crystallographic methods, pri marily x-ray diffraction analysis, penetrated into materials sciences, mol ecular physics, and chemistry, and also into many other branches of science. Later, electron and neutron diffraction structure analyses be came important since they not only complement x-ray data, but also supply new information on the atomic and the real structure of crystals. Electron microscopy and other modern methods of investigating mat ter-optical, electronic paramagnetic, nuclear magnetic, and other res onance techniques-yield a large amount of information on the atomic, electronic, and real crystal structures. Crystal physics has also undergone vigorous development. Many re markable phenomena have been discovered in crystals and then found various practical applications. Other important factors promoting the development of crystallog raphy were the elaboration of the theory of crystal growth (which brought crystallography closer to thermodynamics and physical chem istry) and the development of the various methods of growing synthetic crystals dictated by practical needs. Man-made crystals became increas ingly important for physical investigations, and they rapidly invaded technology. The production of synthetic crystals made a tremendous impact on the traditional branches: the mechanical treatment of mate rials, precision instrument making, and the jewelry industry.

This monograph was begun with two objectives in mind. The first was to provide a review of research involving the application of neodymium isotopic measurements to pro blems in earth science. In the process of organizing to do this, I realized that the research in this field had produced a need for an updated review of the underlying paradigms. This need had arisen because of the special properties of the samarium-neodymium isotopic system, and because the research had transgressed the traditional boundaries be tween the subfields of earth science. Without such a review, the significance of the results seemed likely to remain un necessarily obscure to interested scientists from related disciplines. Consequently, the second objective became the provision of a theoretical framework for the application of neodymium isotopic studies. Much of what this contains is not new, but it is drawn together here for the first time. At the time the writing was initiated, the literature of the field was still relatively limited. Over the past 5 years it has grown enormously. Considering the rate at which the writing progressed, it became clear that this could not be a fully up-to-date review and still reach completion. The selection of material for the review sections is biased toward earlier studies. Part I presents most of the background information."

1 The content ofthis article is based on a German book version ) which appeared at the end of the year 1986. The author tried to incorporate - as far as possible - new important results published in the last year. But the literature in the field of "convection and inhomogeneities in crystal growth from the melt" has increased so much in the meantime that the reader and the collegues should make allowance for any incompleteness, also in the case that their important contributions have not been cited. This could for example hold for problems related to the Czochralski growth. But especially for this topic the reader may be refered to the forthcoming volume of this series, which contains special contributions on "Surface Tension Driven Flow in Crystal Growth Melts" by D. Schwabe and on "Convection in Czochralski Melts" by M. Mihelcic, W. Uelhoff, H. Wenzl and K. Wingerath. The preparation of this manuscript has been supported by several women whose help is gratefully acknowledged by the autor: Mrs. Gisela Neuner for the type writing, Mrs. Abigail Sanders, Mrs. Fiona Eels and especially Prof. Nancy Haegel for their help in questions of the English language and Mrs. Christa Weber for reading corrections. Also the good cooperation with the Springer Verlag, especially Mrs. Bohlen and with the managing editor of Crystals, Prof. H. C. Freyhardt, who critically read the manuscript, is acknowledged.

Time is a major factor in Quaternary science. Without a trustworthy chronometer any interpretation of changes in proxy data of stratigraphical origin is on weak ground. In fact, any attempt at a sound reconstruction of timing and rates of past climatic change as well as the response of the biosphere can only be achieved on the basis of a reliable chronology. Moreover, all correlations and comparisons through time on a continental or global scale depend heavily on the reliability of the time-scale used. Therefore the establishment of an absolute time-scale is a fundamental goal. In this contribution we refer to the term "absolute time-scale" as a time-scale consisting of ages determined on the basis of sidereal years. Traditional stratigraphical methods of absolute dating include the Swedish glacial varve chronology, already developed early in this century by De Geer (1912) and since then continuously improved (e.g. Stromberg 1985; Cato 1987). Unfortunately, however, a spatial correlation with other stratigraphies outside Fennoscandia is difficult.

The reserves, or extractable fraction, of the fuel-mineral endowment are sufficient to supply the bulk of the world's energy requirements for the immediately forseeable future-well into the next century according to even the most pessimistic predictions. But increasingly sophisticated exploration concepts and technology must be employed to maintain and, if possible, add to the reserve base. Most of the world's fuel-mineral resources are in sedimentary rocks. Any procedure or concept that helps describe, under stand, and predict the external geometry and internal attributes of major sedimentary units can therefore contribute to discovery and recovery of coal, uranium, and petroleum. While conceding the desirability of renewable and nonpolluting energy supply from gravitational, wind, or solar sources, the widespread deployment of these systems lies far in the future-thus the continued commercial emphasis on conventional nonrenewable fuel mineral resources, even though their relative significance will fluctuate with time. For example, a decade ago the progilostications for uranium were uniformly optimistic. But in the early 1980s the uranium picture is quite sombre, although unlikely to remain permanently depressed. Whether uranium soars to the heights of early expectations remains to be seen. Problems of waste disposal and public acceptance persist. Fusion reactors may ultimately eliminate the need for uranium in power generation, but for the next few decades there will be continued demand for uranium to fuel existing power plants and those that come on stream. This book is, to some extent, a hybrid."

