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Sixth Form Pure Mathematics, Volume 2, provides an introduction to inverse trigonometric functions, hyperbolic and inverse hyperbolic functions, and a range of mathematical methods including the use of determinants, the manipulation of inequalities, the solution of easy differential equations, and the use of approximate numerical methods. Complex numbers are defined and the various ways of representing and manipulating them are considered. Polar coordinates, curvature, an elementary study of lengths of curves and areas of surfaces of revolution, a more mature discussion of two-dimensional coordinate geometry than was possible in Volume 1, and an elementary introduction to the methods of three dimensional coordinate geometry comprise the geometrical content of the book.  Throughout, the authors have tried to preserve the concentric style which they used in Volume 1 and the many worked examples and exercises in each chapter are designed or chosen to provide a continuous reminder of the work of the preceding chapters. Except for Pure Geometry, the two volumes cover almost all of the syllabuses for Advanced Pure Mathematics of the nine Examining Boards.  This book provides an adequate course for mathematical pupils at Grammar Schools and a useful introductory course for Science and Engineering students in their first year at University or Technical College or engaged in private study.

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Group Theory in Quantum Mechanics: An Introduction to its Present Usage introduces the reader to the three main uses of group theory in quantum mechanics: to label energy levels and the corresponding eigenstates; to discuss qualitatively the splitting of energy levels as one starts from an approximate Hamiltonian and adds correction terms; and to aid in the evaluation of matrix elements of all kinds, and in particular to provide general selection rules for the non-zero ones. The theme is to show how all this is achieved by considering the symmetry properties of the Hamiltonian and the way in which these symmetries are reflected in the wave functions.  This book is comprised of eight chapters and begins with an overview of the necessary mathematical concepts, including representations and vector spaces and their relevance to quantum mechanics. The uses of symmetry properties and mathematical expression of symmetry operations are also outlined, along with symmetry transformations of the Hamiltonian. The next chapter describes the three uses of group theory, with particular reference to the theory of atomic energy levels and transitions. The following chapters deal with the theory of free atoms and ions; representations of finite groups; the electronic structure and vibrations of molecules; solid state physics; and relativistic quantum mechanics. Nuclear physics is also discussed, with emphasis on the isotopic spin formalism, nuclear forces, and the reactions that arise when the nuclei take part in time-dependent processes.  This monograph will be of interest to physicists and mathematicians.

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Index to Reviews, Symposia Volumes and Monographs in Organic Chemistry

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Index to Reviews, Symposia Volumes and Monographs in Organic Chemistry for the Period 1940-1960 presents a resume of published monographs, reviews, and symposia lectures in organic chemistry.   The editors adopted the plan of listings by symposia volume or journal, backed up by the total subject and author indexes. In this way the user can readily locate a particular article through the author index or the subject index; or should he recall that an article appeared in a particular source, the chronological listing in that source can be scanned quickly. The Index gives a convenient overview of the accomplishments of organic chemists during this very prolific period of the growth of the field. Frequently, several articles on the same or similar subject appear, hence the historical perspective can be sensed by rapid evaluation of the reviews selected.   This Index will be useful to research workers, teachers and students. It will also assist editors and authors to select specific areas which require critical review.

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Norman Kharasch, Walter Wolf, Elaine C. P. Harrison

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Concrete describes the properties of concrete, its manufacture, and use in building and civil engineering construction. A scientific approach to the properties of materials and concrete has been united with a practical approach to methods of construction.  The book begins with an introduction to the properties of concrete. Concrete is a constructional material which consists essentially of a binding agent and a mineral filler. The binding agent is a hydraulic cement which develops its strength when mixed with water. Separate chapters cover the manufacture and properties of concrete materials; mix design, i.e. proportioning of various constituents of concrete to produce the desired properties in both the plastic; concrete manufacturing; and quality control. Also discussed are the resistance of concrete to deterioration, surface treatment of concrete, and special concretes.  This book is intended to be useful to the student and graduate engineer as well as a reference book for the site engineer. To this end the theoretical and practical considerations have been combined in a degree found necessary in the author's practical experience.

