346 SCIENCE PROGRESS 



An Introduction to the Use of Generalised Co-ordinates in Mechanics and 

 Physics. By William Elwood Byerly, Perkins Professor of Mathe- 

 matics Emeritus in Harvard University. [Pp. viii + 118.] (Boston, New 

 York, Chicago, London : Ginn & Co., 1916. Price $s. 6d.) 

 This is an exceedingly valuable working text-book, and it is marked by excep- 

 tionally good examples and summaries of the contents of chapters, which will be 

 most useful to students engaged in the work of revision. The introductory chapter 

 is on co-ordinates and various aspects of the dynamics of a particle and rigid 

 dynamics, and Lagrange's equations are introduced almost at once. The second 

 chapter is devoted to the Hamiltonian equations, Routh's modified Lagrangian 

 expression, and the ignoration of co-ordinates ; in it the "canonical form" of the 

 Hamiltonian equations is not given, but is postponed to the fourth chapter, and 

 the equations considered are of the form usually known as " Poisson's." A very 

 good feature is the use of such equations in a few problems already solved by the 

 Lagrangian process, so that the student is familiarised with the actual working of 

 the Hamiltonian forms. The third chapter is on impulsive forces ; the only 

 criticism that we have to offer here is that the author so closely follows Routh 

 that an impression may be given to the student that Gauss's principle of least 

 constraint is merely a principle for use in problems on impulsive forces (p. 71). 

 The fourth chapter is on conservative forces, and it is for these forces that 

 Hamilton's principle and the principle of least action are derived. However, in a 

 note on p. 90 it is shown that Hamilton's principle is of wider signification. The 

 fifth chapter is on applications to physics, and here we have a short treatment of 

 the important question of concealed bodies. Two Appendices contain respec- 

 tively a brief syllabus of rigid dynamics and a useful summary of part of the 

 calculus of variations. Philip E. B. Jourdain. 



ASTRONOMY 



A Manual of Field Astronomy. By Andrew H. Holt. [Pp. x + 128.] (New 

 York : John Wiley & Sons, Inc. ; London : Chapman and Hall, Ltd., 191 7. 

 Price 6s. net.) 

 There are so many books on Field Astronomy that the appearance of another 

 almost demands an apology from the author as a matter of course. The present 

 volume has been written with a definite aim — to provide a more complete treat- 

 ment of the methods of determining longitudes, latitudes, azimuths, and time than 

 is usually given in text-books on surveying, but at the same time something more 

 elementary and less extensive than is given in books on field astronomy. It is 

 intended for use by civil engineers and to give sufficient information to enable 

 the observations and computations required in general engineering and surveying 

 to be made. The need was a real one, and is well met by this volume. 



The arrangement of the subject is admirable ; a brief but sufficiently adequate 

 treatment of the fundamentals — the celestial sphere and systems of co-ordinates — 

 is followed by a more detailed description of the measurement of time, the use of a 

 Nautical Almanac and various problems in conversion of time. The more common 

 methods for the determination of latitude, azimuth, time, and longitude are then 

 given, and the various corrections necessary are explained. At the end of the 

 book is collected a number of actual observations by the various methods to illus- 

 trate how systematically to record and compute the observations in the field. A 

 " summary of observations " is collected together in one chapter, with sufficient 

 facts to determine what data are necessary for any observation, and which is the 

 most convenient method to use under any given circumstance. 



