The fifth volume in this series is focused on the chemical and physical interactions between rocks undergoing metamorphism and the fluids that they generate and that pass through them. The recognition that such pro cesses can profoundly affect the course of metamorphism has resulted in a number of recent papers and we consider that it is time for a review by some of the interested parties. We hope our selection of contributors provides an adequate cross section and demonstrates some of the flavor of this rapidly developing field. A cursory examination of the volume will reveal that there are widely divergent opinions on the compositions of metamorphic fluids and on the ways in which they interact physically and chemically with the rocks through which they pass. Since our own views are extensively discussed in Chapters 4 and 8, we leave the reader to determine his own brand of the "truth. " We wish to thank D. Bird, S. Bohlen, D. Carmichael, G. Flowers, C. Foster, C. Graham, E. Perry, J. Selverstone, R. Tracy, J. Valley, and R. Wollast for their chapter reviews. Thanks are also due C. Cheverton for her editorial assistance, and the helpful staff at Springer-Verlag New York."

This book is written as an introduction to the theory of error-free computation. In addition, we include several chapters that illustrate how error-free com putation can be applied in practice. The book is intended for seniors and first year graduate students in fields of study involving scientific computation using digital computers, and for researchers (in those same fields) who wish to obtain an introduction to the subject. We are motivated by the fact that there are large classes of ill-conditioned problems, and there are numerically unstable algorithms, and in either or both of these situations we cannot tolerate rounding errors during the numerical computations involved in obtaining solutions to the problems. Thus, it is important to study finite number systems for digital computers which have the property that computation can be performed free of rounding errors. In Chapter I we discuss single-modulus and multiple-modulus residue number systems and arithmetic in these systems, where the operands may be either integers or rational numbers. In Chapter II we discuss finite-segment p-adic number systems and their relationship to the p-adic numbers of Hensel 1908]. Each rational number in a certain finite set is assigned a unique Hensel code and arithmetic operations using Hensel codes as operands is mathe matically equivalent to those same arithmetic operations using the cor responding rational numbers as operands. Finite-segment p-adic arithmetic shares with residue arithmetic the property that it is free of rounding errors."