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Applied Geophysics, U. S. S. R. illustrates a collection of selected papers that demonstrates methods in geophysical research. The journal presents the developments, done by Russian scientists, in the field of geophysics with bias toward the application of geophysical methods to the search for oil.  The compendium is divided into four parts encompassing 17 chapters. The articles are grouped into topics that discuss seismic methods, gravimetry, electrical sonde methods, and geophysical methods of logging. Certain chapters focus on simplified methods for determining the intensities of purely longitudinal waves and how the different parameters of the medium affect their frequency rate. The methods for measuring the force of gravity at sea; methods of electrical exploration in inaccessible regions of Siberia; and studies on use of radioactive logging in bore-hole investigations are covered as well.  The book will be of interest to geophysicists, geologists, applied physicists, and students of physics and geology.

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Fatigue of Metals provides a general account of the failure of metals due to fatigue, a subject of great practical importance in the field of engineering and metallurgy.  The book covers a wide range of topics on the study of the fatigue of metals. The text presents in the first three chapters the characteristics and detection of fatigue fractures; methods of fatigue testing; and the fatigue strengths of different materials. The resistance of materials to fatigue under complex stress; the determination and effects of stress concentration; influence of surface treatment on fatigue strength; and effects of corrosion and temperature are also studied in detail. In relation to the previous chapters of fatigue information, a chapter is devoted to engineering design to prevent fatigue. The last two chapters provide a brief historical survey of the developments of the study of the mechanism of fatigue and fatigue of non-metallic materials such as wood, plastic, rubber, glass, and concrete.  Mechanical engineers, designers, metallurgists, researchers, and students will find the book as a good reference material.

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A Course of Mathematics for Engineerings and Scientists

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A Course of Mathematics for Engineers and Scientists offers a mathematics course for undergraduate students reading science and engineering at British and Commonwealth Universities and colleges. The aim of this volume is to generalize and develop the ideas and methods of earlier volumes so that the student can appreciate and use the mathematical methods required in the more advanced parts of physics and engineering.  This book begins with elementary ideas of vector algebra which are generalized and developed in two ways. The first is an account of vector analysis and the differential and integral operations and theorems concerning vectors. These ideas find their first generalization in tensor analysis and the transformation of coordinates, including orthogonal curvilinear coordinates. The second development is to matrices, where the properties of arrays of elements, linear equations, and quadratic forms are shown to be the generalizations of elementary algebra and, using 'vector space', of familiar geometrical ideas to n dimensions. The solution of differential equations by series provides a general method for the solution of ordinary and some partial differential equations.   A discussion of the properties of the solutions in the light of the Sturm-Liouville theory introduces the conceptions of eigenvalues and orthogonal functions, forming a link with matrices. A chapter on the special functions gives some of the better known properties of Bessel, Legendre, Laguerre, and Hermite functions, which commonly occur in the solution of boundary and initial value problems.

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Proceedings of the Seventh National Conference on Clays and Clay Minerals

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Clays and Clay Minerals, Volume 5 contains the proceedings of the Seventh National Conference on Clays and Clay Minerals held in Washington, D.C., on October 20-23, 1958. The papers explore developments in clays and clay mineralogy and cover topics such as differential settling tendencies of clay minerals in saline waters; effect of seawater on clay minerals; clay mineralogy of bottom sediments; relationships in the montmorillonite group of clay minerals; and water content of vermiculite. Advances in X-ray diftractometry of clay minerals are also discussed.  This book is comprised of 23 chapters and begins with an analysis of differential settling velocities of individual clay mineral types and clay mineral mixtures in quiet saline water. The reader is then introduced to rapid dissolution of allophane and kaolinite-halloysite after dehydration; formation of chlorite-like structures from montmorillonite; regional clay mineral patterns in the Gulf of Mexico; and quantitative X-ray determinations of some aluminous clay minerals in rocks. The geology of clay deposits in parts of Washington and Idaho is also examined, along with the influence of exchangeable cations on the viscosity of clay suspensions. The final chapter presents the results of X-ray analysis of soil colloids by a modified salted paste method.  This volume will be of value to earth scientists, mineralogists, and those interested in clays.

