Magnetohydrodynamic Flow in Ducts

are not generally known to the average reader are moreover explained in the text. The Chapters III, IV, and V contain a coherent account of three-dimensional positions theory for 2, 3, 4, or more positions, respectively, and for both finitely separated and consecutive positions. In slightly over 100 pages classical results are derived in a new way and others are either new or appear for the first time in an English textbook. The next chapter is devoted to the study of continuous spatial kinematics. The properties of the instantaneous tangents, principal normals and binormals are carefully exposed. The same can be said with regard to the developables of moving planes and the ruled surfaces generated by lines of the moving space. Here once more one sees many new aspects, both in the way of presentation and in regard to the results. Chapter VII contains a neat survey of spherical kinematics, following the scheme: finitely separated positions, consecutive positions, and time-dependent motions. The next chapter deals with plane kinematics. It is a lucid self-contained treatise of about 90 pages, proceeding along the lines set by the scheme just mentioned. Chapter IX is about special motions. The authors analyze such spatial motions as the Frenet-Serret motion, Darboux's, Mannheim's, Schoenflies' and Krames' motion. From plane kinematics they select the four-bar motion, the special cases thereof and the cycloidal motion. There follows a chapter on ^-parameter motions. It contains among other things an outstanding treatment of the second-order properties of the general 2-parameter spatial motion. There is a nice section on two-parameter plane motion. Chapter XI deals with a mapping of plane displacements on the points of a three-dimensional space, first introduced (1911) by . Grunwald and by Blaschke. The mapping is treated in an elementary way. One of the applications given by the authors is to the four-bar motion. They show, seemingly effortless, how to obtain a parametrization of the coupler curve of a general four-bar by means of Jacobi elliptic functions. In addition it is shown how to parametricize the coupler curves of folding four-bars, these being, as is well-known, rational curves. Chapter XII is devoted to kinematics in other geometries. Although emphasis is laid on equiform kinematics, affine, elliptic and hyperbolic kinematics are not neglected. A chapter on special mathematical methods in kinematics concludes the text. An important feature of the book is the fact that the authors present some material without proof. This material is generally set in small print and denoted "Example. " These examples are mainly formulated as exercises and must be regarded as an essential part of the text. There are somewhat over 800 examples. A careful student of the book will have no difficulty whatsoever in dealing with this material. There is an extensive bibliography up to 1977 of about 225 items and a reliable index. There are few misprints and the book is well produced. The authors must have done a great deal of preliminary work, before they could sit down to compose this outstanding book which is in the opinion of this reviewer a highly valuable asset to kinematic literature. As such it should be in the library of each researcher and advanced student in the field of theoretical kinematics and the closely connected theory of mechanisms. The scholarly merits of the book are matched by its didactical quality. It has the style of a classic.