618 



REPORT 1884. 



the motion will become shorter and shorter, and the amplitudes smaller and 

 smaller, and the motions will approach more and more nearly those of two perfectly 

 rigid groups of material points, moving through space and rotating according to the 

 well-known mode of rotation of a rigid body having unequal moments of inertia 

 about its three principal axes. In one case the ideal nearly^ rigid connection 

 between the particles is produced by massless exceedingly stiff springs ; in the other 

 case it is produced by the exceedingly rapid rotation of the fly-wheels in a system 

 which, when the fly-wheels are deprived of their rotation, is perfectly limp. 



The drawings (Figs. 1 and 2) before you illustrate two such material systems. 

 The directions of rotation of the fly-wheels in the gyrostatic system (fig. 2) are 

 indicated by directional ellipses, which show in perspective the direction of rotation 

 of the fly-wheel of each gyrostat. The gyrostatic system (fig. 2) might have been 

 constituted of two gyrostatic members, but four are shown for symmetry. The 

 enclosing circle represents in each case in section an enclosing spherical shell to 



Fig. 1. 



prevent the interior from being seen. In the inside of one there are fly-wheels, in 

 the inside of the other a massless spring. The projecting hooked rods seem as if 

 they are connected by a spring in each case. If we hang any one of the systems up 

 by the hook on one of its projecting rods, and hang a weight to the hook of the 

 other projecting rod, the weight when first put on will oscillate up and down, and 

 will go on doing so for ever if the system be absolutely unfrictional. If we check 



1 In fig. 1 the two hooked rods seen projecting from the sphere arc connected by 

 an elastic coach spring. In fig. 2 the hooked rods are connected one to each of two 

 opposite corners of a four-sided jointed frame, each member of which carries a gyro- 

 stat so that the axis of rotation of the fly-wheel is in the axis of the member of the 

 frame which bears it. Each of the hooked rods in fig. 2 is connected to the frame- 

 work through a swivel joint, so that the whole gyrostatic framework may be rotated 

 about the axis of the hooked rods in order to annul the moment of momentum of 

 the framework about this axis due to rotation of the fly-wheels in the gyrostats. 