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International Series of Monographs on Pure and Applied Biology Division: Modern Trends in Physiological Sciences

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Coronary Vasodilators assesses the state of knowledge of the pharmacological effects, the mechanisms responsible for these effects, and the therapeutic importance of classical drugs as well as recent medications on which experimental and clinical investigations are still too few to allow of definite judgment.    The book is organized into four chapters. Chapter I is devoted to the influences controlling coronary blood flow. Chapter II reviews the experimental methods commonly used in pharmacological research with a critical assessment of their possibilities and limitations. Chapter III discusses methods recommended by clinical research workers for evaluating the effectiveness of anti-anginal medications in the patient. Chapter IV describes pharmacology and clinical features of coronary vasodilators. The substances considered are group into four sections. The first contains the coronary vasodilator drugs actually used in cardiovascular therapeutics. The second consists of sympathicomimetic substances which modify general and local hemodynamic conditions profoundly and thus produce increased coronary flow. In the third section are brought together drugs used on man for particular therapeutic properties which have coronary vasodilator action, uncertain in the case of some, and which, for various reasons, cannot be used in the treatment of angina. The fourth section collects together a variety of substances, most of which are not drugs, reported in the literature as having vasodilator activity at coronary circulation level.

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International Series of Monographs in Analytical Chemistry

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Enzymatic Methods of Analysis attempts to cover all the aspects of modern enzymatic analysis. Enzymes possess a great potential usefulness in analytical chemistry. The specificity of enzymes can solve the primary problem of most analytical chemiststhe analysis of one substance in the presence of many similar compounds that interfere in the analysis.   The book begins with two introductory chapters devoted to general considerations of enzymes as reagents and methods of analysis of enzymatic reactions. The next four chapters deal with methods for the assay of specific enzymes, and substrate, activator, and inhibitor analysis using enzymes. In the last two chapters the immobilization of enzymes and the automation of enzymatic reactions are discussed. In addition, a listing of all commercially available enzymes is given in an appendix. It is hoped that the information presented will prove interesting and stimulating to all individuals engaged in research and development.

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George G. Guilbault, R. Belcher, H. Freiser

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The Physical Foundation of Biology: An Analytical Study offers a detailed account of the relationship between physics and biology. The discussion is based on a threefold development in theoretical science: the theory of automata (often designated as computers); the theory of information (mainly developed in communication engineering); and the theory of microscopic measurement in the atomic and molecular domain (based largely on quantum mechanics).  This book is comprised of five chapters and begins with an overview of the physical foundation of biology, paying particular attention to preformationism and the theory of epigenesis. The first chapter explores feedback and control by comparing the control apparatus of a more differentiated organism, the nervous system, with the corresponding achievements of electronic engineering. The reader is then introduced to the theory of information, focusing on the idea that certain quantitative aspects of the information content of messages can be separated from the specific physical features of the device sending the message. The following chapters deal with the importance of storage or memory devices for a complex functional mechanism; the compatibility of biotonic laws with the ordinary laws of physics; and physical interpretation of the theory of microscopic processes.  This monograph will be of interest to physicists, biologists, and chemists.

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Hydrodynamics of Oceans and Atmospheres is a systematic account of the hydrodynamics of oceans and atmospheres. Topics covered range from the thermodynamic functions of an ideal gas and the thermodynamic coefficients for water to steady motions, the isothermal atmosphere, the thermocline, and the thermosphere. Perturbation equations, field equations, residual equations, and a general theory of rays are also presented.  This book is comprised of 17 chapters and begins with an introduction to the basic equations and their solutions, with the aim of illustrating the laws of dynamics. The nonlinear equations of thermodynamics and hydrodynamics are analyzed using the methods of perturbation theory, with emphasis on the zero-order solution; zero-order states of an ideal gas; the first-order equations; the additive barotropic terms; and boundary conditions. The following chapters focus on the steady component of atmospheric pressure; free steady motion with or without rotation; field equations and general theorems relating to such equations; and the stratification of the Earth's atmosphere, oceans, and lakes. The next two chapters present calculations concerning the isothermal atmosphere, with particular reference to plane level surfaces with or without rotation. The final chapter looks at spherical level surfaces with rotation.  This monograph will be of interest to physicists, oceanographers, atmospheric scientists, and meteorologists.

