Otto E. Nomography

Burlington: Elsevier, 2014. — 314 p.Literature in the field of nomography is nowadays so extensive that in many languages textbooks of nomography and collections of nomograms for various branches of technology are published separately.
This book is not a collection of nomograms but a manual to teach nomography. The examples contained in it are not meant to give ready-made solutions for the use of engineers but serve as illustrations of the methods of constructing nomograms ; that is why most of them are given without any comment regarding the technical problems from which they have arisen.
The importance of geometrical transformations, and particularly projective transformations of a plane, has been specially stressed. The traditional method of providing the best form of a nomographic drawing within the given variability limits of the parameters occurring in the equation, a method consisting in a suitable choice of units for various functional scales, has been replaced in this manual by a method of transforming an arbitrary nomogram satisfying the given equation. Thus the finding of the so called modules, which is different for every type of equations dealt with in nomography, has been replaced by one method: a projective transformation of an arbitrary quadrilateral into a rectangle.
Accordingly, Chapter I begins with the necessary information on the projective plane and collineation transformations. They have been approached both from the geometrical and the algebraical point of view: the geometrical approach aims at permitting the use of elementary geometrical methods in drawing collineation nomograms consisting of three rectilinear scales (§§ 10-13) while the algebraical treatment concerns nomograms containing curvilinear scales. The necessary algebraic calculation has been developed as a uniform procedure involving the use of the matrix calculus. The chapter ends with information on duality in the plane.
Chapter I I contains the fundamental data concerning functional scales. In the first part of Chapter I I I those equations are singled out which can be represented by elementary methods without the use of a system of coordinates. Those equations are most frequent in practice and it has seemed advisable to give the simplest methods for them. The remaining cases (§§ 15-19) require the use of algebraic calculation. The second part of Chapter I I I deals with nomograms with a binary field (lattice nomograms) : it has been stressed that from the algebraical point of view it is only necessary to pass from the coordinates of a point to the coordinates of a straight line. In Chapter IV the methods discussed in the preceding chapters are used for constructing combined nomograms. Chapter V is an introduction to mathematical problems which have arisen in the analysis of the methods of constructing nomograms. Besides solutions known in literature, such as the so called Massau method and the criterion of Saint Robert, § 31 contains an algebraic criterion of nomogrammability of functions, which is a realisation of an idea of Duporq (Comptes Rendus 1898).
It finally solves a problem which has only partially been solved by other authors, who have been using complicated, practically inapplicable methods.