A collection of papers in memory of Sir William Rowan Hamilton

BOOK REVIEWS. A COLLECTION OF PAPERS IN MEMORY OF SIR WILLIAM ROWAN HAMILTON. The Scripta Mathematica Studies, Number Two. 82 pages, 17 X 25 cms. New York, Scripta Mathematica, 1945. Price $1.5o. The year 1943 marked the one hundredth anniversary of the discovery of quaternions by Sir William Rown Hamilton. Unfortunately the war prohibited fitting celebration at the time, so this volume has been prepared in his honor. J. L. Synge discusses the life and early work of Hamilton emphasing his other great i d e a - the principal or characteristic function. Algebra's debt to Hamilton forms the subject of C. C. MacDuffee's paper. He points out t h a t the presentation of the complex number field as a theory of couples of real numbers was a more fundamental concept in algebra than the spectacular quaternion. An elementary explanation of the theory of quaternions is offered by F. D. Murnaghan. In the field of dynamics Hamilton also made important contributions. A summary of his work in this field and its subsequent influence on modern thought is presented by H. Bateman. The concluding article by Vladimir Karapetoff is entitled "The Constancy of the Velocity of Light." The various papers here gathered form a n appropriate tribute to this great Irish mathematician. GEORGE E. PETTENGILL. THE CHEMICAL CONSTITUENTS OF PETROLEUM, by A. N. Sachanen. 451 pages, tables and illustrations, 16 X 23 cms. New York, Reinhold Publishing Corporation, 1945. Price 88.50. The subject of this book is one in which considerable work has been done but where a broad unexplained field exists. Many problems, particularly in the field of chemistry of lubricating oils, petroleum wax, resins and asphaltic constituents have not been crystalized into commonly accepted theories. New methods and conspicuous improvements in classical methods open new possibilities in attacking problems related to the composition of petroleum. The enormous complexity of petroleum, though rather a drawback to investigation today may become a great stimulus tomorrow. The work opens with a treatment of the Chemical composition of petroleum gases and the light gasolines produced from them and then proceeds into physical methods of determining hydrocarbons in distillates including distillation, crystallization, separation by solvents, adsorption and desorption, specific gravity and refractive index, refractory intersept etc. The chemical methods are next taken up and they include determination of the H:C ratio, ring analysis, sulfonation of aromatics, aromatic hydrocarbons, and fourteen others. In the coverage of hydrocarbons of straight run distillates it is pointed out t h a t the commercial value of petroleum products is determined rather by their bulk chemical composition than by specific individual hydrocarbons and that "it seems certain however t h a t the wide commercial segregation of individual hydrocarbons from liquid petroleum products is a problem of the near future." Subsequent chapters are devoted to hydrocarbons of synthetic distillates, petroleum wax, oxygen compounds where reference is made that the origin of low molecular weight fatty acids still awaits solution, sulfur and nitrogen compounds knowledge of which is limited, resins and asphaltic compounds, and classification of crude oils. There is an author and subject index in the back. The book is a review of a great amount of literature coupled with first hand knowledge of the subject, leading to the point where research can well begin. R. H. OPPERMANN. 253