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Cilia, Ciliated Epithelium, and Ciliary Activity

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International Series of Monographs on Pure and Applied Biology: Modern Trends in Physiological Sciences

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Cilia, Ciliated Epithelium, and Ciliary Activity reviews the state of knowledge of the activity of cilia and of the role these structures play in maintaining the normal physiology of the body, especially in the respiratory and genital systems. It relates the diversity of manifestations shown by cilia and ciliated epithelium in health and disease, and the effect of the physicochemical agents studied which influence the life and death of these structures.   The volume is organized into five sections. Section A provides a general discussion on the history of studies on the ciliated epithelium; the distribution and morphology of cilia; development, regeneration and transformation of ciliated cells; and culture of cilia and ciliated epithelium. Section B deals with ciliary activity while Section C examines the effects of physical and chemical agents on cilia. Section D takes up the function of cilia. Section E contains a list of references of the literature on these topics from the historical beginning of studies in the field to the time of writing.   This volume is intended to be a ready-made reference source for workers in the fields of biological sciences and medicine.

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José A. Rivera, P. Alexander, Z. M. Bacq

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Based on Lectures Given at the Manchester College of Science and Technology

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Introduction to Petroleum Chemicals emerged from a series of lectures on the petroleum chemical industry given at the Manchester College of Science and Technology during the fall and winter of 1959. The book does not claim to be an exhaustive treatment of petroleum chemicals, but attempts to a survey of the important aspects of the industry at its present level of development. The course was given by chemists and chemical engineers engaged in the chemical industry of Britain, giving the text a British and European, as distinct from American, flavor.  The book begins with a discussion of the cracking to olefins of liquid hydrocarbons. This is followed by separate chapters on separation processes for olefins; derivatives of ethylene and propylene; olefin polymerization process; and properties of polyethylenes and polypropylenes. Subsequent chapters cover the production and utilization of butadiene and isobutylene; aromatics production; manufacturing, properties, and uses of styrene and polystyrene; production of acetylene from hydrocarbons; and the carbon black industry.

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International Series of Monographs on Organic Chemistry

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Homolytic Aromatic Substitution deals with the theoretical aspects of homolytic aromatic substitution reactions. The effect of various kinds of free radicals on the substitution of atoms or groups (usually hydrogen) attached to aromatic nuclei is examined, and the preparative use of homolytic substitution reactions is also considered.  This book is comprised of seven chapters and begins with an introduction to the general characteristics of homolysis, along with homolytic and heterolytic aromatic substitution. The discussion then turns to the various theoretical approaches used to rationalize aromatic substitution, particularly those that are germane to a consideration of the problems of orientation and reactivity in homolytic substitution. The following chapters explore homolytic arylation reactions, including those between aryl radicals and aromatic substrates; relative rates of arylation and partial rate factors for phenylation; the reaction mechanism underlying intramolecular arylation; and homolytic alkylation reactions. The final chapter deals with hydroxylation and some other substitution reactions such as benzoyloxylation, acetyloxylation, halogenation, amination and amidation, and mercuration.  This monograph will be of interest to organic chemists.

