INFLUENCE OF SUSPENSION ON WATCH. 365 



problem thus presented, seem to have originated 

 the great dynamic problem of the vibrations 

 of stable systems. 



When a system of particles displaced from a 

 position of equilibrium experiences in consequence 

 forces in simple proportion to the displacements of 

 its different parts, its motion may be thoroughly 

 investigated by a generalisation of this problem of 

 Bernoulli and Etilcr. The solution involves an 

 algebraic equation of the same degree as the 

 number of independent motions which may be 

 given to the system. When the roots of this 

 equation, which are necessarily all real, are all 

 positive, the equilibrium of the system is stable. 

 It is convenient to confine our attention to this 

 case ; but it is interesting and important to remark 

 that all the statements we make in reference to it 

 arc applicable by a proper mathematical extension 

 of the language, to cases of unstable equilibrium. 

 Each of the roots of the algebraic equation used 

 in other formulae belonging to the solution, deter- 

 mines a particular proportion of different possible 

 displacements, which, if made simultaneously, will 



