236 POPULAR LECTURES AND ADDRESSES. 



perfectly imitated in a model consisting of rigid 

 links joined together, and having rapidly rotating 

 fly-wheels pivoted on some or on all of the links. 

 The imitation is not confined to cases of equili- 

 brium. It holds also for vibration produced by 

 disturbing the system infinitesimally from a 

 position of stable equilibrium and leaving it to 

 itself. Thus we may make a gyrostatic system 

 such that it is in equilibrium under the influence 

 of certain positive forces applied to different 

 points of this system ; all the forces being 

 precisely the same as, and the points of applica- 

 tion similarly situated to, those of the stable 

 system with springs. Then, provided proper 

 masses (that is to say, proper amounts and 

 distributions of inertia) be attributed to the 

 links, we may remove the external forces from 

 each system, and the consequent vibration of 

 the points of application of the forces will be 

 identical. Or we may act upon the systems of 

 material points and springs with any given forces 

 for any given time, and leave it to itself, and do 

 the same thing for the gyrostatic system ; the con- 



