(1) A School Algebra (2) A Treatise on Hydromechanics (3) Les Appareils d'Intégration (4) Einführung in die höhere Mathematik für Naturforscher und Aerzte (5) Elements of the Precision of Measurements and Graphical Methods (6) Matrices and Determinoids

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(i)MESSRS. LANE'S “Algebra” looks as if it would prove a useful school-book. In dealing with the binomial and exponential series the authors state certain properties, with the explicit warning that they are not proving them. This is as it should be; but the chapter on exponentials and logarithms is not so clear as it might be; in particular, Arts. 135–7 would be better if arranged in the reverse order. In the earlier pages we have the old fallacious and meaningless statement: “to multiply a number a by a second number b, we do to a what is done to the unit to obtain b.” It would be much better to give the rule of signs as a rule pure and simple, and then to show by cases of (a – b)(c – d) that it does actually work out in practice. There are hundreds of examples—some, alas, of a highly artificial character; for instance, “If the hypotenuse of a right-angled triangle is x, and the other sides are y and z units of length, show that (1) A School Algebra. By F. O. Lane J. A. C. Lane. Pp. viii + 333. (London: Edward Arnold, n.d.) Price 3s. 6d. (2) A Treatise on Hydromechanics. Part ii. Hydrodynamics. By A. S. Ramsey. Pp. xiii + 360. (London: G. Bell and Sons., Ltd., 1913.) (3) Les Appareils d'Intégration. By H. de Morin. Pp. 208. (Paris: Gauthier-Villars, 1913.) Price 5 francs. (4) Einführung in die höhere Mathematik für Naturforscher und Aerzte. By Dr. J. Salpeter. Pp. xii + 336. (Jena: Gustav Fischer, 1913.) Price 12 marks. (5) Elements of the Precision of Measurements and Graphical Methods. By Prof. H. M. Goodwin. Pp. 104. (London: Hill Publishing Co., Ltd.; New York: McGraw-Hill Book Co., 1913.) (6) Matrices and Determinoids. By Prof. C. E. Cullis. Vol. i. Pp. xii + 430. (Cambridge University Press, 1913.) Price 215. net.