40 Scientific Proceedings, Royal Dublin Society. 



block, and g the acceleration of gravity. If /3 is the value of 9 

 when the body began to fall, 



dO 



dt 



-J^v^FF. 



and if the time is reckoned from the moment the block began to 

 fall, 



; J + A'-li 2 



= Jwgl l0g 



and the time to fall to the vertical is 



1 4Wgl * j3 



where a is the value of 9 in that position. From this expression 

 for T it will be easily seen that if the arc of tilting, i. e. (a - j3) is 

 small, T also is small, tending to the limiting value of when /3 

 equals a, and that if the arc be large, that is, if j3 be small, T is 

 much greater, tending to the limiting value of infinity when /3 = : 

 that is to say, it would take an infinite time to fall from the posi- 

 tion of unstable equilibrium which the body is in when the centre 

 of gravity is vertically over the edge. 



At Professor Fitz Grerald's suggestion, who pointed out to me 

 the nature of the motion, experiments were undertaken with the 

 view of verifying the above expression for the time. Owing to the 

 difficulty of making observations with the ordinary bodies to be 

 met with on account of their coming to rest so soon, a heavy iron 

 wheel was fixed on a square iron axle, each end of which rested on 

 an iron table. The wheel rocked between these supports, first on 

 one edge of the axle, then back and on to the other edge. This 

 arrangement was highly satisfactory, as it could keep rocking 

 without much decrement at any required arc, thus permitting the 

 time to be observed. The following table exhibits some of the 

 results of the observations made with it. In the first column is the 

 arc fallen through as read off a scale ; in the second is the time in 



seconds taken to do so ; in the third column is log- 



/3 



in the fourth the ratio of the time to this, which is seen to be very 



