Book Reviews - April 2008 - Volume 108 (4)

Experimental Researches in Electricity

Author: Michael Faraday
Dover Publications, Inc., 31 East 2nd Street, Mineola, NY 11501
2004; xiv + 336 pages, Paperback $19.95

Reviewer: John Whitmer
Western Washington University (emeritus), Bellingham, WA 98225

Science writing many generations removed from the present can often give valuable perspectives on scientific styles and personal traits of scientists as well as the historical context in which they worked. This is especially true, as here, when major scientists describe their own work. Experimental Researches in Electricity by Michael Faraday (1791-1867) is a collection of selected parts from a 3-volume series published between 1839 and 1855. This collection, first published in London in 1914, was republished unabridged by Dover in 2004. It is largely Faraday's electrochemical researches from 1832 to 1839, providing the foundations of electrochemistry (the basis, for example, of all batteries, fuel cells, and electro-plating processes). His notebooks - reproduced verbatim here - are meticulously detailed descriptions, including figures, of his equipment, procedures, observations, and conclusions, all in concise, sequentially numbered paragraphs, which was the notebook format for all his scientific work. It is not necessary to read all these in detail to marvel at his experimental ingenuity, observational acuity, and clarity of expression - qualities which make Faraday arguably the greatest experimental scientist of the 19th century. The electrical charge of a mole of electrons, the faraday, and the unit of electrical capacitance, the farad, are named in his honor.

The book opens with a preface by the British science historian, F. Sherwood Taylor, outlining the reasons Faraday's writings are still valuable. The preface concludes:

“What can we learn from Faraday's work today? Principally the merit of hard work and simple experiments closely observed. Sealing wax and string have departed from the modern laboratory, but even today discoveries of beautiful simplicity are made.... The easy way is to elaborate upon the work of others; the way of genius is to draw profound conclusions from the simplest phenomena.” (p. vi)

Also included is a biographical section by John Tyndall (of “Tyndall effect” fame) written in 1869 shortly after Faraday's death. Faraday had little formal education. He was apprenticed to a bookseller as a teenager, was a prodigious reader, and at age 21 became a laboratory assistant of Sir Humphry Davy, one of the most revered British scientists of the time. Faraday made the most of this opportunity, soon producing work comparable to Davy's and attracting wide attention. Surprisingly he was largely unschooled in mathematics, but his experimental skill was unsurpassed and his ability to visualize and describe results accurately, concisely, and almost devoid of mathematical formalism is remarkable. Personally he was modest, deeply religious, and had little interest in fame or money, often declining financial and honorary awards that increasingly came his way.

This book would probably find limited use in most science classrooms. Its appeal is to those wishing to understand some of the ways science was done in the early 19th century and to those wanting a glimpse of the disciplined mind, superb methods, and expositional clarity of one of our greatest experimental scientists.

Topics in Graph Automorphisms and Reconstruction

Authors: Josef Lauri and Raffaele Scapellato
Cambridge University Press, 40 West 20th Street, New York, NY 10011-4211
2003; 159 pages, Hardback $65.00, Paperback $23.00

Reviewer: Medhat H. Rahim
Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1

The text Topics in Graph Automorphisms and Reconstruction has been prepared for readers who possess an exposure to a first course in graph theory and some discrete mathematics and linear algebra. Such readers would include mathematics teachers, graduate students and other interested individuals whose interest have been sufficiently aroused in receiving a more in-depth coverage of some particular areas of graph theory. These particular areas of graph theory covered in this text have been chosen largely due to the authors' research interests. In particular, the flavor of these topics covered in this text has been mainly algebraic, with emphasis on symmetry properties of graphs. At the beginning of the text, the authors presented standard topics in graph theory such as the automorphism group of a graph, Frucht's Theorem, Cayley graphs and coset graphs, and orbital graphs. These standards topics in graph theory were meant to serve as a background for most of the advanced work in later chapters such as graphic regular representations, pseudosimilarity, graph products, hamiltonicity of Cayley graphs and special types of vertex-transitive graphs.

The first chapter of the text covers preliminaries for graphs and groups such as graphs and digraphs, Edge-automorphisms and line-graphs. Chapter 2 covers various types of graph symmetry such as transitivity, asymmetric graphs, graph symmetries and the spectrum, simple eigenvalues, and higher symmetry conditions while Chapter 3 deals with Cayley graphs. Chapter 4 deals with orbital graphs and strongly regular graphs; it starts with definitions and basic properties necessary to cover rank 3 groups, strongly regular groups, the integrality condition, and Moore graphs. Chapter 5 covers graphical regular representations and pseudosimilarity while Chapter 6 deals with products of graphs such as general product, categorical product and Cartesian products. Chapter 7 presents treatments of special classes of vertex-transitive graphs and digraphs. Chapters 8 and 9 deal with the reconstruction conjectures and reconstructing from subdecks respectively. Chapter 10 covers counting arguments in vertex-reconstruction in treating essential concepts such as Kocay's Lemma, counting spanning subgraphs and the characteristics and the chromatic polynomials. Finally, Chapter 11 deals with counting arguments in Edge-reconstructions through homomorphisms of structures and Lovasz and Nash-William Theorems. The authors offer exercises, notes and guide to references at the end of each of the eleven chapters.

The authors have tried to present proofs and results that are rare in similar texts so that those reader who can digest the text's content, will be well prepared to enter the ongoing research in several aspects of graph theory. In particular, this text, Topics in Graph Automorphisms and Reconstruction, is suitable for graduate students (and mathematics/science teachers) who are interested to carry out research in one of the covered areas of graph theory.

In sum, this text, once covered well, would be a useful means for understanding the current state of research in graph theory and as such, it would be a valuable reference in any library.