August 18, 1905.] 



SCIENCE. 



205 



The second part deals with the dynamics of 

 rigid bodies. The author here develops, with 

 considerable detail, the mechanics of systems 

 which admit of representation by means of 

 vectors, a method used throughout the volume 

 wherever possible. Under this head come 

 screws and wrenches, moments of inertia, and 

 the special kinematics of a rigid body rotating 

 about a fixed or moving point. Special atten- 

 tion is devoted to the dynamics of rotating 

 bodies. The top comes in for detailed treat- 

 ment and many of the curious phenomena 

 exhibited are deduced from the equations of 

 motion. Pictorial illustrations are given of 

 .the instruments and of the curves which have 

 been actually obtained by the author to show 

 how closely observation may be made to agree 

 with theory. 



The third part opens with a chapter on the 

 Newtonian potential function. This will 

 probably be found to be the least satisfactory 

 in the whole volume from the student's point 

 of view. Although it may be quite logical to 

 start vnth the properties of point-functions 

 and develop them in detail before proceeding 

 to the applications, it is frequently tedious to 

 read through many pages of mathematics 

 leading to isolated geometrical results without 

 indications of the uses to be made of those 

 results. A rearrangement in which concrete 

 problems are stated and solved, gradually lead- 

 ing the student step by step to each new 

 mathematical investigation as he sees the need 

 for it, would seem to better achieve the end 

 the author has in view and would avoid the 

 danger of wearying the student and losing his 

 interest. The next two chapters contain the 

 dynamics of deformable bodies. The theory 

 of stresses and strains is worked out and the 

 illustrations are derived .chiefly from problems 

 in hydrostatics and hydrodynamics. The 

 final chapter on 'the latter is perhaps the most 

 interesting in the book. After obtaining the 

 general equations of motion, the author treats 

 briefly, but sufiiciently for his purposes, vortex 

 motion, including tidal problems and sound 

 waves. An appendix contains notes on cer- 

 tain portions of algebra and analytic geometry. 



It is to be regretted that a little more care 

 has not been exercised in the wording of the 



statements and definitions, especially in the, 

 earlier parts. For example, in the statement 

 of the second law of motion, Newton's ' change 

 of motion ' should be paraphrased ' rate of 

 change of momentum,' and not ' acceleration.' 

 On page 31, the reason for the necessary slight 

 modification of Kepler's third law is given as 

 due to the motion of the sun, instead of to the 

 fact that the mass of the planet is not infi- 

 nitely small compared with the mass of the 

 sun. On page 35 the impression is conveyed 

 that a motion is periodic when a system is in 

 the same position after a certain interval of 

 time, whereas it must also have the same 

 velocities. It is not clear what is meant by 

 the statement on page 96 that the principles 

 of conservation of energy, of the motion of 

 the center of mass, and of moment of mo- 

 mentum ' suffice for the treatment of all me- 

 chanical problems.' On page 131 it is stated 

 that Jacobi's dynamical method furnishes a 

 means of integrating the equations of motion 

 of a dynamical problem; this method is really 

 a transformation which replaces the problem 

 of solving 2n ordinary differential equations 

 each of the first order, by that of solving a 

 partial differential equation of the first order 

 in n -}- 1 variables. 



Whatever criticisms we may be disposed to 

 make on minor points, we can heartily con- 

 gratulate Professor Webster on having pro- 

 duced a book which is in many respects a 

 notable contribution to the literature of the 

 subject. Even if it served no other purpose 

 than to draw the attention of students and 

 teachers to the necessity for a more profound 

 study of the mathematics of physics, it will 

 have achieved useful results. As a class book 

 with an efficient instructor, it will be found 

 to be of value for students who have had a 

 fairly good training in algebra, ^he calculus 

 and elementary mechanics, and who wish to 

 go further either in experimental work or in 

 the mathematics of physics. It will also be 

 found useful as a place of reference for the 

 main outlines of the various subjects treated. 



We hope that Professor Webster's work will 

 be the forerunner of other volumes on similar 

 lines intended not to replace, but to be read in 



