the procedures and concepts employed by those who study the inorganic world. Physical science, like all the natural sciences, is concerned with describing and relating to one another those experiences of the surrounding world that are shared by different observers and whose description can be agreed upon. One of its principal fields, physics, deals with the most general properties of matter, such as the behaviour of bodies under the influence of forces, and with the origins of those forces. In the discussion of this question, the mass and shape of a body are the only properties that play a significant role, its composition often being irrelevant. Physics, however, does not focus solely on the gross mechanical behaviour of bodies, but shares with chemistry the goal of understanding how the arrangement of individual atoms into molecules and larger assemblies confers particular properties. Moreover, the atom itself may be analyzed into its more basic constituents and their interactions. The present opinion, rather generally held by physicists, is that these fundamental particles and forces, treated quantitatively by the methods of quantum mechanics, can reveal in detail the behaviour of all material objects. This is not to say that everything can be deduced mathematically from a small number of fundamental principles, since the complexity of real things defeats the power of mathematics or of the largest computers. Nevertheless, whenever it has been found possible to calculate the relationship between an observed property of a body and its deeper structure, no evidence has ever emerged to suggest that the more complex objects, even living organisms, require that special new principles be invoked, at least so long as only matter, and not mind, is in question. The physical scientist thus has two very different roles to play: on the one hand, he has to reveal the most basic constituents and the laws that govern them; and, on the other, he must discover techniques for elucidating the peculiar features that arise from complexity of structure without having recourse each time to the fundamentals. This modern view of a unified science, embracing fundamental particles, everyday phenomena, and the vastness of the Cosmos, is a synthesis of originally independent disciplines, many of which grew out of useful arts. The extraction and refining of metals, the occult manipulations of alchemists, and the astrological interests of priests and politicians all played a part in initiating systematic studies that expanded in scope until their mutual relationships became clear, giving rise to what is customarily recognized as modern physical science. For a survey of the major fields of physical science and their development, see the articles physical science and Earth sciences. Additional reading Eric M. Rogers, Physics for the Inquiring Mind: The Methods, Nature, and Philosophy of Physical Science (1960), is especially good on the origins of astronomy and mechanics, with minimal mathematics. Of the many general student texts, the Berkeley Physics Course, 5 vol. (196571), covering mechanics, electricity and magnetism, waves, quantum physics, and statistical physics; and David Halliday and Robert Resnick, Fundamentals of Physics, 3rd ed. (1988), are recommended. The Feynman Lectures on Physics, 3 vol. (196365), by Richard P. Feynman, Robert B. Leighton, and Matthew Sands, instructs students and teachers in the whole range of physical concepts, with characteristically revealing insights. See also Jefferson Hane Weaver (ed.), The World of Physics: A Small Library of the Literature of Physics from Antiquity to the Present, 3 vol. (1987), an anthology covering the history of the major concepts of physics.Expositions of more limited scope, reflecting on general principles for the benefit of nonspecialists, include H. Bondi, Assumption and Myth in Physical Theory (1967); Richard P. Feynman, The Character of Physical Law (1965); and J.M. Ziman, Public Knowledge: An Essay Concerning the Social Dimension of Science (1968). At a more advanced level, M.S. Longair, Theoretical Concepts in Physics (1984); and Peter Galison, How Experiments End (1987), illustrate typical research procedures by means of case studies. Ernst Mach, The Science of Mechanics, 6th ed. (1974; originally published in German, 9th ed., 1933), is both a detailed history and a classic critique of fundamental assumptions. E.T. Whittaker, A History of the Theories of Aether and Electricity, vol. 1, The Classical Theories, rev. and enlarged ed. (1951, reprinted 1973), is equally detailed but less philosophically oriented.Special topics in more recent physics are treated by Albert Einstein, Relativity: The Special & the General Theory (1920; originally published in German, 1917), and many later editions; Wolfgang Rindler, Essential Relativity: Special, General, and Cosmological, rev. 2nd ed. (1979); Steven Weinberg, The Discovery of Subatomic Particles (1983), and The First Three Minutes: A Modern View of the Origin of the Universe, updated ed. (1988); Nathan Spielberg and Bryon D. Anderson, Seven Ideas that Shook the Universe (1985); P.C.W. Davies, The Forces of Nature, 2nd ed. (1986); A. Zee, Fearful Symmetry: The Search for Beauty in