Mathematics in Science and Engineering , Volume 6: Differential- Difference Equations. Richard Bellman and Kenneth L. Cooke. Academic Press, New York and London. 462 pp. 114s. 6d.

Applied Cryogenic Engineering. R. W. Vance and W. M. Duke {Editors). John Wiley & Sons, London. 1962. 510 pp. Illustrated. 132s. When almost weekly there is news of yet another initially rocket propelled body being put into an Earthly orbit or sent on a longer and more complex course, popular opinion tends to regard these most impressive achievements as being extremely scientific developments of the second secret weapon of the late War, the V2. This may be correct, but the military rocket certainly has had a long history during the greater part of which its development has not been scientific, but was empirical. In China, in the 13th century A.D., rockets propelled by a chance discovered mixture termed lazy powder (in reality, a slow burning gunpowder) were used for military purposes. Further and rather surprisingly, towards the end of the next century, due largely to the observations of an Arab, Ibn Albaith (Son of the Horse Doctor) and to the meditations thereon of his book-writing compatriot, Nedshm Eddin (Star of Faith) knowledge of such weapons was fairly widely dispersed over the Continent of Asia. Certainly towards the end of the 18th century rockets were effectively used against British troops, and in particular against their cavalry, by Tippo Sahib of Mysore in his two battles in the neighbourhood of Seringapotam. This enemy weapon superiority in a quite unexpected area, led, naturally enough, to strong criticism of the Home Authorities. The ultimate result of this was that about a generation later, due to the inventive ability of William Congreve (stimulated and materially helped by his father, Comptroller of the Royal Laboratory at Woolwich, and by what Was doubtless in those days, a powerful influence, the patronage of the Prince Regent) there were effective British military rockets. These weapons and developments therefrom continued for nearly half a century to be a part of military equipment until increase in range and accuracy of field guns eliminated their significance. Here might end this note on the history of military rockets, but it rightly does not. After a pause approaching a century in length, study, generally followed by experiments with the object of increasing the range, accuracy and speed of rockets intermittently took place; leading, inter alia, to the German conclusion that these aims could, in part, be met by the use of cryogenics—literally meaning a freezing mixture but, in the case under consideration, and, in the book under review, implying the use of one or more liquid gases under such conditions that the engineering problems arising from very low temperatures had to be met. The book consists of a compilation of a graduate level series of lectures organised by the University of California's Departments of Engineering. It deals with some of the cryogenic engineering problems of space exploration. The work has two editors (one of whom is part author of one of the lectures) and fourteen other specialist contributors. This team, with great clarity, sets out the significant properties of what are now regarded as the main cryogenic fluids: further the lectures indicate the engineering problems arising from their characteristics and in some cases indicate solutions. This book contains fifteen chapters at the end of each of which is an adequate bibliography. In addition to this last, there are three appendices and an above average index. In the space of 510 pages there cannot, of course, be a complete enumeration of all cryogenic problems and provision of satisfactory engineering solutions to all of them. The book does, however, constitute a thoroughly good review of the present state of the art and provides lucid indications of "where we should go from here".—P. L. TEED. An Introduction to Magneto-fluid Mechanics. V. C. A. Ferraro and C. Plumpton. Oxford University Press, London. 1961. 181 pp. 25s. The declared intention of this book is "to meet the undoubted need of physicists and engineers for an introductory account of magneto-fluid dynamics". During the past five years this introduction has been supplied mainly by the Interscience publications of Spitzer and Cowling. This book by Ferraro and Plumpton covers very much the same basic material as those previous publications. The book starts with an interesting historical introduction to the subject of magneto-fluid dynamics. Thereafter it has been divided into two parts, the first is called "Magnetohydrodynamics" and the second, "Plasma Dynamics". It has been assumed that the reader has had an introductory course in theoretical physics and is fully acquainted with Maxwell's equations, together with the general equations of fluid motion. Vector methods have been extensively used throughout. Part I begins with a brief discussion of the relevant equations and includes chapters of magnetohydrostatics, magnetohydrodynamic waves, turbulence and shock waves. Part II is concerned with the motion of charged particles in magnetic fields and also contains an elementary discussion of the dynamics of fully ionised gases from the macroscopic viewpoint based on the kinetic theory of gases. A final chapter deals with fundamental wave systems which may be excited in plasmas. As stated by the authors, the Bibliography is by no means exhaustive. However, it contains references to books and papers dealing with the more important aspects of the subject together with short summaries. Selected reading from this bibliography helps considerably in gaining a better physical insight to some of the problems considered in the text. Scientists and engineers, who are likely to be engaged in magnetohydrodynamic power generation or space flight, would have undoubtedly appreciated some discussion of these practical subjects in the main text. In writing the book it appears that brevity has been a ruling factor. Such a condition must necessarily be at variance with its intended introductory nature when too strictly applied.—j. p. APPLETON.