F 39 ] 



IV. 



ON THE MOTION OF A BODY NEAE POINTS OF UNSTABLE 

 EQUILIBBIUM, AND ON THE SAME WHEN CAPABLE 

 OF INTEBNAL VIBBATION. By FBEDEBICK T. 

 TBOUTON, B.E. 



[Read January 18, 1888.] 



Probably everyone will recollect often having heard such things 

 ns forms or stools, after getting a tilt insufficient to overset them, 

 vibrating from side to side, and gradually settling down, all the 

 while getting faster and faster until stopping. Sometimes plates 

 and dishes will he heard to do the same, also coins after spinning, 

 and such like. 



The nature of the motion may be best seen by considering the 

 simple case of a tall rectangular block, which has been tilted over one 

 edge into the position shown in the diagram. From this position 

 the block rotates back round the edge 

 until it regains the vertical, then, owing i 



to its momentum, it tilts up on the other 1 



side, rotating round the opposite edge, 1 



and so on each time, tilting up a little 1 



less than before, until at length it comes | 



to rest. From the following considera- lie/' 1 



tions, it will be seen to what a great lj.' I 



extent the time of returning to the ver- | J 



tical depends on the amount of the arc 



through which the body has been tilted. If be the angle made 

 with the vertical by the line joining the centre of gravity to the 

 «dge about which the block is tilted, and if 9 be small, i.e. if the 

 block be tall as compared to its width, we have 



where I is the moment of inertia round the edge, and / is the 

 distance of the centre of gravity from it, and W the weight of the 



SCIEX. PHOC. R.D.S. — VOL, VI., I>T. II. E 



