C. B. WARRING. 127 



there is an approximation to equality of upward and 

 downward tendencies. 1 



Now we can see what becomes of the energy which 

 ordinarily would be expended in acceleration. It is em- 

 ployed in resisting the action of gravitation. 



We can also understand why the horizontal movement 

 becomes (sensibly) uniform, provided the rate of rotation 

 undergoes no change, and so long as the axis remains 

 nearly horizontal. 



One question remains — a question of a good deal of 

 importance. I have said the upward and downward 

 tendencies experience an approximation to equality. 

 Why not say, reach equality, and consequently that a 

 frictionless gyroscope would never fall, and so agree 

 with General Barnard and Sir William Thomson \ 



I cannot say so, because it has been shown that such a 

 statement implies the monstrous absurdity of attributing 

 infinite power of resistance to an instrument that I can 

 turn with my finger ; and I have shown experimentally, 

 that a frictionless gyroscope does fall. If it falls there 

 must be a reason why, and what that is I shall now at- 

 tempt to show : 



The formula, h varies as ^, h being the time of hori- 

 zontally, shows, as has been said, that h would be in- 

 finite if v were infinite, i. e., if the reversal took abso- 

 lutely no time at all. The interval required in that case 

 for A and B, fig. 6, to reverse being zero, the downward 

 velocity acquired, d, would also be zero. Hence our 

 formula, d X Ters c e ° d s s ^ 2a , would give zero, or, in other 

 words, there would be, in case of infinite velocity of ro- 

 tation, no downward movement at all, and the horizon- 



1 1 wrote first " the upward and downward movements ; " but this conveys a wrong 

 meaning, or at least, a meaning not intended. 



I do not think that there is an oscillatory or vibrating movement, but there are two 

 tendencies, or stresses, by virtue of which the path described by the free end of the gyro- 

 scope is a very slightly descending spiral, the action of gravity being a little more than suf- 

 ficient to overcome the upward tendency due to the acceleration. 



Ill 



