REVIEWS 683 



field and the derivation of the equation of wave propagation. There the usual 

 text-book leaves him after, perhaps, an application to the limited cases of a plane 

 wave or a spherical wave. To those who are desirous of pursuing this part of the 

 subject further from a mathematical point of view, Dr. Bateman's book will provide 

 excellent guidance. Even readers with a limited mathematical equipment can 

 easily follow the development, which is original and suggestive. A nodding 

 acquaintance with Spherical Harmonics and Bessel Functions, such as is obtained 

 from one of the usual text-books on Differential Equations, and with the notation 

 of modern Vector Analysis, will serve very well. 



Maxwell's Equations are reduced to two in number by the introduction of the 

 complex field vector, and two very general types of solution of the wave equation 

 are obtained, one of which includes the well-known solution for the Hertz dumbbell 

 oscillator as a particular case. Chapters on transformation to polar and cylindrical 

 co-ordinates follow, with a very full discussion concerning the problems of scatter- 

 ing by spherical obstacles, and of propagation of waves along a wire. The 

 pressure of radiation and electrical vibrations on variously shaped bodies are 

 dealt with, and Sommerfeld's multiform solution of the wave equation is applied 

 to diffraction past a straight edge. Solutions, using ellipsoidal and toroidal 

 co-ordinates, are also obtained, and there are short accounts of the method of 

 solution due to Stieltjes and the method due to Green. A very suggestive chapter 

 on the singularities of wave functions and their bearing on the problem of the 

 structure of the ether concludes the book. 



Within the limits of 160 pages the author has compressed a considerable body 

 of work of the highest value, and ample references compensate for the necessarily 

 brief treatment of certain parts. A good many results are given in the form of 

 questions, and offer the adventurous student ample opportunity of trying his 

 'prentice hand on this most fascinating branch of Mathematical Physics. 



J. Rice. 



An Introduction to the Mechanics of Fluids. By E. H. Barton, D.Sc, 

 F.R.S.E., F.P.S.S. [Pp. xiv 4- 249, with Diagrams and Examples.] 

 (London : Longmans, Green & Co. Price 6s. net.) 



There is a good deal more in this book than its title would convey. It begins 

 with three chapters on fundamental mechanical ideas and principles, followed by 

 a chapter on the summation of certain series, which enables the author to dispense 

 with the notation of the calculus in subsequent chapters, and forms an introduction 

 to the calculus, thus simplifying the work for the beginner and involving a minimum 

 of change to those who pass to the calculus at a later stage. 



Two chapters are devoted to liquids in equilibrium and flotation, and contain a 

 very complete elementary account concerning centre of pressure, metacentre and 

 hydrometers. A chapter on Hydrokinetics treats of Bernouilli's Theorem, Torri- 

 celli's Theorem on the velocity of efflux, the Vena Contracta, and the surface of 

 a rotating liquid. A desirable addition here would have been a few pages on 

 viscosity, with reference to the important problems of the motion of a solid body 

 through a viscous fluid, and the flow of a viscous liquid through a pipe. This 

 omission is the only serious defect in an otherwise excellent treatise. Some fifty 

 pages are devoted to a very good account of the behaviour of gases, of Hygrometry 

 and Barometry ; and a further forty pages contain descriptions of many types of 

 illustrative apparatus from siphons to compression pumps, Geryk and Gaede 

 pumps, turbines and ejectors, forming a very valuable addition to the preceding 

 theoretical discussion. 