Archaean Geochemistry 1972 - 1984 The realisation that the continental crust contains well-preserved relics which date as far back as 4/5 of the Earth's age has given a great impetus to the study of early Precambrian terrains. As late as the mid-sixties the Archaean still constituted the 'terra-in cognita' of earth science. High metamorphic grades, poor out crop, and not least a widely assumed obliteration of early crustal records by convective recycling and thermal reworking had com bined to discourage research in this field. Many excellent local studies existed, notably around gold mining centres, but remained unrelated to a broader regional and theoretical understanding. This situation has changed as the consequence of two inter-related factors: (1) advances in isotopic methods and their application to Precambrian rocks, and (2) the recognition that some of the oldest terrains have retained a wealth of primary igneous and sedi mentary textures and even geochemical characteristics."

Drilling deep into the earth holds a fascination for earth scientists derived in part from the fact that the drill hole is the ultimate test of a hypothesis. When surface exploration methods have been fully uti lized and all the geological inferences drawn about the structure be neath the surface, we must finally drill to sample directly the third dimension of the crust of the earth. The drill is thus the tool of choice of the energy and minerals re sources industry. Because of high cost, drilling has been only sparing ly used for solving fundamental problems in the earth sciences. But now, having used the quite sophisticated methodology of exploration geophysics, the exciting structural detail emerging from seismic re flection profiling in particular has led several nations to begin a major program of scientific drilling to solve some of the major prGb lems in the earth sciences. Hhat is described in this volume are the blueprints for national re search programs in France, the Federal Republic of Germany, Japan and the United States. The Soviet Union has already embarked on a major drilling effort, the results of which are soon to be published. Results, of course, are still few, and this first volume is more concerned with the problems to be solved."

Copper belongs to those metals whose concentrations in nature arise from a broad diversity of endogeneous and exogeneous pro- cesses, which applies to essentially all genetic classes of ore deposits. This is the first proceedings volume on copper metallogeny to cover the worldwide distribution of the four main groups of cop- per deposits, including in Part I: copper-nickel deposits with cobalt and platinum group elements; Part II: copper-molybde- num-gold deposits with silver, zinc, and lead; Part III/IV: copper- zinc-lead deposits (with silver etc.). On the occasion of the 27th International Geological Congress in Moscow, USSR, a symposium on copper metallogeny was held, dealing with metallogenesis and mineral deposits. The symposium was organized and sponsored by three international societies en- gaged in the field of ore deposits: The Society of Economic Geol- ogy (SEG), the Society of Geology Applied to Mineral Deposits (SGA) and the International Association on the Genesis of Ore Deposits (IAGOD). Invited papers were presented in four ses- sions: (1) Copper deposits in mafic and ultramafic complexes, (2) Porphyry copper deposits, (3) Copper deposits of volcanic-hydro- thermal association, and (4) Sediment-hosted copper deposits. The sessions were chaired by A. D. Genkin, A. J. Naldrett, J. D. Ridge and G. I. Gorbunov; V.1. Sotnikov, A. Soregaroli, R. H. Sillitoe and V. A. Evstrakhin; F. M. Vokes, A.1. Krivtsov, M. Solomon and N. I. Eremin; G. H. Friedrich, Yu. V. Bogdanov, A.C. Brown and F.P. Krendelev.

This book is intended primarily for exploration geologists and post graduate students attending specialist courses in mineral exploration. Exploration geologists are engaged not only in the search for new mineral deposits, but also in the extension and re-assessment of existing ones. To succeed in these tasks, the exploration geologist is required to be a "generalist" of the Earth sciences rather than a specialist. The exploration geologist needs to be familiar with most aspects of the geology of ore deposits, and detailed knowledge as well as experience play an all important role in the successful exploration for mineral commodities. In order to achieve this, it is essential that the exploration geologist be up to date with the latest developments in the evolution of concepts and ideas in the Earth sciences. This is no easy task, as thousands of publications appear every year in an ever increasing number of journals, periodicals and books. For this reason it is also difficult, at times, to locate appropriate references on a particular mineral deposit type, although this problem is alleviated by the existence of large bibliographic data bases of geological records, abstracts and papers on computers. During my teaching to explorationists and, indeed, during my years of work as an explorationist, the necessity of having a text dealing with the fundamental aspects of hydrothermal mineral deposits has always been compelling. Metallic mineral deposits can be categorised into three great families, namely: (I) magmatic; (2) sedimentary and residual; (3) hydrothermal."

