Mr. Basset's Elementary Treatise on Hydrodynamics and Sound

Abstract

WHEN the Senate of the University of Cambridge decided to adopt the suggestion of the Special Board for Mathematics to include the elements of hydro-dynamics and the theory of sound among the subjects of Part I. of the Tripos, teachers of these subjects naturally looked to Mr. Basset to provide a text-book that should meet the wants of students preparing for the examination, and he has responded to the demand with great promptitude. The present treatise is designed, he tells us, for those who are reading for this examination and others in which a knowledge of these subjects is required. If the purpose of the book had been different—if, for instance, it had been written as a purely scientific training for hydraulic engineers, or for use in a physical laboratory—it would have had to be conceived in a very different vein. We should have looked for full explanations of elementary concepts, frequent appeals to experiment, constant arithmetical interpretation of the analysis, and a large proportion of physical reasoning. If, however, the book is to be judged by the standard it aims at, it must be regarded as an admirable specimen of an examination book. The propositions are clearly set out in a methodical order. They are isolated from each other as much as possible, and proved individually by the use of appropriate principles. The examples are for the most part well chosen, and calculated to initiate the student into a great variety of the tips and dodges with which the examiners are likely to be familiar; and no more is generally given than would be useful in writing out book-work and solving problems. We proceed to a detailed account of the work. The treatise is divided into two parts, of which the first deals with hydrodynamics, and the second with the theory of sound. In the first part there are five chapters. Chapter i. treats of the kinematics of fluids and of the general equations of motion. We are glad to see that the author has given prominence to the “flux method,” and has had the courage to restore the elementary parallelepiped which Prof. Greenhill affects to despise; for the purposes of an elementary treatise the value of this artifice is too great to be lost. Very welcome also is the proof of the important principle at the foot of p. II, first stated exactly in the larger treatise, vol. ii. p. 234, and apparently due to Prof. Greenhill (“Encyc. Brit.,” Art. “Hydromechanics”). We could wish that the theory of the bounding surface had been as fully explained. The same chapter i. contains a short account of sources, doublets, and images, and electric and magnetic analogies are given which add much to the usefulness of these sections. An Elementary Treatise on Hydrodynamics and Sound. By A. B. Basset. (Cambridge: Deighton, Bell, and Co. London: George Bell and Sons. 1890.)