264 Notices respecting New Books. 



discusses degrees of freedom of a mass-chain up to the eighth 

 order, and gives an account of Reciprocal, Impulsive, Instanta- 

 neous, and Harmonic chains, and of Principal and Conjugate 

 screw-chains of Inertia. 



The last chapter contains the Theory of Screws in Non- 

 Euclidian space. We confidently recommend it as a model in the 

 method of introducing an unfamiliar subject. The admirable 

 clearness of the author's style is here conspicuously apparent. 



Part of our object has now been accomplished if we have 

 succeeded in showing that this large book is full of matter of the 

 most varied and interesting kind. The fundamental conceptions 

 of the theory have found a permanent place in dynamics. We 

 believe that many of the methods of this volume will occupy 

 places no less permanent in many different branches of mathe- 

 matics. It may be that useful applications of screw-coordinates 

 will be made in analytical geometry . It is surely time to replace 

 the cumbrous phrase " parameter of distribution " of a ruled 

 surface by the more suggestive term " pitch," — the pitch of the 

 screw about which a generator can be twisted to occupy the 

 position of an adjacent generator. We have noticed an applica- 

 tion to the linear complex, and merely want of space prevents us 

 mentioning others. The treatment of non-Euclidian space has 

 been profoundly modified. Reflections such as these prove beyond 

 question the suggestiveness of the theory of Screws. 



It is perhaps unique in the history of Science that within ten 

 years the same chair should have been occupied by the originators 

 of two new mathematical methods inseparably connected with 

 their names and wholly foreign to the subject they professed. 

 Though elaborated along independent lines, the methods are 

 intimately related by many bonds. A twist bears the same rela- 

 tion to a rigid body that a vector does to a point. The theory of 

 Quaternions may be regarded as the theory of vectors, and the 

 theory of Screws as the theory of vector pairs. The Biquaternions 

 of Clifford are the fruits of their union. 



We wish we could believe that this great work will be read 

 extensively by students in our universities. In mathematics, at 

 any rate, this is an age of second-hand knowledge. We are too 

 often content with the partial presentment of a subject by a mere 

 compiler of text-books, and we forego the immense advantage of 

 learning from one who must have studied his subject from very 

 many points of view. Our students are too often forced to 

 exchange the light of genius for a glimmer paled by successive 

 reflections from examiner and from coach. To Sir Robert Ball 

 and to the readers of his book we may apply the concluding words 

 of ' The Dynamical Parable ': — " They have been engaged in the 

 study of Nature, they have approached the problem in the true 

 philosophical spirit, and the rewards they have obtained prove that 

 o 



1 Nature never did betray 

 The heart that truly loved her.' ' 