Few knowledgeable people would deny that the field of mineral exploration is facing some difficult times in the foreseeable future. Among the woes, we can cite a worldwide economic uneasiness reflected by sluggish and at times widely fluctuating metal prices, global financial uncertainties, and relentless pressures on costs despite a substantial slowing down of the rate of inflation. Furthermore, management is forced to tum to more sophisticated and expensive technologies and to look farther afield to more remote regions, as the better quality and more easily accessible ore deposits have now been revealed. This rather gloomy outlook should persuade explorationists to cast about for a new philosophy with which to guide mineral exploration through the challenging decades ahead. Once already, in the early 1960s, a call for change had been heard (Ref. 30 in Chapter 1), when it became obvious that the prospecting methods of yesteryear, so successful in the past, could not keep up with the rapidly growing demand for minerals of the postwar period. The answer, a massive introduction of sophisticated geophysical and geochemical technologies backed by new geo logical models, proved spectacularly successful throughout the 1960s and the 1970s. But for both economic and technological reasons, the brisk pace of the last two decades has considerably slowed down in the early 1980s, as if a new threshold has been reached."

The problem of time-and strata-bound formation of ore deposits has during the past decade become one of the most debated topics in cur rent international discussion. Due to the amazing results of modern mineral exploration and world-wide geophysical research, the mutual relationship between the complex geological history pf a crustal seg ment and the development of distinct metallogenic provinces (ore belts) has received much interest. Reviewing the earth's history in this light one can now recognize metallogenic epochs even of global range which document the existence of world-wide time-bound ore enrich ments. The knowledge of these metallogenetic processes has been growing step by step for several decades. It began with simple observations and sceptic interpretations, which at first threw heretical spot lights on to the edifices of the prevailing theories on granitic differentiation as the favoured source of ore deposits. It was obvious that the new ideas at first referred to ore enrichments in sedimentary sequences, nowadays summarized under the term strata-bound, and mainly interpreted as stratiform or sedimentary ore deposits. Moreover, the modern term "strata-bound" also includes ore mineralizations which are bound to distinct units of layered (intrusive or extrusive) igneous complexes as a general descriptive term without genetical restriction Albert Maucher is one of the representatives of the initial era who discussed these genetical questions critically in the decade before the 2nd World War."

Metals in the hydrological cycle represent a very broad subject covering all parts of the geological cycle. The present version of this book, therefore, would not have been possible without the comments and suggestions for improvement on draft ver- sions of the various chapters by a large number of colleagues. We wish to express our gratitude to: P.A. Cawse (AERE, UK), J.N. Galloway (University of Virginia, USA) and S.E. Lindberg (Oak Ridge National Labo- ratory, USA) for reviewing the chapter on atmospheric trace metals. G. Batley (CSIRO, Australia) and B.T. Hart (Chisholm In- stitute of Technology, Australia) for reviewing the chapter on speciation of dissolved metals. E.K. Duursma (Delta Institute, The Netherlands), J.M. Bewers and P.H. Yeats (Bedford Institute of Oceanography, Canada) and D. Eisma (Netherlands Institute for Sea Re- search, the Netherlands) for reviewing the chapter on estuaries. P. Baccini (EAWAG, Switzerland) and W. Davison (Fresh- water Biological Association, UK) for reviewing the chapter on lakes. E.T. Degens (University of Hamburg, W-Germany) for re- viewing the chapter on the oceans, and J.P. Al (Public Works Department, The Netherlands) for reviewing most of the indi- vidual chapters. Without the collaboration of these colleagues this book would not have been possible in its present form.

The preparation of a volume on this topic was undertaken with some hesitancy on my part because the ramifications of the mineralogy of apatite involve both bio logical and physical sciences in very elaborate ways. This hesitancy may have arisen in part from the realization that considerable skill would be required in order to extract the meaning from the thousands of papers that have appeared within the past twenty years; the task of attempting to extract and assemble the usable information seemed gigantic. Greatly adding to the difficulty was the fact that a considerable portion of these journal articles contain nothing of value and further confuse a most complex topic. Nevertheless, it was thought that some of my formal education in the bio logical sciences, which has been greatly extended and augmented during the past fifteen years, might be integrated with my more extensive education and experience in chemistry, crystallography, mineralogy, geology and physics in order to pro duce something that would relate to the mineral apatite and its extremely diverse occurences in nature. At the same time it seemed essential to point out some of the many important aspects in which this knowledge bears on geology, agriculture, chemical engineering, medicine and dentistry."

