128 AN EMPIRICAL STUDY OF GYRATING BODIES. 



tality would be forever. Thus, by two roads, we arrive 

 at tlie same result. 



But we have to do with velocities far below infinite. 

 It takes some time — very small indeed — for our tee- 

 square, or section, to reverse, and there is one position 

 (that in which the arms are vertical) in which the lateral 

 acceleration adds nothing to the lifting power, and an- 

 other (when the arms are horizontal) 1 in which the action 

 of gravity adds nothing to the acceleration ; yet gravity 

 acts all the time, and during these exceedingly short 

 moments, each a mere infinitessimal of a revolution, it 

 acts unimpeded. It is to these intervals of no influence 

 that the fall is due. 



Since the length of these periods depends upon the 

 time it takes the tee (or section) to pass through what, 

 for lack of a better name, I may style the zero regions 

 it is not difficult to see why the gyroscope falls faster 

 the slower the wheel revolves, for the greater the time of 

 a revolution, the greater the fraction of it spent in those 

 regions, and consequently gravity has more time to pro- 

 duce downward motion. 



HEAVY AND LIGHT GYROSCOPES. 



If it were possible to make a gyroscope whose ring 

 and axle were without weight or mass, we should find, 

 all other things being the same, that a heavy and a light 

 gyroscope would have equal horizontal movements and 

 equally slow descent. The reason is this : A heavy and 

 a light body fall with the same velocity, and the motion 

 acquired in falling is the source of all the other move- 

 ments. 



WHEN A LOAD IS PUT ON THE TWO GYROSCOPES, 



There is then no longer identity of results. In the 



1 If a tee-square be held so that its arms are horizontal (the leg also being horizontal) and 

 the standard at the left and, as in fig. 5, and it be let fall a little, both arms will move 

 equally to the left ; hence neither will tend to produce horizontal rotation about the point 

 of support. The same reasoning applies when the arms are vertical and we are considering 

 a lateral force. 



112 