Modern Physics (1986); and Tony Hey and Patrick Walters, The Quantum Universe (1987).The principles of catastrophe theory are presented, without mathematical detail, in V.I. Arnold, Catastrophe Theory, 2nd rev. and expanded ed. (1986; originally published in Russian, 2nd ed. enlarged, 1983), which is notably scornful of speculative applications. A full treatment is provided in Tim Poston and Ian Stewart, Catastrophe Theory and Its Applications (1978).Introductions to chaotic processes are found in A.B. Pippard, Response and Stability: An Introduction to the Physical Theory (1985); and James Gleick, Chaos: Making a New Science (1987). More systematic is J.M.T. Thompson and H.B. Stewart, Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists (1986). Anthologies of influential early papers are Bai-Lin Hao (comp.), Chaos (1984); and Predrag Cvitanovic (comp.), Universality in Chaos (1984). Sir A. Brian Pippard Concepts fundamental to the attitudes and methods of physical science Fields Newton's law of gravitation and Coulomb's electrostatic law both give the force between two particles as inversely proportional to the square of their separation and directed along the line joining them. The force acting on one particle is a vector. It can be represented by a line with arrowhead; the length of the line is made proportional to the strength of the force, and the direction of the arrow shows the direction of the force. If a number of particles are acting simultaneously on the one considered, the resultant force is found by vector addition; the vectors representing each separate force are joined head to tail, and the resultant is given by the line joining the first tail to the last head. In what follows the electrostatic force will be taken as typical, and Coulomb's law is expressed in the form F = q1q2r/4pe0r3. The boldface characters F and r are vectors, F being the force which a point charge q1 exerts on another point charge q2. The combination r/r3 is a vector in the direction of r, the line joining q1 to q2, with magnitude 1/r2 as required by the inverse square law. When r is rendered in lightface, it means simply the magnitude of the vector r, without direction. The combination 4pe0 is a constant whose value is irrelevant to the present discussion. The combination q1r/4pe0r3 is called the electric field strength due to q1 at a distance r from q1 and is designated by E; it is clearly a vector parallel to r. At every point in space E takes a different value, determined by r, and the complete specification of E(r)that is, the magnitude and direction of E at every point rdefines the electric field. If there are a number of different fixed charges, each produces its own electric field of inverse square character, and the resultant E at any point is the vector sum of the separate contributions. Thus the magnitude and direction of E may change in a complicated fashion from point to point. Any particle carrying charge q that is put in a place where the field is E experiences a force qE (provided the other charges are not displaced when it is inserted; if they are E(r) must be recalculated for the actual positions of the charges). A vector field, varying from point to point, is not always easily represented by a diagram, and it is often helpful for this purpose, as well as in mathematical analysis, to introduce the potential f, from which E may be deduced. To appreciate its significance, the concept of vector gradient must be explained. Gradient Figure 6: Definition of a vector gradient (see text). The contours on a standard map are lines along which the height of the ground above sea level is constant. They usually take a complicated form, but if one imagines contours drawn at very close intervals of height and a small portion of the map to be greatly enlarged, the contours of this local region will become very nearly straight, like the two drawn in Figure 6 for heights h and h + dh. Walking along any of these contours, one remains on the level. The slope of the ground is steepest along PQ, and, if the distance from P to Q is dl, the gradient is dh/dl or dh/dl in the limit when dh and dl are allowed to go to zero. The vector gradient is a vector of this magnitude drawn parallel to PQ and is written as grad h, or h. Walking along any other line PR at an angle q to PQ, the slope is less in the ratio PQ/PR, or cos q. The slope along PR is (grad h) cos q and is the component of the vector grad h along a line at an angle q to the vector itself. This is an example of the general rule for finding components of vectors. In particular, the components parallel to the x and y directions have magnitude h/x and h/y (the partial derivatives, represented by the symbol , mean, for instance, that h/x is the rate at which h changes with distance in the x direction, if one moves so as to keep y constant; and h/y is the rate of change in the y direction, x being constant). This result is expressed by the quantities in brackets being the components of the vector along the coordinate axes. Vector quantities that vary in three dimensions can similarly be represented by three Cartesian components, along x, y, and z axes; e.g., V = (Vx, Vy, Vz).

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