The idea for a book on anorthosites came to me in January of 1986 while returning to Houston after holiday festivities in Dallas. The original idea was a review paper on anorthosites, but by the time I reached Houston, the subject material I contemplated induding was obviously too extensive for a single paper. The Director of the Lunar and Planetary Institute, Kevin Burke, was receptive to the idea of a book, and suggested that I contact Peter Wyllie, who serves as Editor of the Springer-Verlag series Minerals and Rocks. This effort, which I originally expected would take about a year, has taken nearly 6. I have many excuses- indolence, moving to another continent, other commitments, etc.-but the basic truth is that writing a book is much larger an undertaking than can be anticipated. Many people are aware of this, and I was duly forewarned. . But why write a book on anorthosites? This is a very good question, which I have considered from many angles. One rationale can be expressed in terms of a comparison between anorthosite and basalt. A first-order understanding of basalt genesis has been extant for many years. By contrast, there is little agreement about the origin of anorthosite. There are good reasons for studying and writing about basalt: it is the most abundant rock type on the Earth's surface, and is also plentiful on the surfaces of the other terrestrial planets.

This book introduces aqueous geochemistry applied to geothermal systems. It is specifically designed for readers first entering into the world of geothermal energy from a variety of scientific and engineering backgrounds, and consequently is not intended to be the last word on geothermal chemistry. Instead it is intended to provide readers with sufficient background knowledge to permit them to subsequently understand more complex texts and scientific papers on geothermal energy. The book is structured into two parts. The first explains how geothermal fluids and their associated chemistry evolve, and shows how the chemistry of these fluids can be used to, deduce information about the resource. The second part concentrates on survey techniques explaining how these should be performed and the procedures which need to be adopted to ensure reliable sampling and analytical data are obtained. A geothermal system requires a heat source and a fluid which transfers the heat towards the surface. The fluid could be molten rock (magma) or water. This book concentrates on the chemistry of the water, or hydrothermal, systems. Consequently, magma-energy systems are not considered. Hot-dry rock (HDR) systems are similarly outside the scope of this text, principally because they contain no indigenous fluid for study. Both magma-energy and HDR systems have potential as energy sources but await technological developments before they can be exploited commercially. Geothermal systems based on water, however, are proven energy resources which have been successfully developed throughout the world.

33 14. 3. 5 REE between Plagioclase and Aqueous Fluid 0 Cullers et al. (1973) measured the distribution of REE at 850 C and 750 bars pressure between a natural plagioclase, An, and gaseous water. The rare earths 65 favored the plagioclase by a factor which varies from about 25 for Ce to 10 for Lu. Data were also obtained for forsterite, diopside, enstatite and two rhyolite glasses, on the one hand, and water on the other hand, thereby permitting estimation of the partition coefficients between all pairs of phases. 14. 4 Chemical Substitution in Natural Feldspars 14. 4. 1 Introduction It is quite impracticable to give all the data on chemical substitution in natural feldspars: indeed many of the details are significant only to some particular pegmatite or rock body. As far as possible, emphasis is placed on features of general interest to crystal chemists and to petrologists. Ironically the well established features can be described more easily than the uncertain ones, and unfortunately it is necessary to use valuable space on data of dubious value. The bibliography is fairly complete, but it was impracticable to locate all data, especially those in obscure journals. Each reference is followed by a list of the elements referred to in the paper, thereby permitting a reader to compile a fairly compre hensive set of references on any chosen element. Not all papers are mentioned in the text. The book on Geochemistry and Mineralogy of Rare Elements, etc."

Glass Chemistry is concerned with the relation of chemical composition, structure and properties of various glasses. The book has been translated from the third German edition, which serves as a textbook for university students in materials sciences and a reference book for scientists and engineers in glass science and production. The central themes of the book are the chemistry and physics of glass. Detailed knowledge of the compositional and structural facts is the basis for the systematic development of new glasses as construction and optical materials.
Glass Chemistry is an interdisciplinary book on the borderlines between chemistry, physics, mineralogy and even biology and medicine. The book represents a well balanced treatment for students, scientists and engineers.

New methods for the determination of the nature, proportion, and distribution of structural defects in microcrystallized lamellar systems are of utmost importance not only to experimentalists but also to theoreticians. Mathematical formalism - indispensable for such analyses - is well-illustrated by various examples, allowing this method to be easily adopted and even to be applied to other solids with lamellar or pseudo-lamellar structures.