134 AN EMPIRICAL STUDY OF GYRATING BODIES. 



The following laws in reference to these undulations 

 are easily experimentally demonstrated : 



1. The less the downward pull, the less the undula- 

 tions. 



2. The greater the rotational velocity, the less the un- 

 dulations. In each case the converse also is true. 



3. In all cases undulations follow a somewhat ab- 

 rupt disturbance of previous conditions. 



THEIR RATIONALE. 



This is best seen by taking the case in which the un- 

 dulations are produced in an instrument which had been 

 gyrating with steadiness— such as is described in the last 

 experiment but one. 



We here have the gyroscope moving " horizontally" 

 under the joint influence of the weight of the wheel and 

 the additional weight attached to the hook at the free 

 end. This horizontal movement, being proportional to 

 the load, is more rapid than it would be if either part of 

 the load acted alone. If, now, the weight is flashed off, 

 the velocity for the instant will be in excess, and the 

 condition is what it would be if, while the instrument 

 was moving under the weight of the wheel alone, the 

 motion was accelerated. But, by our first law, accelera- 

 tion makes the gyroscope rise, and rising tends to make 

 it go backward ; and going backward tends to make it 

 fall ; and making it fall tends to send it forward. At 

 the same time, the remaining weiglrt — that of the wheel 

 — tends to drive it steadily forward. There results from 

 the two motions a series of up-and-down, fast and slow 

 (relatively) movements, which are the undulations. To 

 apply this to the case of a starting gyroscope, we need 

 only to remember that the forward motion — the gyra- 

 tion — is the result of the falling motion ; and that there 

 is an instant, after the fall begins, before the lateral mo- 

 tion conies into play, while the fall continues unchecked. 



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