CONTENTS OF VOLUME II
Part III
CONTINUOUS COMPUTERS
1. Introduction
A. IDEA OF A CONTINUOUS COMPUTER 3
B. AMPLIFIERS AND STABILITY 3
C. PROBLEM RANGE 4
D. CONTINUOUS COMPUTATION 6
2. Differentials and Multipliers
A. INTRODUCTION TO MECHANICAL
COMPONENTS 7
B. ADDERS 8
C. MULTIPLYING BY A CONSTANT 12
D. SIMILAR TRIANGLE MULTIPLIER 15
E. RESISTANCE AND MECHANICAL
COMPONENTS 17
F. DIVISION 22
3. Cams and Gears
A. CAM THEORY 26
B. FUNCTION CAMS 27
C. INVOLUTE GEARS AND WRAPAROUNDS 31
D. LOG AND SQUARE CAM MULTIPLIERS 33
E. BACKLASH 34
4. Mechanical Integrators, Differentiators,
and Amplifiers
A. INTEGRATORS 37
B. DIFFERENTIATORS 39
C. MECHANICAL AMPLIFIERS 43
5. Circuit Theory
A. INTRODUCTION 48
B. NOTION OF A CIRCUIT 48
C. THE CIRCUIT EQUATIONS 50
D. MESH EQUATIONS 52
E. SOLUTION OF THE CIRCUIT PROBLEM 53
F. THE MESH CURRENTS AS SOLUTIONS OF
DIFFERENTIAL EQUATIONS 54
G. THE NATURE OF THE SOLUTION 54
H. THEVENTN S THEOREM 55
i. APPLICATIONS OF THEVENTN S THEOREM 56
J. COMPLEX CIRCUIT THEORY AND
ILLUSTRATIONS; FILTERS 63
6. Electrical Computing
A. INTRODUCTION 69
B. POTENTIOMETERS 69
C. ELECTRICAL ADDITION 75
D. CONDENSER INTEGRATION 77
7. Amplifiers
A. THE BASIC NOTION OF AN AMPLIFIER 81
B. VACUUM TUBES AS AMPLIFIERS 81
C. FEEDBACK AMPLIFIERS 88
D. STABILITY 91
E. DRIFT COMPENSATION 95
F. SUMMING AMPLIFIERS 97
G. INTEGRATING AMPLIFIERS 101
8. Electromechanical Components
A. MOVING WIRE IN FIELD 103
B. MECHANICAL ANALOGS OF ELECTRICAL
CIRCUITS 106
C. WATT HOUR METER 107
D. SYNCHRO SYSTEMS 109
9. Electrical Multiplication
A. INTRODUCTION 112
B. TIME DIVISION MULTIPLIER 113
C. MODULATION MULTIPLIER 118
D. STRAIN GAUGE MULTIPLIER 118
E. STEP MULTIPLIER 119
F. CATHODE-RAY MULTIPLIERS 120
10. Representation of Functions
A. FUNCTION TABLE 123
B. SCOTCH YOKE AND OTHER RESOLVERS 125
C. THE ELECTRICAL REPRESENTATION
OF FUNCTIONS 127
D. POTENTIOMETER METHODS OF
REPRESENTING A FUNCTION 128
E. MULTI-DIODE FUNCTION GENERATOR 129
F. CATHODE-RAY TUBE FUNCTION
GENERATOR 134
G. MAGNETIC MEMORY METHODS 135
H. FOURIER SERIES REPRESENTATION 1 36
I. REPRESENTATION OF SPECIAL
FUNCTIONS 140
11. Linear Equation Solvers
A. INTRODUCTION 144
B. TWO-WAY CONTINUOUS DEVICES 144
C. MANUAL ADJUSTMENT 146
D. GOLDBERG-BROWN DEVICE 149
E. POSITIVE DEFINITE CASE OF ADJUSTERS 151
F. MACHINES USING THE GAUSS-SEIDEL
METHOD AND THE MURRAY-WALKER
MACHINE 153
G. STABLE AUTOMATIC MULTIVARIABLE
FEEDBACK IN THE LINEAR CASE 156
H, STABLE MULTIVARIABLE FEEDBACK 159
12. Harmonic Analyzers and Polynomial
Equation Solvers
A. INTRODUCTION 165
B. HARMONIC ANALYSIS AND SYNTHESIS 165
C. FINITE FOURIER ANALYSIS 166
D. HARMONIC ANALYZERS 167
E. CONTINUOUS ANALYZERS AND
SYNTHESIZERS 169
F. POLYNOMIAL REPRESENTATION BY
HARMONIC ANALYZERS; ZEROS;
SPECIAL DEVICES 170
G. THE REPRESENTATION OF THE
COMPLEX PLANE 172
H. CHARACTERISTIC EQUATIONS 172
13. Differential Equation Solvers
A. INTRODUCTION 178
B. INTRODUCTORY DISCUSSION AND SETUP
OF MECHANICAL DIFFERENTIAL
ANALYZERS 178
C. THE SHANNON THEORY FOR THE SCOPE
OF MECHANICAL DIFFERENTIAL
ANALYZERS 180
D. REFERENCES 187
E. INTRODUCTORY DISCUSSION OF
ELECTROMECHANICAL DIFFERENTIAL
ANALYZERS 187
F. PRELIMINARY SETUP 188
G. SCALING AND LOAD CONSIDERATIONS 189
