PREFACE. IX 



number of miscellaneous methods and subsidiary theories, relating 

 to impulses, initial motions, small oscillations, and the motion 

 of chains, and it includes also some further applications of the 

 principles of energy and momentum. The order is very different 

 from that adopted in most English text-books; in the ordinary 

 course Mechanics is subordinated to Geometry, the order being 

 that of geometrical difficulty. The order here adopted is meant 

 to be that of the difficulty of the physical notions involved. 

 There can be no doubt that the mechanical meaning of equations 

 of motion in general is easier to grasp than that of equations 

 of initial motion, and the theory of collision involves special 

 hypotheses subsidiary to the general principles of dynamics. 



The class of students for whom the book is intended may 

 be described as beginners in Mathematical Analysis. The reader 

 is supposed to have a slight acquaintance with the elements of 

 the Differential and Integral Calculus, and some knowledge of 

 Plane Coordinate Geometry. He is not assumed to have read 

 Solid Geometry or Differential Equations. The apparatus of 

 Cartesian Coordinates in three dimensions is described, and the 

 solutions of the differential equations that occur are explained. 

 It not infrequently happens that analytical methods are preferred 

 to geometrical ones, as likely to be more helpful to the students 

 whose wants are in view. Chapter XL, and isolated Articles in 

 other chapters, are marked with an asterisk to indicate that in a 

 * first reading they may with advantage be omitted. These Articles 

 usually contain matter of such a degree of difficulty that they 

 are likely to be more easily understood after the rest of the book 

 has been read, and further progress in Pure Mathematics has 

 been made. A student attempting to read the book without the 

 guidance of a teacher is recommended to pay the greatest attention 

 in the first place to the unmarked Articles in Chapters IV., IX., X., 

 and XII., and to work out the Examples inserted in the text and 

 attached to such Articles, passing lightly over the more theoretical 

 Chapters, and reverting to them wherever they are referred to. 

 He cannot expect to grasp the whole subject at once in its logical 

 order, and he will find it advisable to read some parts two or three 

 times, connecting them with different special applications. 



