578 Prof. T. R. Lyle on Mechanical Analogy to the 



formulae referred to. It is easy to show that if the wheels 

 or rollers are constructed as I have described, this correction 

 is equal to 



o ^ 2 + I 



"(R + r) 2 ' 



where fi is the mass and I the moment of inertia of each 

 complete roller, R the radius of a wheel, and r the radius of 

 a spindle. 



The agreement between the observed and computed natural 

 periods will enable one to judge of the perfection of the 

 model. 



Now impart motion to the system, the initial conditions 

 being those already specified in § § 4, 5. 



To do this, first bring the system to rest, then steady the 

 beam with one hand and with the other hold the bob of the 

 first pendulum slightly deflected, and then let bob and beam 

 go simultaneously. 



It will be seen that the second pendulum begins to swing 

 and continues with increasing amplitude, while the amplitude 

 of the first at the same time diminishes. This goes on to 

 a certain point when the reverse takes place, and the transfer 

 of energy forwards and backwards many times between the 

 two pendulums is strikingly demonstrated. 



From this motion the resultant frequencies co 1 and co 2 can 

 easily be obtained by observation. 



For the motion of the second pendulum is given by 



2 —p 2 a— ■< cos o)it — cos co 2 t > 



E . ft) 2 — ft>i . 6) 2 + ftJi 



= zp 2 a—sm — 7^ — t sin — ~ — t, 

 1 c 2 2 



which shows that it is a vibration whose amplitude 



~ E . ft) 9 — G)i 



zp 2 a — sin — - — t 



c £ 



varies harmonically with a frequency 



=40 2 — &>!), 



while the oscillations of the pendulum have a frequency of 

 Hence, if we count the number of double swings the 



