iv PKEFACE 



If I have taken some space to express my private convictions, it 

 is because the method I have embodied in the present book arises 

 directly out of these convictions. Mathematical analysis is, of 

 course, not excluded from the book, because without mathematics 

 there can be no serious study of mechanics, but I have tried to 

 reduce the amount of mathematics to a minimum, and I have 

 regarded it (hi the present book) as the servant and not as the 

 master. Again, practical applications of mechanics have not been 

 excluded, on the contrary, these have been introduced wherever 

 possible as illustrations of principles or results, but I have tried 

 to place principles first and applications second. And problems 

 have not been excluded : I have inserted a great number, because 

 the solution of problems seems to me to be the one and indis- 

 pensable way of emphasizing a group of abstract principles and of 

 fixing them in the mind of the student. But I have regarded the 

 problems as an adjunct to the study of the principles, and not the 

 principles as a framework round which to build problems. 



Besides explaining the method and objects of a book, a preface 

 may be expected to explain where the book starts and where it 

 ends. The present book is intended to start from the very begin- 

 .ning of its subject, assuming no previous knowledge of mechanics 

 on the part of the student. The question of how much knowledge 

 of mathematics ought to be assumed has been a more difficult one 

 to settle. I finally decided to rely as little as possible on the stu- 

 dent's knowledge of trigonometry, and to employ the calculus as 

 little as possible in the earlier chapters, but felt that the subjects 

 of the later chapters could not be advantageously treated without 

 a very considerable use of the calculus. Until the later chapters 

 the use of the calculus is confined almost exclusively to unimpor- 

 tant branches and extensions of the subject, and to the working of 

 illustrative examples. Thus a student who has no knowledge at 

 all of the calculus will, I hope, be able to omit the sections of the 

 book in which it is used, while at the same time acquiring a con- 

 siderable and continuous knowledge of the essentials of theoretical 

 mechanics. 



