ynomial matrices," "Unitary and Eutronic structure, chemical properties, clidean spaces," "Bilinear and quadratic and nuclear properties. Separating the forms," "Linear transformations of bi-rare-earth elements, methods of anallinear-metric spaces," and "Multilinear ysis, and the economics of the metals functions. Tensors." considered are also discussed. Various Much of the book's success stems methods used for reduction and purifrom the author's wholesome attitude fication are reviewed, and the available toward the various formulations from data, reported during recent years, on which the subject may be approached. their physical, mechanical, and chem-"In linear algebra one studies three ical properties are tabulated. kinds of objects: matrices, linear spaces, A chapter devoted to binary constiand algebraic forms. The theories of tutional diagrams of the rare-earth these objects are so closely related that metals, with one another and with most problems of linear algebra have other metals, contains more than 100 equivalent formulations in each of the diagrams, many of which are incomthree theories. The matrix point of plete, as one would expect. The alloyview, which underlies the present exing behavior of the metals, as it is position, is the one best adapted to related to basic physical principles, is actual calculations. On the other hand, briefly reviewed. The final chapter is most problems of linear algebra that a review of the use of the rare-earth arise in geometry and mechanics lead elements in alloys, and it is interesting to algebraic forms, while the best un-to observe that the only widespread use derstanding of the internal connections is that of misch metal, principally for between different problems of linear lighter flints. The addition of rarealgebra is obtained by means of linear earth metals to magnesium does, howspaces. Therefore the ability to pass ever, increase its strength at elevated from one type of formulation to antemperatures, and several commercial other is one of the most important alloys are available. Reports with reskills to acquire in the study of linear spect to the influence of rare earths algebra." added to steels are quite conflicting; H. J. RYSER some reports tell of dramatic improve-Department of Mathematics, ment, but others say there is no im-Syracuse University provement or that there is actual impairment. The Technology of Scandium, Yttrium, and the Rare Earth Metals. Eugene V. Kleber and Bernard Love. Adaptation Tolerance Pergamon, London; Macmillan, New York, 1963. x + 205 pp. Illus. Parasitism. An introduction to parasit-$7.50. ology and immunology for students of biology, veterinary science, and Within recent years scandium, yttri-medicine. J. F. A. Sprent. Univerum, and the lanthanons, atomic numsity of Queensland Press, Brisbane, bers 57 through 71, have been pre-Australia; Bailliere, Tindall, and Cox, pared as "high-purity" metals. Their London, 1963. x + 145 pp.
35s. physical and mechanical properties have been investigated, and constitu-Among the several recent...
