C. B. WARRING. 107 



to be accepted by all writers upon the subject as beyond 

 question that " the fall of the gyroscope is due only to 

 loss of rotary velocity." 



But it is not true that, but for the loss of rotary veloci- 

 ty, the gyroscope would staj^ up forever. As General 

 Barnard's paper is before me, I shall speak especially of 

 that. At the same time, I add, that I know of no one 

 who disagrees with him. 



In his statements which I have quoted, one is struck 

 by the implied assertion that the rate of rotation is of 

 no consequence, providing that it remains uniform. It 

 is true that elsewhere General Barnard says the rotation 

 must be very rapid ; but, in all cases, when speaking of 

 the cause of the descent which occurs, he uses sub- 

 stantially the same language : " If the rotary motion re- 

 mained constant, the reflecting force would be just suffi- 

 cient to lift the axis back to the original position ; " or 

 u the descent is due only to a loss of rotary velocity." 

 How absurd this is, becomes evident when we reflect 

 that, if true, a gyroscope would stay up forever if it 

 turned on its axis only a small fraction of a revolution in 

 an hour, provided this rate continued without decrease. 



But, undoubtedly General Barnard intended the speed 

 should continue uniformly very great. Then we have 

 this difficulty. One hundred times a second is very 

 great, while a fortiori one hundred and fifty is also 

 great. We have, consequently, the curious result that 

 a gyroscope revolving "uniformly" one hundred and 

 fifty times a second will stay up "forever," and one re- 

 volving "uniformly," one hundred and forty, or one 

 hundred and thirty, or one hundred and twenty, or one 

 hundred and ten, or one hundred times, will also stay 

 up "forever," but if the rate diminishes from one 

 hundred and fifty to one hundred and forty, or to one 

 hundred, the gyroscope will fall ; while, if there had 



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