Grundlagen der Hydromechanik Leçons sur l'hydrodynamique Hydro- und Aeromechanik nach Vorlesungen von L Prandtl

Abstract

(1) THESE three books all deal with hydro- dynamics, but differ widely in scope, and appeal almost to different types of mind. Prof. Lichtenstein, well known for his elegant investigations of some special problems, here undertakes a systematic survey of the science from a strictly logical point of view, incorporating an account of the researches on the existence-theorems of the subject on which he has been engaged for a number of years. He submits to a rigorous scrutiny the various conceptions which lie at the base of the science, as well as the assumptions which have been made implicitly in its development. This task is here essayed for the first time in the present connexion. The classical writers and their followers have been accustomed to pass lightly over such matters and to be guided (often unconsciously) by physical intuitions rather than logical deductions. In this they were entirely justified, for it is hard to see how they could otherwise have got on with their own primary business, to construct a mathematical scheme which should represent as well as might be the processes of natural phenomena. But at length the pure mathematician comes into the field. He is attracted by the interest and beauty of the mathematical structure which the classical writers have by degrees built up, but his keen logical eye detects flaws here and there; he is impelled to strive after precision where he finds vagueness in fundamental conceptions, and to supply lacunœ in the logical processes.

Grundlagen der Hydromechanik

Prof. Leon Lichtenstein. (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, herausgegeben von R. Courant, Band 30.) Pp. xvi + 506. (Berlin: Julius Springer, 1929.) 38 gold marks.

Leçons sur l'hydrodynamique.

Prof. Henri Villat. (Chaire de mécanique des fluides et applications, Fondation du sous-secrétariat d'État de l'aéronautique.) Pp. viii + 296. (Paris: Gauthier-Villars et Cie, 1929.) 50 francs.

Hydro- und Aeromechanik nach Vorlesungen von L. Prandtl.

Dr. O. Tietjens. Band 1: Gleichgewicht und reibungslose Bewegung. Pp. viii + 238. (Berlin: Julius Springer, 1929.) 15 gold marks.