Notices respecting Neio Books. 307 



matics ; or, in the words of the author " the science which teaches 

 how to describe motion accurately, and how to compound different 

 motions together, is called Kinematic (wj/jj/ia, motion)" (p. 2). 

 The existence of a distinction between Kinematics and Dynamics 

 was recognized long ago, perhaps in the first instance by Ampere* ; 

 but up to the present time it has only been obtaining recognition 

 gradually in the Mechanical Treatises most commonly in use. The 

 Kinematical part of Applied Mechanics, it is true, received separate 

 and systematic treatment long ago in Professor Willis's ' Elements 

 of Mechanism ; ' and in Professor Rankine's ' Applied Mechanics ' 

 there is a separate Part (III.) on the " principles of Cinematics, or 

 the comparison of Motions," in addition to a Part (IV.) on the 

 " theory of Mechanism." But long after the publication of the 

 former of these works the distinction was simply ignored in the 

 text-books of Theoretical Mechanics commonly in use ; or where 

 that was hardly possible (as in treating the motion of a rigid body 

 about a fixed point), a few kinematical propositions were introduced 

 under some such heading as " the Geometrical Nature of a Body's 

 Motion about a Fixed Point," or " the Geometry of the Motion of a 

 Rigid Body," &c. In fact the distinction was not worked out com- 

 pletely until the appearance of the first (and hitherto the alone 

 published) volume of Thomson and Tait's ' Natural Philosophy.' 



When a subject consists of two distinct branches, that alone is a 

 sufficient reason for their separate treatment; but if a further reason 

 for the separation were needed, it would be found in the fact that, 

 in consequence of the customary indirect treatment of Kinematics, 

 parts of it seem to escape the attention of students. Thus, though in 

 the course of their Dynamical studies most students obtain indi- 

 rectly an acquaintance with the geometry of translatory and rota- 

 tional motion, comparatively few (as we have reason to believe) 

 have any acquaintance with the geometry of strains. 



The work before us will doubtless confirm the existing tendency 

 towards a separate study of the theory of pure motion; but this 

 may be regarded as one of its least merits. The most marked pe- 

 culiarity of the volume is the unusual form in which even the most 

 elementary parts of the subject are set forth. To all appearance 

 the author has established for himself a peculiar point of view from 

 which to regard the whole subject of Dynamics ; and consequently 

 his exposition of the kinematical part follows lines quite wide of the 

 beaten tracks. This does not indeed appear at first sight ; for he 

 treats it under its most obvious subdivisions of Translations, Rota- 

 tions, and Strains ; but when the details of any one of these sub- 

 divisions are examined the originality of the treatment becomes at 

 once apparent. For example, the second chapter of the first book 

 is headed "Velocities," and occupies nearly a fourth part of the 

 volume. Although it treats in great part of matters familiar to 

 every student of Mathematics, the form in which they appear is 

 very unlike that in which they are commonly treated, and is appa- 

 rently the author's own : e. g., instead of introducing the reader 

 * See Whewell, 'Phil. Ind. Sci.' vol. i. p. 152. 

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