PREFACE. 



JLhe science of Dynamics may be variously classified. In by far the 

 greater number of universities in both Europe and America it is dealt 

 with by professed mathematicians, and is properly considered an essential 

 part of mathematical discipline. Nevertheless it is but an application of 

 mathematics to the most fundamental laws of Nature, and as such is of 

 the highest importance to the physicist. The whole of modern Physics 

 experiences the attempt to "explain" or describe phenomena in terms of 

 motion, with conspicuous success in the departments of Light, Electricity, 

 and the Kinetic Theory of Gases. It is therefore evident that no one 

 can expect to materially advance our knowledge of Physics who is ignorant 

 of the principles of Dynamics. It is nevertheless to be feared that this 

 subject is often slighted by the physical student, partly on account of its 

 difficulty, and partly because of the fact that the many excellent treatises 

 on Dynamics existing in English address themselves chiefly to the mathe- 

 matician, and often seem to lay more stress on examples in analysis or 

 trigonometry than on the elucidation of physical laws. The aim of this 

 book is to give in compact form a treatment of so much of this fundamental 

 science of Dynamics as should be familiar to every serious student of 

 physics (and in my opinion no less should suffice for the student of 

 mathematics). The classical English treatises usually fill one or even two 

 large volumes with one of the subdivisions of the subject, such as Dynamics 

 of a Particle, Rigid Dynamics, Hydrodynamics or Elasticity. The student 

 confronted with the five volumes of Routh, the three of Love, and the 

 large work of Lamb is likely to be appalled at the size of the task before 

 him. It is practically impossible for the physical student, while spending 

 the necessary amount of time in the laboratory, to read through all these 

 or similar works , and thus his knowledge of the whole subject generally 

 remains fragmentary. The great work of Lord Kelvin and Tait, while 

 treating the whole subject, is far too difficult for most students, though 

 it must ever remain a mine of information for those sufficiently advanced. 

 This book has grown out of the lectures which I have given at 

 Clark Universitiy during the last fourteen years primarily to my own 

 students of Physics. It is obvious that it leads to no particular examinations, 

 from which we in America are to a large extent fortunately free. The 

 text is not interrupted by examples for the student to work, which are 

 found in great numbers in the usual treatises, and to which I could hardly 

 add. The attempt has been made to treat what is essential to the under- 

 standing of physical phenomena, leaving out what is chiefly of mathematical 

 interest. Thus the subject of Kinematics is not treated as a subject by 

 itself, but is introduced in connection with each subdivision of Dynamics 



