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INTRODUCTION TO Electronic Analogue Computers BY C. A. A . W A S S formerly Superintendent of the G. W, Dynamical Analysis Division, Royal Aircraft Establishment, Farnborough, Hants AND K. C. G A R N E R Lecturer in Control and Simulation, Department of Electrical and Control Engineering, The College of Aeronautics, Cranjield, Beds. SECOND AND REVISED ENLARGED PERGAMON EDITION PRESS OXFORD • LONDON . EDINBURGH . NEW YORK PARIS • FRANKFURT Pergamon Press Ltd., Headington Hill Hall, Oxford 4 & 5 Fitzroy Square, London W . l Pergamon Press (Scotland) Ltd., 2 & 3 Teviot Place, Edinburgh 1 Pergamon Press Inc., 122 East 55th St., New York 22, N . Y . Pergamon Press GmbH, Kaiserstrasse 75, Frankfurt-am-Main Copyright © 1965 Pergamon Press Ltd. First edition 1955 Second revised and enlarged edition 1965 Library of Congress Catalog Card No. 65-12670 2139 FROM T H E PREFACE TO T H E FIRST EDITION THIS monograph is based on the ideas and experience of a group of workers at the Royal Aircraft Establishment, Farnborough, Hants. This group was formed in 1945 under the leadership of W . R . Thomas, then at R.A.E., who adopted and developed computing techniques employed at the Telecommunications Research Establishment, Malvern (now part of the Radar Research Establishment) by a team which included F. C. Williams, F. J. U. Ritson, R . J . Lees, R . Aspinall and H . Sutcliffe. TheR.A.E. group has grown continuously since that time, both in numbers of staff and number and complexity of computers, until it is now one of the largest groups of its kind in the country. Substantial contributions to the work of this group have been made by: D . W . Allen, E . G. C.Burt, W . A. Elfers, J. J. Gait, O. H . Lange, F. R . J. Spearman, H . T. Ramsay, M. Squires, W . R . Thomas. The names of members of the group associated with particular developments are mentioned where appropriate, although references are not always given because the relevant reports have not been published. Many inventions and improvements have been made by other workers, both in Britain and abroad, and acknowledgements are made on the text. I offer my apologies for any inadvertent omissions. I am particularly indebted to two of my friends and colleagues; J. J. Gait, for his careful and helpful reading of the manuscript and proofs, and K . C. Garner, who undertook the considerable task of preparing the diagrams and made a number of valuable suggestions. Without sustained encouragement and assistance from my wife this monograph would not have been completed. I have to thank the Chief Scientist, Ministry of Supply, for permission to publish this monograph. Farnborough C. A. A. W A S S viii P R E F A C E TO T H E SECOND E D I T I O N THIS book is a revised version of the book with the same title that I wrote in 1 9 5 5 . The revision is almost entirely the work of my friend and former colleague Mr. K . C. Garner, of the College of Aeronautics, Cranfield. C. A. A. W A S S Sheffield A T the time when the first edition of this book appeared the analogue computers then in use were nearly all special-purpose machines, designed for the solution of particular military problems, often with little or no thought for versatility or for convenience for the user. Since that time there has been an enormous widening of the range of problems solved by analogue computers, and this now covers activities as diverse as civilian air-crew training [ 1 2 8 ] and the blood circulation system in the foetus of a lamb [ 1 2 9 ] . Furthermore, whereas it was customary for the intending user to design, and often build, his own machine, there is now an extensive selection of commercially-built computers and ancillary apparatus available, offering every facility for the so