H. WIRING AND OUTPUT CONNECTIONS 192
I. IMPLICIT SYSTEMS OF DIFFERENTIAL
EQUATIONS 193
J. COMMERCIALLY AVAILABLE
EQUIPMENT 195
K. REFERENCES 196
14. Error Analysis for Continuous Computers
A. INTRODUCTION 198
B. THE TYPES OF ERROR 199
C. LINEARIZATION 200
D. THE NOTION OF FREQUENCY RESPONSE 202
E. A ERROR EFFECT 203
F. THE a ERROR; SENSITIVITY
EQUATIONS 204
G. THE ft ERROR AND NOISE 206
H. SOLUTION OF LINEAR DIFFERENTIAL
EQUATIONS WITH CONSTANT
COEFFICIENTS 208
15. Digital Check Solutions
A. USE OF DIGITAL CHECK SOLUTIONS 212
B. STABILITY OF DIGITAL CHECK
SOLUTIONS 214
C. THE ACCURACY OF DIGITAL CHECK
SOLUTIONS 216
Part IV
TRUE ANALOGS
1. Introduction to "True
Analogs"
A. THE CONCEPT OF "ANALOG" 223
B. ANALOG APPLICATIONS 224
C. MATHEMATICAL PROBLEMS SOLVED BY
ANALOGS 225
2. Dimensional Analysis and Models
A. INTRODUCTION
B. MEASUREMENTS
C. DIMENSIONALLY COMPLETE RELA
TIONS
D. BUCKINGHAM S THEOREM 229
E. MODELS 231
F. APPLICATIONS 231
3. Electrolytic Tanks and Conducting
Sheets
A. INTRODUCTION 233
B. ELECTROLYTIC TANKS 233
C. CONDUCTING SHEETS 236
D. REPRESENTATION OF THE COMPLEX
PLANE 236
E. ELIMINATION OF ERRORS DUE TO
FINITE SHEETS 239
F. POTENTIAL FLUID FLOW 241
G. SPECIAL FLOW PROBLEMS 243
4. Membrane Analogies
A. INTRODUCTION 245
B. DIFFERENTIAL EQUATION OF
MEMBRANE 245
C. RUBBER SHEET MODELS 247
D. SOAP FILM MODELS 250
E. SOURCES OF ERROR 251
5. Photoelasticity
A. INTRODUCTION 252
B. THEORY OF ELASTICITY 252
C. PHOTOELASTIC MODEL 255
D. PHOTOELASTIC EFFECT 255
6. Analogies Between Two-Dimensional
Stress Problems
A. AIRY S STRESS FUNCTION 259
B. BOUNDARY CONDITIONS 260
C. ANALOGIES 265
7. Electromechanical Analogies
A. DEFINITION OF MECHANICAL
SYSTEM 273
B. CONNECTION DIAGRAMS 273
C. MATHEMATICAL RELATIONS IN
CONNECTION DIAGRAMS 275
D. ELECTRICAL ANALOGIES 276
E. MASS-CAPACITANCE ANALOGY 277
F. IDEAL TRANSFORMERS 278
G. MASS-INDUCTANCE ANALOGY 283
H. ELECTROACOUSTIC ANALOGIES 286
I. ELECTROMECHANICAL SYSTEMS 288
J. APPLICATIONS 292
8. Two-Dimensional Electromechanical
Analogies
A. TWO-DIMENSIONAL LUMPEDCONSTANT
SYSTEMS 294
B. ELASTICITY 297
9. Network Representation of Partial
Differential Equations
A. INTRODUCTION 305
B. SCALAR-POTENTIAL EQUATION 305
C. RECTANGULAR LATTICE 306
D. NETWORK REPRESENTATION 307
E. METHOD OF FINITE DIFFERENCES 309
F. BOUNDARY CONDITIONS AND APPLI
CATIONS 310
G. CURL RELATIONS 311
H. RECTANGULAR LATTICE 312
I. CONNECTION DIAGRAM AND NETWORK
ANALOG 313
j. MAXWELL S EQUATIONS 317
K. DERIVATION OF EQ. IV.9.C.3, 4, 5 320
PartV
MATHEMATICAL INSTRUMENTS
1. Introduction
A. MATHEMATICAL INSTRUMENTS 329
2. Algebraic and Elementary Transcendental
Operations
A. FIXED PURPOSE COMPUTERS 331
B. SLIDE RULES 332
C. PLOTTING DEVICES 333
D. TRANSFORMATIONS OF THE PLANE 335
E. GENERAL THEORY AND THE CONSTRUC
TION OF CURVES 337
3. Instruments for the Differential and
Integral Calculus
A. DIFFERENTIATORS 340
B. INTEGRATION AIDS 341
C. VARIABLE SPEED DRIVE DEVICES
D. AREA-MEASURING DEVICES
Planimeters
A. BASIC PRINCIPLES
B. EXAMPLES OF LINEAR PLANIMETERS
C. INTEGROMETERS
D. GRAPHS IN POLAR COORDINATES
342 5. Integraphs

A. INTRODUCTION 353
B. INTEGRAPH INSTRUMENTS 353
C. THE INTEGRAPH OF ABDANK
ABAKANOWICZ 354
D. STEERING WHEEL INTEGRATORS 354
INDEX 357