MECHANICAL PARADOXES. 



clearly showing that this was the direction in 

 which they were tending to fly at the moment 

 of liberation, and clearly showing, too, what is 

 the direction in which every particle in the rim 

 of a spinning wheel is tending to fly at each 

 moment. 



In Fig. 8, let A B C be a view, edge on, of 

 a gyroscope which is spinning so that the back 

 is going up and the front down. The top at 

 A will be coming forwards and the bottom 

 at C going backwards. The particles at the 

 back, on the level of the axle G H, will then 

 be moving directly upwards, and will tend to 

 fly straight up in the direction B M. 



Now tilt the gyroscope so that it lies in 

 the plane DBF and its axis is in the direction 

 K L. The particles at the back will now tend 

 to fly in the direction B N. Suppose that the 

 rim of the instrument is spinning at the rate 

 of 100 feet per second. Then if the rim sud- 

 denly broke into small fragments, those at 

 the back would fly 100 feet in the direction 

 B N in one second, whereas, before the tilt, 

 they would, on the supposition of breaking 

 up, have flown 100 feet per second in the direc- 

 tion BM. The effect of the tilt, then, is to 

 give to these fragments, in addition to the 

 flight B M which they get in virtue of the 

 spin, a further flight from M to N in virtue 

 of the tilt. When B M is 100 feet per second, 

 suppose M N represents 30 feet per second. 



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