122 AN EMPIRICAL STUDY OF GYRATING BODIES. 



I think we may safely estimate the revolutions of a 

 gyroscope at twenty in a second, or forty reversals. 

 But the effective falling time is only half the time of a 

 reversal, since as soon as the arms of our tee pass the 

 horizontal, they begin to act in the opposite sense. We 

 have, then, to consider instants of only one-eightieth 

 of a second. A freely-falling body in that time would 

 acquire a velocity of one-eightieth of thirty-two feet, or 

 a little less than five inches per second. If angle a=40° 

 — about the average of gyroscopes — the falling rate 

 would be 0.925 of this, or about four and one-half inches 

 per second. 



On trial, however, it will be found that the actual fall 

 of a gyroscope is very much less than this, 1 in fact often 

 not exceeding one one-hundredth of an inch. 



A higher rate of rotation would, of course, leave a 

 less residual velocity. Somewhere I have read that 

 someone's gj^roscope makes two hundred revolutions a 

 second. That would reduce the downward rate given by 

 the formula to a little less than one-half an inch per 

 second ; but, even this is many times greater than the 

 actual rate even of a slow instrument — say one of twenty 

 revolutions per second like mine — and needs to be dis- 

 posed of. 



The momentum of the ends of our tee-square, brought 

 by the reversals on alternate sides of the axis, suffices to 

 explain all the phenomena yet presented, and it will be 

 seen that it also suffices for all the phenomena discussed 

 in the rest of this paper. Also, in very many instances, 

 it has enabled me to say what the instrument would do 

 in new and untried conditions, and sometimes has led 

 to unexpected results which experiment verified. I con- 

 clude therefore that the force, or whatever it is, which 

 disposes of this residuum, must act in the same sense as 



1 In my instrument the weight of the ring is wholly got rid of by counterbalancing it. 



