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LXXVII. Notices respecting New Books. 



A Treatise on the Analytical Dynamics of Particles and, Rigid Bodies ; 

 with an Introduction to the Problem of Three Bodies. By E. T. 

 Whittaker, M.A. University Press, Cambridge. 1904. 



rpHIS treatise differs in many respects from the usual kind of 

 -■- English text-book on dynamics. With few exceptions these 

 may be described as more or less ingenious collections of modes of 

 solution of abstract problems which may correspond to something 

 natural. The authors of most of such books have had present to 

 their mind the needs of a student whose knowledge of dynamical 

 methods is to be tested sooner or later in an examination hall. 

 One mischievous effect of this system was to bring into special 

 prominence solvable cases without due consideration of why they 

 should be solvable. Eor why should a candidate waste his precious 

 time over the difficult question of solvability when he was certain 

 to be examined only on cases which could be solved, that is, 

 reduced to elliptic functions ? Ever since the publication of 

 Thomson and Tait's ' Natural Philosophy,' there has gradually 

 grown up a healthier public opinion ; and there has been a 

 marked advance in the preparation of our best physical treatises. 

 And now Mr. Whittaker has given us a treatise, the aim of which 

 is to lead up to the best recognized methods of analytical dynamics 

 as a means towards a great end, namely, the interpretation of 

 nature. Chapter L, on kinematic preliminaries, gets us almost 

 immediately into touch with the real essence of rotation. In the 

 succeeding chapter on the equations of motion, the convenient 

 term holonomic is introduced, Lagrange's equations established, 

 and the Lagrangian Function or Kinetic Potential defined and 

 used. Chapter III., on principles available for integration, discusses 

 ignorable coordinates and the general principle of moment of 

 momentum and energy. Then, and not till then, do we encounter 

 the ordinary well-known simpler problems of particle dynamics. 

 Chapters V. and YI. deal with the dynamics of rigid bodies. The 

 theory of small vibrations about equilibrium configurations form 

 the subject of chapter VIL; and with chapter VIII., on non-holo- 

 nomic and dissipative systems, the more elementary part of the 

 book may be said to end. It corresponds fairly well with the kind 

 of dynamics which the examination paper can attain to ; and yet 

 it is but a preparation for the more abstruse developments which 

 follow. Without particularizing too much, we ma} r say that the 

 powerful methods and developments associated with the names of 

 Gauss, Hamilton, Jacobi, Liouville, Lie, Poincare, Bruns, and 

 others are brought forward and discussed w T ith admirable skill, the 

 later chapters dealing with the problem of three bodies and the 

 general theory of orbits. Like Lagrange's great classic, this 

 treatise is remarkable in the entire absence of a single diagram. 



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