PBEFACE. 



THE foundations of Mechanical Science were laid by Newton, 

 and his achievements in this department constitute perhaps his 

 most enduring title to fame. Later writers have developed his 

 principles analytically, and have extended the region of their 

 application, but, in regard to the principles themselves, they have 

 acted the part of commentators. Nevertheless we may trace a 

 tendency in modern investigations, which is of the nature of a 

 gradual change in the point of view : there is less search for 

 causes, more inclination to regard the object to be attained as a 

 precise formulation of observed facts. On another side there is 

 an important respect in which modern writers have departed 

 from the form of the Newtonian theory. The philosophical 

 dictum that all motion is relative stands in pronounced contra- 

 diction with Newton's dynamical apparatus of absolute time, 

 absolute space, and absolute motion. It has been necessary to 

 reconsider in detail the principles, and the results deduced from 

 them, in order to ascertain what modification would be needed 

 to bring the theory of Rational Mechanics founded by Newton 

 into harmony with the doctrine of the relativity of motion. 



The purpose of this book is didactic ; it is meant to set before 

 students an account of the principles of Mechanics, which shall 

 be as precise as possible, and which shall be in accordance with 

 modern ideas. 



The book is divided into three parts. The first part is pre- 

 liminary in character, and is intended to accustom the student to 

 the idea of acceleration, and to the fact that a precise description 

 of any motion can be given by a statement of the accelerations 

 involved. In the first Chapter attention has been paid to the 

 determination of position, the essential relativity of position being 

 the key to much that follows. In the second Chapter is intro- 

 duced the idea of a Vector, and it proves useful to recognise classes 



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