






Features
CONTENTS 
1. SCALES 
Nature and Properties of Scales 
Methods for Constructing Scales 
Altering Moduli of Scales 
Standard Scales 
Mechanical Aspects of Scale Construction 
Exercises 
2. CALCULATING WITH SCALES 
Adjacent Scales 
Parallel Scales With Index Line 
Standard Slide Rules 
Slide Rule Routines 
Special Slide Rules 
Methods of Reproduction 
Other Forms of Special Slide Rules 
Differential Gear Rules 
Exercises 
3. GRAPH PAPERS 
Common Types of Graph Papers 
Construction of Graph Papers 
Exercises 
4. CALCULATING WITH GRAPH PAPERS 
Hyperbolic Paper 
Linear Paper 
Semilogarithmic Paper 
Logarithmic Paper 
Exercises 
5. GRAPHS 
Relationship of Graph to Table and Function 
Graphs of Regular Functions 
Interpolation and Extrapolation 
Graphs of Empirical Data 
Complex Graphs 
Condensed Graphs 
Exercises 
6. CALCULATING WITH GRAPHS 
Position Relationships 
Vertical and Horizontal Displacements 
General Distance Relationships 
Isometric Translation 
Slopes; Graphical Differentiation 
Areas; Graphical Integration 
Exercises 
7. NOMOGRAPHY 
Nomographic Methods 
Some Characteristics of Nomographs 
8. NOMOGRAPHS BY SYNTHETIC METHODS 
Synthetic Methods 
Figures With One Straight Index Line 
Figures With Two Parallel Index Lines 
Figures With Perpendicular Index Lines 
Review of Synthetic Methods 
Exercises 
9. NOMOGRAPHS WITH CARTESIAN
COORDINATES, 
Relationship of Defining Equation to Type 
Matrix Transformations 
Exercises 
10. NOMOGRAPHS WITH HYPERBOLIC
COORDINATES 
The Semihyperbolic Coordinate System 
Application to Construction of Nomographs 
11. PRACTICAL ASPECTS OF CONSTRUCTING
NOMOGRAPHS 
Nomographs With Parallel Scales 
Nomographs With Oblique Scales 
Nomographs With Curved Scales 
Exercises 
12. USE OF GENERAL HYPERBOLIC
COORDINATES 
Hyperbolic Plane Coordinates 
The VType Nomograph 
Fitting Nomograph to a Rectangle 
13. THREEDIMENSIONED NOMOGRAPHS 
ThreeDimensional Hyperbolic Coordinates 
Defining Equation for Nomographs 
Applications 
14. PROPERTIES OF HYPERBOLIC
COORDINATE SYSTEMS 
Hyperbolic Plane Coordinates 
Semihyperbolic Coordinates 
Hyperbolic Solid Coordinates 
Semihyperbolic Solid Coordinates 
15. NOMOGRAPHS FROM GRAPHS AND TABLES 
Relationship of Graph to Nomograph 
Constructing Nomographs From Tables:
Symmetrical 
Constructing Nomographs From Tables:
General 
APPENDIX 
Values of x = p/pr and 1  x
INDEX 
PREFACE
There is a steadily growing interest in the capabilities of
graphical methods in the field of computation and an increasing
demand for applications of these methods to a broad
spectrum of scientific and engineering formulasscientific
principles or laws expressed in mathematical symbols.
Over the years, man's scientific endeavors have resulted
in the accumulation of ponderous volumes of these formulas
involving computation for their application to engineering
problems. At the same time, man has developed a number
of devices for reducing the labor of these computations, numerical
devices such as the abacus and tables of logarithms,
mechanical devices such as adding machines and desk calculators,
electronic devices such as the modern computer,
and graphical devices such as the slide rule and the nomograph.
It is this last class of devices with which we are now
concerned.
The calculation of a series
of values required for the solution of an engineering problem
(e.g., the design of a column for the fractionation of a hydrocarbon
mixture) can be quickly performed with all required
accuracy by the use of charts contained between the covers
of a handbook at the engineer's fingertips.
Many scientists and engineers that use graphical devices
have little idea of the relative merits and applicability of
the various types of devices, and virtually no knowledge of
the underlying theory of their construction. Yet, the mathematics
of this theory is so simple that mathematics advisers
on projects for high school science fairs would do well to
consider some of the methods described herein, such as
construction of special slide rules, nomographs for formulas
of current interest, and threedimensional nomographs.
There is no lack of technical literature in this field, but
what is lacking is a systematic approach to the subject as
a whole, from the standpoints of both organization and
theory.
This book is an outgrowth of very earnest efforts towards
unifying my own knowledge in this field. Having made a
thorough study of nomographic methods and theory, I nevertheless
found myself in poor shape to produce a series of
nomographs based on certain polynomials describing the
characteristics of flight of helicopters.
A modification of
existing theory greatly simplified the procedure for representing
polynomials; however, it also pointed the way towards
the development of a new theory of nomographic representation,
the hyperbolic coordinate method from which have grown
generalizations and extensions covering the entire field of
nomography. At the same time, extension of the idea of the
scale equation into the areas of graph papers, graphs, and
slide rules has simplified the application of these devices in
the field of computation.
Although some topics (e.g., the hyperbolic coordinate
method of nomography) are treated in much detail because
of the lack of thorough treatment elsewhere, other topics
(e.g., graphical integration and differentiation) are recognized
as being adequately covered in other sources and are here
given only introductory discussions by way of recognizing
their family relationships.