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G. H. Williams, D. H. R. Barton, W. Doering

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Introduction to the Mechanics of the Solar System

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Introduction to the Mechanics of the Solar System introduces the reader to the mechanics of the solar system and covers topics ranging from the periods of the planets to their flattening and its effects on the orbits of satellites. Kepler's three laws of planetary motion are also discussed, along with the law of gravity; the two-body problem; and perturbations in the motions of the moon and the planets.  This book is comprised of four chapters and begins with an analysis of the kinematics of a single planet, focusing on the work of Johannes Kepler, particularly his determination of the orbits of the Earth and Mars and his formulation of his three laws of planetary motion. The following chapters explore systems of ordinary differential equations; determination of orbits using Laplace's method and Gauss' method; the equations of motion and their integrals; the perturbation equations of celestial mechanics; and Lagrange's solution of the three-body problem. The notations of the Earth and the moon are also considered.  This monograph is intended for astronomers and astronomy students.

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Reports from the First Interdisciplinary Conference in the Behavioral Science Division Held at the University of New Mexico

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Decisions, Values and Groups, Volume 1 contains the proceedings of the First Interdisciplinary Conference of the Behavioral Sciences Division of the Air Force Office of Scientific Research, held at the University of New Mexico in 1957. The papers explore the roles of decisions, values, and groups in the behavioral sciences and cover topics ranging from the use of mathematical models in decision making to the contribution of the laboratory to the study of individual differences. Theoretical contributions to small group research are also discussed.  This book is comprised of 22 chapters and begins with an overview of the merging of mathematical and statistical techniques with the empirical method in the study of behavior, as well as the place of decisions, values, and groups in behavioral science research. The reader is then introduced to the applications of mathematical models to decision processes, with particular reference to the automation of decision making. The following chapters focus on conceptualizations and designs for research in values and evaluative processes; theoretical aspects of small group research; and psychodynamic patterns of behavior; and special problems in the military. A non-introspective approach to the study of human motivation is described.  This volume will be of interest to behavioral scientists and social scientists.

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Theory of Elastic Thin Shells discusses the mathematical foundations of shell theory and the approximate methods of solution. The present volume was originally published in Russian in 1953, and remains the only text which formulates as completely as possible the different sets of basic equations and various approximate methods of shell analysis emphasizing asymptotic integration.  The book is organized into five parts. Part I presents the general formulation and equations of the theory of shells, which are based on the well-known hypothesis of the preservation of the normal element. Part II is devoted to the membrane theory--the most widely used approximate method of analysis of shells that was formulated at approximately the same time as the more general bending theory. In Part III methods of analysis of circular cylindrical shells with the aid of trigonometric series are considered. Part IV is essentially mathematical in character and its purpose is to justify the approximate methods of shell analysis. In Part V approximate methods of analysis of shells are formulated.

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A. L. Gol'Denveizer, Th. Von Kármán, H. L. Dryden

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How to Find Out in Mathematics: A Guide to Sources of Information, Second Revised Edition presents updated topics about probability and statistics, dictionaries and encyclopedias, computing, and mathematical education. The book discusses the modifications of the content of professional actuarial examinations; the assimilation of modern mathematics into the school curriculum; and the establishment of government departments to administer financial support for mathematical research. The text also describes the efforts to improve communication between mathematicians (i.e. the inception of the Mathematical Offprint Service and the publication of Contents of Contemporary Mathematical Journals by the American Mathematical Society). People who are studying, teaching, or applying mathematics will find the book helpful.

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Selected Constants Relative to Semi-Conductors

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Tables of Constants and Numerical Data Affiliated to The International Union of Pure and Applied Chemistry

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Selected Constants Relative to Semi-Conductors presents the physical constants of semiconductors in Table form. The values of the electronic properties of semiconductors presented in the Table are parameters intended for use in theoretical and phenomenological equations relative to the band theory for these materials. In addition to data specific to band structure, the Table also includes mobilities of electrons and holes and their variation with temperature. Data of a general physical character are also presented, since the researcher very often finds use for values of this type. The following quantities are given when available: symmetry group and crystal parameters, refractive index, dielectric constant, effective ionic charge, work function, photoemission work function, piezoresistance coefficient, elastic coefficients, phonon temperature, Debye temperature, magnetic susceptibility, coefficient of linear expansion, fusion temperature, sublimation temperature, specific heat at constant pressure, latent heat of fusion, latent heat of sublimation, thermal conductivity, disorder factor, and density.